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1,600 | ecompositional Modeling through Caricatural easoning Brian C. Williams and Olivier Raiman Xerox Palo Alto Research Center 3333 Coyote Hill Road, Palo Alto, CA 94304 USA {bwilliams, raiman)@parc.xerox.com Abstract Many physical phenomena are sufficiently com- plex that the corresponding equations afford lit- tle insight, or no analytical method provides an exact solution. Decompositional modeling (DM) captures a modeler’s tacit skill at solving non- linear algebraic systems. DM divides statespace into a patchwork of simpler subregimes, called caricatures, each of which preserves only the dominant characteristics of that regime. It then solves the simpler nonlinear system and identifies its domndn of validity. The varying patchwork reflects how variations in the parameters change the dominant characteristics. The patchwork is built by extracting equational features consisting of the relative strength of terms, and then ex- agerating and merging these features in different combinations, resulting in the different caricatu- ral regimes. DM operates by providing strategic guidance to a pair of symbolic manipulation sys- tems for qualitative sign and order of magnitude algebra. The approach is sufficient to replicate a broad set of examples from acid-base chemistry. Introduction Much work within the qualitative reasoning commu- nity (?; Falkenhainer & Forbus 1991; Nayak, Joskow- icz, &L Addanki 1991; Weld 1991) has concentrated on methods for selecting and composing sets of models with a diversity of underlying modeling assumptions, and a strong emphasis has been placed on managing t,he diversity of these models. This is a fruitful avenue. Yet it. is also important to realize that this diversity arises in each physical domain from a small, core set of principles, such as Newton’s laws or Maxwell’s equa- tions. The application of these principles are taught from the start of a modeler’s education. Thus of equal importance is the skill of a modeler t,o adapt these principles to the phenomena being accounted for. In this paper we introduce a complementary, domain independent approach called decomposition& modeling (OM). The t,ask we address is finding analyt,ic solu- tions t,o systems of nonlinear equations, couched in the domain of analytical chemistry. Instead of solv- ing a system directly, DM partitions the behavior of each equation into a patchwork of regimes where dif- ferent. behaviors dominate, and the equations in each regime are simplified to reflect only what. is significant. Regimes for the overall system are then constructed by composing the regions of the individual equations, and then solving the system of simplified equations, to describe the behavior within each of the system’s regimes. In addition to the overall decompositional process, this work is novel for its use of the concept of a caricature to extract the appropriate regimes, and the demonstrat,ion of the power of qualitu.tiz~e algebraic resoZu.tion at all stages of the modeling process. An Example From Chemistry To ground our approach, consider the application of decomposit,ional modeling to the analysis of the equi- librium behavior of a simple reaction - the dilution of acid molecules, AH, into water. The dilution is charact,erized by the react,ions Hz0 + H+ + OH- and AH = H+ + A-; its equilibrium is governed by: (11) Charge balance: h+ = oh- + a-, (12) Mass balance: C, = ah+a-, (13) Water equilibrium: rw (14) Acid equilibrium: Kath 1 ;:IbT; where ah, a-, hf , hzo, and oh- d enote concentration at equilibrium of the species AH, A-, H+, HZO, and OH-, respectively. Note that although the concentra- tion of species S is tradit,ionally denoted [S], this con- flicts with the use of [ 1, within qualitative reasoning, to denote a quantity’s sign. K, and K, are equilib- rium constants for the water and acid ionizat,ion, and C, denotes the initial concentration of AH. Determining the equilibrium concent,rations in terms of constants K,, K, and AH directly requires the so- lution of four nonlinear equations in four unknowns. For example, solving for H+ ions yields the equilibrium concentration equation: h+3 + K,hC2 - (Ii& + K,)h+ = K,K,. The derivation of this equation was highlighted in text (Beckwith 1985) (chapter 5) to demonstrate the dan- gers of using brute force. Even for this simple case Modeling 1199 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. the concentration equation is a third degree polyno- mial in hf , whose roots are difficult to solve for by hand. Recent developments in the automatic solution of nonlinear equations provides some additional lati- tude. However, problems arise for slightly more com- plicated cases. For example, for polyprotic acids - acids with more than one replaceable hydrogen ion H+, such $s HsP04 - the degree of the equations increases with the number of replaceable ions. Thus for exam- ple HsP04 has three replaceable ions and results in a concentration equation of degree five. There are no general closed form solutions to algebraic equations of degree five or higher (by Galois), and it is difficult to derive insight from such equations directly. For more interesting chemical systems, such as those studied in atmospheric modeling, the number of reactions range in the hundreds. In this situation the application of a direct method clearly breaks down and even when numeric methods are applied, approximations are per- formed liberally. Instead, a chemist is taught to proceed as follows (taken from (Beckwith 1985), chapter 5). First, hav- ing introduced equations 11-14 governing the reaction’s equilibrium, the chemist guesses several interesting simplifying assumptions (Al-4) about what the domi- nant species may be: Al: The acid is weak (a- < C,). A2: The acid is strong (ah < C,). A3: The solution is essentially neutral (a- < h+). A4: The solution is strongly acidic (oh- < h+). Combining, for example, assumptions A2 and A4 and applying them to the charge and mass balance equations (11,12) produces h+ ==: a- (11’) and C, ==: a- (12’). Solving for h+ results in h+ z C,, a far simpler result than produced through a direct solution without simplification. Applying other combinations of assumptions produces: A2 R3 A4 R4 Al,A4 R5 Al R6 none R-7 The remaininl Simplified Concentration Eqns. h+ 2 CL El hS2 z K, E2 ht2 - C,h+ z K, E3 h+2 + K,h+ = C,K, E4 ht2 = C,K, E5 h+” z C,K, +K, E6 h+3 + K,ht2 - (K&z + K,)h+ = KJL E7 step is to determine the domain of validity for each set of assumptions - the constraints that the assumptions impose on the givens, K,, K, and C,. Returning to the pair of assumptions A2 and A4, from A2 (ah << C,) the chemist derives Ci/K, << C, by substituting for ah and a- using the simplified acid equilibrium (14)) acid concentration (El) and mass balance (12’) equations. And from A4 (oh- < h+) the chemist derives K,/C, < C, by sub- stituting for oh- and h+ using the simplified acid con- centration (El) and water equilibrium (13) equations. These two constraints define a region, Rl, whose fringe corresponds to the two bold lines in the tipper right corner of the region diagram in figure 1 (taken from (Beckwith 1985), p. 75). The domains of validity R2- R7 for the remaining sets of assumptions partitions the reaction’s behavior into simpler regimes according to the values of C, and K,. Given these results, the prob- lem of identifying a solution’s acidity for given values of C, and K, involves identifying the appropriate region and applying the corresponding simplified concentra- tion equation. I I I I I For Kw = lo -14 a<b when a/b< 0.1 -14 -a -2 lo&W Figure 1: The different combinations of simplifying as- sumptions divide the space of values for C, and K, into simpler regimes of dominant behavior. Its given that Ii, = lo-l4 and a << b when a/b < 0.1. Decompositional Modeling and Caricatures In this example we saw that the analytical chemistry task is in essence one of solving a system of simul- taneous, nonlinear equations, and that the modeling process is fundamentally decompositional. This ap- proach results in behavioral descriptions that are more tractable to manipulate and provide greater insight. The example also demonstrates the five major steps of DM: 1) identify simplifying assumptions about the dominance of parameters, 2) combine these assump- tions to define different subregimes of dominant be- havior, 3) simplify the system of equations based on the assumptions of a particular subregime, 4) solve the simplified equations to obtain the system’s dominant behavior over that subregime, and 5) identify the do- main of validity over which the simplified behavior is valid. This provides a layer of structure for the model- ing process, but it doesn’t explain where the simpli- fying assumptions come from, or provide a conceptual viewpoint of the overall process. For this we use, the metaphor of a caricature. In decompositional modeling the patchwork of regimes, corresponding to dominant behaviors are derived by reinforcing the “prominent features” of the system’s behavior. From a commonsense standpoint a caricature of an object is a description which exagerates prominent fea- 1200 Qualitative Reasoning tures and eliminates insignificant features. For exam- ple caricatures of Richard Nixon reduce his face to little more than a nose with an exaggerated slope. Apply- ing this concept to modeling, given a system of initial equations DM constructs a caricature of the system by exagerating one or more of the equation’s prominent features. In this paper, we take “prominent” to mean that one term a of an equation E dominates another term b: [al > /bl; that is, a is further from zero than b. DM exagerates this feature by making Ial much greater than lb/, thus making a dominant and b insignificant: )a/ > lb/ u a > b. We call this relation a caricaturul assumption. By using this assumption to simplify E, DM produces a curicuturul equation, that eliminates the insignificant features. For example, given that all concentrations are pos- itive, two prominent features of equation 12 (C, = ah+a-) are IC,l > lahl and IC,I > la-1 (note that all concentrations are positive). Exagerating IC,( > IahJ introduces the caricatural assumption C, >> ah, and allows 12 to be replaced by the caricatural equation C, 25 a-. This corresponds to the chemist’s notion of a strong acid (i.e., essentially all AH dissociates). Conversely, exagerating IC,( > la- I introduces the assumption C, >> a-, and produces the caricature CC2 ==: ah, the chemist’s notion of a weak acid (i.e., a negligible fraction of the acid AH dissociates). Of course an alternative approach might take a quantity or subterm from any two equations and pre- sume one dominates another. However, the number of potential assumptions would be prohibitively large. Instead the concept of caricature allows us to use ex- isting features of the initial equations as clues to what relations are worth exaggerating. What is striking is that the restricted set generated through caricatures matches the simplifying assumptions introduced in a variety of acid-base chemistry examples. Summarizing the observations of this section, the DM algorithm is: Decompositional Modeling: Given a system of non-linear equations E with state variables x and pa- rameters p: 1. 2. 3. 4. 5. Generate the caricatural assumptions C, for each Ei E E. Merge the sets of assumptions of the Ei, producing a set C whose elements are sets of combined assump- tions corresponding to dominance regimes. Then, for each set c E C, use c to extract the caricatu*z of each Ei E E, pro- ducing E’; solve for x in the system of caricatures E’, and derive from c and E the domain of validity. DM relies heavily on the computational machin- ery of qualitative algebraic reasoning(Williams 1991; Raiman 1991) to perform tactical inferences. This cor- responds to the rote algebraic manipulations taught informally to a modeler early on, and is discussed in the next section. The art of the modeler is the strate- gic guidance given to these manipulations. This is the contribution of t*his paper, and is the focus of the re- maining sections. ualitative Algebraic Inference DM operates by strategically guiding the inferences of two symbolic manipulation systems, one for a sign algebra, and a second for order of magnitude equa- tions. We provide here an overview of the algebraic foundation underlying DM. Representationally it is unified as a set algebra that captures knowledge of order and dominance. Computationally it is unified through qualitative resolution. Decompositional mod- eling involves reasoning about three types of informa- tion: non-linear equations, such as K,ah = h+a-, in- equalities between magnitudes, such as Ia- I < Jh+l, and order of magnitude information, such as la- I << Ih+ I and la- I x Ih+ I. Both equations and inequali- ties are expressed as equations in the hybrid qualita- tive/quantitative algebra SRl (Williams 1991) (an al- gebra combining signs and reals). The domain of SRl extends the reals to include signs (i.e., + 3 (0, inf), ^ G (- inf, 0) and ? = (- inf, inf)). The operators of SRl extend the standard operators of the reals (+,-,x and /) to this larger domain, resulting for example in the combination of a real and sign algebra. As usual [r] maps a real T to its sign. In SRl an inequality, such as C, > ah is expressed by the hybrid equa- tion [C, - ah] = $, and IC, I > lahl is expressed by [Ci - ah”] = 4. S‘ mce the elements of the algebra are sets, expressions are related using c as well as =. In addition, the set relation ==: represents non-empty intersection. Dominance relations and other types of order of magnitude information are captured as equations in the algebra of Estimates (Raiman 1991). The domain of Estimates extends the reals to include E, a set of infinitesimal values around 0 that are negligible with respect to 1. Like SRl, Estimates’ algebra extends the standard operators and includes the same set relations as SRl. The dominance relations are represented by: a >> b f b c EU, and a z b f a c (1 + c)b. Intuitively EU denotes the set of all values much smaller than a, and (1 + E)U denotes all values close to a. Note that, although seemingly disparate, SRl and Estimates are both instances of set algebras over the reals, and as such share many properties - in par- ticular a common algebraic inference structure. For both algebras the basic inference involves combining two equations, and is performed through three steps: solve for a shared variable in one equation, substitute the solution into the second equation, and simplify the composite result. For example, consider the compo- sition of SRl equations s + [a] z u and t - [a] z o. First, the shared variable [a] is solved for in the first Modeling 1201 Initial Sign prominent caricatural Eqns Eqns feature assumptions ht =oh-+a- (11) [a-] = i-,[oh-] = -i- Ih+I > (oh-1 hS >> oh- (Ad) h+ =oh-+a- (11) [oh-] = $,[a-] = -?- lhfl > la-l h+ > a- (A3) Ca=ah+a- (12) [ah] = 4, [a-] = $ IGI > la-1 C, ,> a- (Al) C,=ah+a- (12) [a-] = i-, [ah] = i- IC,I > lahl C, > ah (A2) K, = h+oh- (13) none none K,ah = h+a- (14) none none Figure 2: The complete set of caricatural assumptions and equatidns. equation, resulting in [a] C u - s. Next, the result. is substituted for [a] in the second equation using sub- stitution of supersets, and results in t - (U - s) z ~7. Finally the result is simplified, producing t - u + s * u or equivalently t + s z u + U. The following are the results of additional examples for the two algebras: s + [a] 25 u, t - [a] z L’ 3 s + t 25 u + u [a - b] = s, [b - c] = t 3 [a - c] c s + t .s$U~U, t-CLZV * s+t~u+v An important property of each example is that it has the flavor of propositional resolution. A term and its negation are identified in the two equations (e.g., [a] and -[a]), .l y t le are eliminated from both equations, and the respective sides of the two equations are com- bined. We refer to this process as quulitutirre reso- lution. The details of qualitative resolution for SRl (performed by Minima and Estimates) are described extensively in (Williams 1991) and (Raiman 1991), respectively. For our purposes we can think of Min- ima and Estimates together as a qualitative resolution black box. What is striking is that each step of de- compositional modeling (DM) maps to a particular set of qualitative resolutions. DM is then performed by framing a qualitative resolution problem at each step. This process is the focus of the remaining sections. Step 1 & 2. Caricatural Assumptions DM first extracts and then exagerates the prominent features of each E, E E, where a prominent feature is a partial order between the absolute values of any two terms. For each E, E E this involves: 1. Nondeterministically select a pair of terms a, b E E,. 2. Infer the ordering (<, =, >) between JuJ and lb/. (a) Create ordering expression 0 = [a” + b”]. (b) Repeatedly resolve 0 with all Ei, and constraints on variable signs ([v] = s). (c) If a sign constant -?- or 1 results, map to an or- dering (e.g., [a2 - b”] = q ---f Ial > lb/). 3. Exagerate any ordering using (al > lb1 -, a > b. For example, given the mass balance equation C, = ah + a- (12) and the fact that a- is positive ([a-] = 4 (Pl)), then DM selects C, and ah, constructs [Ci + 1202 Qualitative Reasoning ah2], and performs the following sequence of resolu- tions: [Ci - ah”] Given. = [(ah + a-)” - ah”] Resolve with C, = ah + a-. = [2aha- + (a-)“] Simplification. C [a(+ + (a-)‘] Resolve with ah c i-. c [2(+)(q) + (G)"] Resolve with a- C T. CT Simplification. Thus [Ci - ah’] = 4 or equivalently lCal > lahl. Fi- nally, exagerating this feature according to Ial > (bl - a >> b produces C, >> ah, which is equivalent. to as- sumption A2 of the example section. The derivation of each feature and its corresponding caricature for all equations is summarized in figure 2. The assumptions just. generat,ed for each equation induce a patchwork of dominant. subregimes local to that equation. DM then combines these local regimes into a set of global regimes. To do this step 2 combines the sets of assumptions. For the moment presume all possible combinations of assumptions are explored sep- arately. We return later with a more sophisticated ap- proach. Having combined the assumptions, t,he next two steps construct a caricature of the system’s com- posite behavior for some subregime. Step 5 makes ex- plicit the boundaries of that subregime. Step 3. Extracting Dominant Behaviors Given a set of caricatural assumptions c defining a sub- regime, each of the E, is simplified using c by Esti- mates, producing a set of curicutud equutions. Es- timates provides a sophisticated strategy for guiding resolution during simplification (see (Raiman 1991)). For completeness we sketch here an extremely simple strategy. Recall that an assumption a << b is encoded as the equation a c eb. Then given E, and assump- tions c, simplification involves repeatly: 1. Identifying variables a, b E El such that (a << b) E c. 2. Resolving E, and a c cb using variable a. For example, consider the pair of caricatural assump- tions: C, >> ah (A2) and h+ >> oh- (A4), correspond- ing to the example at the beginning of the paper. To simplify the mass balance equation C, = ah + a- (12), DM identifies that the pair of variables C, and ah also appear in A2, and then through resolution DM derives the caricatural equation C, z a- (12’): ah + a- = C, Equation I2 to simplify. ah C EC, Estimates equation for A2. a- = C, - ah Cancellation on 12. a- C C, - EC, Resolving for ah in 12, A2. a- C (1 + e)C, Simplification. This caricatural equation is equivalently a- z C,. Likewise, to simplify charge balance h+ = a- + oh- (Il), DM resolves it with A4, resulting in h+ z a- (11’). Finally, resolving 13 and 14 with A2 and A4 pro- vides no simplification. Step 4. Solving Caricatural Equations Next the caricatural equations are solved for the ml- known concentrations. Specifically, given a set. of knowns h’, caricat,ural equations E’ and unknowns U, DM repeatedly resolves all pairs of equations that share an unknown. A solut,ion is a resulting equation that contains exactly one unknown. For example, DM solves for h+ in terms of the givens K,, , K, and C,, using the caricatural equations just derived: (1 + c)li+ - a- > 0 Estimates eqn. for 11’. (1 + e)C, - a- > 0 Estimates eqn. for 12’. (1 + E)hf - ( 1 + E)C, > 0 Resolving a-. Equivalently h+ ==: C, (El). Equilibrium concent*ra- tions for ah, a- and oh- are derived analogously. Solv- ing systems of equations by resolution will be costly for large systems. A more desirable alternative is to use a package for solving nonlinear systems of equations. Such a package, however, must be able to manipulate error terms to ensure that the cancellation of two dom- inant terms does not cause the error, introduced during exageration, to become significant. Step 5. Identifying Domains of Validity Having just constructed a caricature of the composite system’s behavior, t,he final step ident.ifies the domain over which the caricatural assumptions are valid. Each bound of the domain of validity corresponds to one of the caricatural assumptions (figure l), where an as- sumption a >> b produces bound a + / - ~b = 0. A boundary is derived from an assumption A by repeat- edly resolving one of the unknown variables of [T that appears in A, with one of the equations in E’. A solu- tion is reached when no variables of IT remain. For ex- ample, from C, >> ah (A2) DM derives K, > C, using 14 (K,ah = h+a-), 12’ (hf ==: cl,), and El (C, z a-). Using a less mechanical notation: C, >> ah Assumption A2 C, >> h+a-/K, Resolving a.11 with 14. C, >> h+C,/K, Resolving a- with El. CL >> C:/K, Resolving h+ with 12’. K, > C, Simplification. This completes DM’s process of constructing the car- icature of a single subregime. The bounds and con- cent*ration equations derived through these five steps correspond exactly t,o those in the example section. Step 2 (cont.) Creating a Patchwork III the section on steps 1 & 2 we glossed over the step of merging assumptions, say ing only that, all combi- nations of assumptions were explored. DM provides a more intelligent coordinat,ion based on the interrela- tionship between sets of assumptions. These are de- picted using the subset/superset, lat,tice of figure 3. {Al) {A31 l-44) - 0 Figure 3: Suhset/superset lattice of caricatural as- sumptions considered by DM. First,, note t,hat. the bottom of the lattice is rooted in t*he original model - since no assumptions are made and no approximations are performed. Moving up- wards through t,he latt,ice results in simpler models, since each new assumption makes an additional term insignificant,, which t,hen drops out of t,he equations. Second, although models higher in the lattice are simpler, their domain of va1idit.y is more restrictive. That is, each caricatural assumpi,ion introduces a new subregime boundary; thus, the region COT responding to t,he domai n of validity of one caricature is a subset. of any caricature appearing below it, in the lattice. Third, when moving-up the lattice the added as- sumptions do not always result in simplification. For example, (A2, A3) p ro d uces the same equation for h+ as does (A3). ’ This explains why Schaum’s out,line (Beckwith 1985) includes a region R3 for {A2}, but. no region for (A2, A3) ( see figure 1). The same argument, applies t’o the absence of {Al, A3). These eliminated sets are depicted by squares in the lat,tice. Likewise, additional assumptions do not. always restrict, the do- main of validity, part,icularly when the boundary t,hey introduce is outside the existing region. Fourth, in some cases a set of caricatural assump- tions is mutually inconsistent, for example, as we pointed out earlier for {Al, A2). This is recognized when the result of a resolut,ion is det,ect.ed to be incon- sistent by Est,imates or Minima. For example, from {Al, A2) Estimates derives C, >> C,. While all caricatures could be generated by simply repeatming steps 3-5 on all combinations of caricatu- ral assumptions, the different combinations share two properties that DM exploits to make this process more ‘But this depends on how many of the equilibrium con- centrations we are interested in. (A2, A3) may allow addi- tional simplification over (A3) for other species. Modeling 1203 efficient. First, by monotonicity each superset of an in- consistent set of assumptions is also inconsistent. Thus to avoid exploring potentially large sections of the lat- tice, DM creates caricatures of each regime by starting at the bottom of the lattice and moving monotonically upwards, ignoring anything above an inconsistent set. In our example, of 16 potential sets of assumptions, 9 prove consistent, 2 are explicitly demonstrated incon- sistent, and 5 are supersets of them and thus need not be explored. The 7 inconsistent sets are marked by X’s in the lattice. Finally, caricatures of regimes are gener- ated incrementally by exploiting monotonicity. Given the caricatural equations E’ for a set of assumptions S, the caricatural equations of its immediate supersets SU(Ai} are computed by further exagerating E’ using assumptions A;. Discussion Decompositional modeling has been demonstrated on several analytical chemistry examples taken from (Beckwith 1985). The first step of DM is implemented in Lisp on top of Minima (Williams 1991). The re- maining four steps are implemented in Prolog on top of Estimates (Raiman 1991). The solutions DM pro- duces are guaranteed to be correct within the condi- tions of negligibility for order of magnitude. This pa- per makes precise the caricature’s metaphor first in- troduced in (Raiman 1988), and the decompositional modelling process introduced in (Raiman & Williams 1992). One clear need of DM is the ability to bound error, such as is available in a variety of approximate or or- der of magnitude systems, such as (McAllester 1981; Mavrovouniotis & Stephanopoulos 1988; Weld 1991; Shirley & Falkenhainer 1990; Nayak 1991; Yip 1993). A second need, highlighted at the end of the section on step 4, is to exploit recent advances in solving nonlin- ear systems, by embodying them with sufficient error bounding capabilities. (Nayak 1991) provides an alter- native to Estimates for performing order of magnitude inference, based on a very interesting mapping to linear programming. An earlier example of a decompositional approach is (Sacks 1987) on piecewise linear approximations. An important difference is that the approximated behav- iors of decompositional modeling remain non-linear. The claim is that the approximation should preserve the essential characteristics of the behavior, and this is often nonlinear. Until recently linear approximations were necessary for a system to be solvable. This is dra- matically changing, however, given recent advances in nonlinear symbolic algebra. Finally, note that our approach only addresses de- compositional modeling applied to algebraic systems, not for example dynamical systems. In this context a caricature would, for example, characterize an ever so slightly decaying satellite’s orbit as a limit cycle (Raiman 1988). A variety of authors have explored this context, including (Weld 1988; Davis 1987). References Addanki, S. and R. Cremonini and J. S. Penberthy. 1989. Reasoning about Assumptions in Graphs of Models. In IJCAI-89. Detroit, MI: Morgan Kauf- mann. Beckwith, D., ed. 1985. Analytical Chemistry. NY: McGraw-Hill. Davis, E. 1987. Order of magnitude reasoning in qualitative differential equations. TR 312, NYU Com- puter Science Department. Falkenhainer, B., and Forbus, K. 1991. Compositional modeling: finding the right model for the job. Artif. Intell. 51. Mavrovouniotis, M. L., and Stephanopoulos, G. 1988. Formal order-of-magnit*ude reasoning in process engi- neering. Computer Chenaica.1 Engineering 12:867-880. McAllester, D. 1981. Algebraic approximation. In Proceedings IJCAI-881, 624-628. Nayak, P.; Joskowicz, L.; and Addanki, S. 1991. Au- tomated Model Selection Using Context Dependent Behaviors. In International Workshop on Qualitative Reasoning. Nayak, P. 1991. Validating Approximate Equilibrium Models. In AA A I Model- based Reasoning Workshop. Raiman, O., and Williams, B. C. 1992. Caricatures: Generating Models of Dominant Behavior. In Inter- national Workshop on Qualitative Reasoning. Raiman, 0. 1988. Caricatural Reasoning. In Inter- national Workshop on Qualitative Reasoning. Raiman, 0. 1991. Order of magnitude reasoning. Artif. Intell. 51. Sacks, E. 1987. ‘Piecewise Linear Reasoning. In Proceedings AAAI-87, 655-659. Shirley, M., and Falkenhainer, B. 1990. Explicit Rea- soning about Accuracy for Approximating Physical Systems. In Working Notes of the Automa.tic Gener- a.tion of Approximations and Abstractions Workshop. Weld, D. S. 1988. Exaggeration. In Proceedings AAAI-88, 291-296. Weld, D. S. 1991. Reasoning about Model Accuracy. Technical Report 91-05-02, Department of Computer Science and Engineering, University of Washington. Williams, B. C. 1991. A theory of interactions: uni- fying qualitative and quantitative algebraic rasoning. Artif. Intell. 51. Yip, K. M. 1993. ‘Model Simplification by Asymp- totic Order of Magnitude Reasoning. In Proceedings AAAI-93, 634-640. 1204 QualitativeReasoning | 1994 | 253 |
1,601 | Comparative Simulation1 Michael Neitzke, Bernd Neumann Universitit Hamburg, FB Informatik, AB KOGS Vogt-Kiilln-Str. 30 22527 Hamburg, Germany { neitzke I neumann} @informatik.uni-hamburg.de Abstract In this paper, a new theory of qualitative comparative descriptions for dynamic system behavior is presented. System deviations and behavior deviations are viewed relative to the normal case. In contrast to existing approaches, a deviation is not only characterized as “less than normal” or “greater than normal” (LGTN), but devia- tions can also be compared with each other in order to avoid ambiguities and provide more precise predictions. A funda- mental problem in comparative behavior prediction is that LGTN deviations can cause non-LGTN effects like a change of the direction of a parameter or a change in the order of events. Such so-called changes in the behavioral topology (10,ll) cannot be handled by existing approaches in a satis- fying way, but are covered by our theory. Our theory is incorporated into the relative simulator RSIM+. RSIM+ can be viewed as an extension of the QSIM simulator (7). It provides a refined system description with qualitative predictions which have not been achieved in other work. In particular, it is guaranteed that all behaviors following from an LGTN deviation are predicted. 1 Introduction In fault diagnosis and system analysis one often has to predict the consequences of system changes to the system’s behavior. When dealing with continuous systems, most changes and consequences can qualitatively be best described by relative descriptions like “less than normal” or “greater than normal” (LGTN). That is, the system is compared to a reference system and the system’s behavior is compared to the reference system’s behavior. While this sort of descriptions has widely been used to analyse static systems or equilibrium states of dynamic systems (2,4,5,6) only few approaches exist that can deal with general dynamic system behaviors (10,ll). Dynamic behavior prediction for system changes with an LGTN character entails some difficulties: 1. LGTN deviations can influence the duration of processes. Therefore, the deviating and the reference behavior can get “out of phase” so that a pointwise compar- ison of behaviors is problematic. See the frictionless spring/block system of Fig. 1’. A higher mass would lead to a higher period of oscillation. It would make no sense to 1. This research was supported by the Bundesminister ftir Forschung und Technologie under contract 01 IW 203 D-3, joint project Behavior. x2” x1* Fig. 1 The spring/block system. compare a mass that is moving to the rest position with a mass that is moving away from that point. Instead, corre- sponding parts of the oscillation process should be compared with each other. 2. An unambiguous prediction of behavior may require the comparison of deviations. This is the case, for example, when the net effect of opposing deviations has to be con&d- ered or two competing-deviations contribute to the system behavior. A higher initial displacement x of the spring, e.g., leads to a higher velocity v. Because of the linearity of Hooke’s law (F=k*x), spring force equals spring constant times displacement, and since F=m*a, (force equals mass times acceleration), x and v are always too high by the same factor, so that the period of oscillation does not change (see 10,ll). This can be deduced, if a comparison of the deviations of x and v is possible and specific broperties of linear relationships can be represented and exploited. 3. Deviations with an LGTN character can have effects with a non-LGTN character, i.e. drastic effects like a change of direction or a different order of events. For example, if a tank, initially partly filled with water, is being completely filled by a pump, a low pump pressure would lead- to a higher duration of the filling p&ess - provided that the pump pressure is still higher than the water pressure in the tank. But if not, the water level in the tank would decrease until the pump pressure is reached. That is, when the pump pressure is too low, the direction of the water flow can change. In the heat exchanger of Fig. 2, hot oil is cooled down. If normally the oil reaches the equilib- rium temperature somewhere inside the heat exchanger and then leaves the heat exchanger completely cooled down, a 2. Our techniques have been used for more complex systems like a steering control loop or a ballast system. To facilitate a better comparison to existing approaches we use well-known systems of the qualitative physics literature in this paper. Most examples stem from (11). Simulation 1205 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. too high oil velocity could prevent the equilibrium temper- ature to be reached. Weld calls such drastic effects changes in the behavioral topology (10) because they involve a structural change of the behavior description. Fig. 2 The heat exchanger (11). (outlet) b-X The first problem has sufficiently been solved by Weld’s concept of perspective (lo), i.e. deviations of parameters are described with respect to other parameters than time. The latter two problems, however, have not been solved in a satisfying way by the existing approaches: In qualitative simulation, usually, linear, underlinear, and overlinear dependencies are not distinguished. Instead, they are covered by the more general monotonic dependency. A comparison of deviations is not provided. In (lo), Weld gives a proof that there does not exist a useful perspective to handle the case of the too high amplitude. In this paper, we present a theory of comparative descriptions where * behaviors can be synchronized in order to allow a sensible comparison of corresponding parts, 0 parameter values can be classified as too low, too high or normal, 0 deviations of parameter values can be compared with each other, * properties of special monotonic relationships can be represented, (This includes linear, overlinear and underlinear relationships as well as “faulty” monotonic relationships like a relationship that is too steep or too flat in comparison to the reference system.) 0 changes of the behavioral topology cCan be handled. This theory is realized by the RSIM+ simulator. RSIM+‘s input and output and parts of the simulation technique are oriented towards QSIM (7). In fact, RSIM+ can be viewed as an extension of QSIM where QSIM’s (absolute) parameter and state descriptions are refined by relative descriptions. These relative descriptions are based on the concept of P values which relate deviations to absolute values (8). In Section 2 we summarize the essential definitions concerning P values and deviations. Section 3 explains RSlM+‘s modeling properties. In Section 4 it is demonstrated how RSlM+ works, and our example problems are solved. Section 5 compares RSIM+ to related approaches, and Section 6 gives a summary. 2 Describing Deviations As it is required in QSIM, each physical quantity, called parameter, is taken to be a “reasonable” function of time, i.e. a continuously differentiable function of time with a finite number of “critical points” (where the derivative is 0) in any bounded interval. We distinguish between a parameter in the disturbed system and the same parameter in the reference system by indexing the latter with “ref”. Def. 2.1 The deviation of a parameter value f(t) from a reference value fre,(t) is called a continuous deviation with regard to a basis landmark 1, if f(t) is on the same side of la as fr&), that is (f(t) < 1, A f&t) c la) v (f(t) > 1, A f&) > la). Otherwise it is called a discontinuous deviation wrt 1, The idea of this definition is to distinguish between deviations that can be described as less or greater than normal and deviations where this is not adequate due to drastic behavior changes. The border between continuous and discontinuous deviations is determined by the basis landmark which also separates “+” and “-” in the sign quantity space. Weld calls arbitrarily small changes in the value of a parameter d@erential, and more drastic changes non-d@ rentiaZ(l1). The essential property of a differential change is that it could be arbitrarily small without falling into a qualitatively different area, i.e. no landmark value may lie between the deviating value and the normal value. Following Weld we call deviations that lie in the same qualitative area, i.e. have the same absolute description as the normal value, differential, and deviations that lie outside this area non-differential. non-differential deviations differential non-diff. .a1 cl ,.m...m . . . . .I~r.4YJ@~?~~~~*~rn~+~*p~ iscontinuous continuous Fig. 3 Differential, non-differential, continuous and discon- tinuous deviations from a reference value f,,-(t) wrt 1,. Differential and continuous deviations are very similar. For quantity spaces with only one landmark like { -, 0, +} both classes are identical. In general, each differential deviation is a continuous deviation and each discontinuous deviation is a non-differential deviation (Fig. 3).The way and the extent f(t) differs from fief(t) can be described by the quotient of the distances of f(t) and f&t) from the basis landmark. We call this quotient the P value of f(t). f(t) - la Def. 2.2 : P(f,t) = f&Ct) - la Note, that P values are relative, but not qualitative. However, we are only interested in qualitative properties of P values. Therefore, we don’t need exact values for the function P. We are working with two different kinds of qualitative information about P values. First, we distin- guish different areas of P values. The relevant distinctions are captured by the function PQ: Def.: PQ(f,t) = too-low ::= 0 < P(f,t) < 1 PQ(f,t) = normal ::= P(f,t) = 1 v f(t)-1, = f&t)-la = 0 PQ(f,t) = too-high ::= P(f,t) > 1 PQ(f,t) = discontinuous::= P(f,t) < 0 v (f(t) - 1, = 0 A f&(t) - 1, <> 0) v (f(t) - 1, <> 0 A frer(t) - 1, = 0) 1206 Qualitative Reasoning Second, we use the relations <, =, and > to compare positive P values. This gives us a handle to refine qualita- tive system descriptions and behaviors, to distinguish more spectic classes of constraints between system parameters, and to diminish some unwanted spurious behaviors. For example, system properties like the linear dependency between two parameters can be described in terms of P values, since the P values of such parameters are equal as well as the P values of their derivatives. In addition to a QSIM-type description where the amount of a parameter is described by an interval or a landmark, and its derivative is described by a sign, in RSIM+, amount and derivative can also be described by a PQ value and relations between P values. Thus we have four description layers providing both absolute and relative descriptions: sign layer, qval layer (intervals or landmarks), PQ layer, and P layer. 3 Modeling Systems An RSIM+ model is given by a set of constraints just as a model in QSIM. In general, every RSIM+ model is a specialized QSIM model because aside from “exact” constraints, like SUM or PRODUCT (Table 2), it comprises specializations of QSIM’s qualitative constraints. These specializations concern monotonic rela- tionships between two parameters: On the one hand, linear, overlinear and underlinear relationships can be distin- guished. On the other hand, it can be expressed that a monotonic relationship in the disturbed system is steeper or flatter than in the reference system. Table 1 shows the following three specializations of QSIM’s Me+ constraint. The definitions are equivalent under qualitative absolute descriptions, but they dilfer under relative descriptions. LINEAR,+(f,g) : u f(t)=H(g(t)) * f,et-W=Wg,&N A H(O)=0 A H’(x)>0 A H”(x)=0 OVERLINEAl+,+(f,g):- f(t)=H(g(t)) A fr,f(t)=H(g,,.t)) A H(O)=0 A H’(x)>0 A H”(x)>0 TOO-FLAT,+(f,g) : - f(O=Wg(O) *f,,f(t)=H,,f(g,,r(t)) A H(O)=0 A H’(x)>0 A H&O)=0 A Href’(xbO * hy: WxkH,,f’(y) Table 1: PQ tupels and P Relationships for Some Special MO+ Constraints (L: too-low, N: normal, H: too-high, D: discont.) Constraint(f,g) LINEA&+ OVERLINEAR,+ TOO-FLATO+ “;t,“,pQ {U.&),(N,N), { (LLMNN), ‘;~;;‘;;;; ((PQ(f),PQ(g)) (H’H)‘(DyD)’ Wh(D D) I (H;H);(&)‘J P relationships If (L L) then between P(f) < P(g) amounts P(f) = P(g) If (N N) then P(f) < P(g) (for positive P(f) = P(g) P values) If (H H) then P(f) > P(g) P relationships If PQ(g)=L then between Rf’NW) derivatives P(f’) = P(g’) If PQ(g)=N then P(f ‘)=P(g’) pcf ‘) < ~(~9) (for positive P values) If PQ(g)=H then P(f’)>P(g’) Table 2: Part of the Definition of the PRODUCT Constraint: h=Trg PQ(f)=N L A P(h)=P( g) N H A P(h)=P(g) D :L * P@WW HA PQ(f)=H vNv H A WO=P(f) W>W * D (H A VWW) WO>Wg) PQ(f)=Di D iDI D (LVNVHVD~ Fig. 4 shows the RSlM+ models of our example systems. It is required that a model and the corresponding reference model may only differ in the specializations of monotonic constraints (i.e. the deviating and the reference system must have the same QSIM model). create-model *spring/block* :quantity-spaces ((x-qs (x2* xl * 0))) ;(qs-name landmarks: :variables ((x x-qs) v vv a f ke pe) :constants (m k te) :constraints ((deriv v x) ;the block’s velocity is the ;derivative of its position (deriv a v) ;acceleration is the derivative of velociq (product f m a) ;force equals mass times acceleration (product f k x) ;force equals spring constant ;times position (square vv v) ;vv is the square of v. (product ke m w) ;Rinetic energy depends on the product ;of mass and the square of velocity (square pe f) ;Weld calls it a “cheating definition ;of potential energy” (11, p.159). (sum te pe ke))) ;Total energy is the sum of ;kinetic and potential energy. create-model *heat-exchanger* :variables (x f q) :constants (v) :constraints ((deriv v x) ;velocity is the derivative of position (deriv f q) ;heat flow is the derivative of heat (non-negative q) ;heat cannot become negative (IinearO- f q))) ;heat flow is a linearly decreasing 3 i ;function of the heat I] Fig. 4 Models for spring/block system and heat exchanger. I~~ _^ I* -,,-“e- I-,A-.-“x^l”A^-,.*” ,“-k- ,ewl”--x-,A.~- -_um---“,- -x____x-_I 4 Describing Behaviors As in most qualitative simulators, RSIM+‘s simulation mechanism is a cyclic process consisting of an intrastate analysis and an interstate analysis. The intrastate analysis takes an incomplete description of a system state as input and generates one or - because of ambiguities - several complete state descriptions. The interstate analysis takes a complete state description and generates an incomplete description of the successor state(s). 4.1 Intrastate Analysis Fig. 5 shows the initial information we have for the spring/- block system with a) too high mass, and b) too high initial Simulation 1207 displacement. Deviations from the reference system may not only concern the model (via special monotonic constraints) but additionally the initial state. Intrastate analysis in RUM+ is done by constraint propagation. On the PQ layer, constraint propagation is based on the sets of allowed PQ value tupels for each constraint relation (Table 1, fist line, Table 2). On the P layer, constraint propagation assigns relations to pairs of P values, so that a consistent graph of P values is generated. Since RSIM+ uses the relations c, =, >, the graph represents a partial or&r of sets of P values. Each set consists of P values of the same magnitude. Propagating constraints on the P layer means increasing the order between the P values of all parameters. The additional information on the P layer helps to avoid spurious behavior on the PQ layer. That is, if a system state is completely described on the PQ layer, it may happen that the corresponding P relationships are inconsistent, for example because of cycles in a path of c relationships. ml b)ziT&7g a) sign(m) :+ Fig. 5 Initial information about the deviating spring/block systems with a) too high mass and b) too high displacement. Constraint propagation on the P layer is governed by two sources: On the one hand, there are relationships between the P values of the amounts of the constraint parameters and between their derivatives (Table 1, lines 2,3, Table 2). For example, in a linear relationship the P values of the parameter amounts are always equal. On the other hand, one can exploit dependencies between the relationships between amount and derivative of the constraint pam.rne- ters. If, for example, (PRODUCT h f g), and P(f) > P(f) and P(g) > P(g’), and sign(f) = sign(f) = sign(g) = sign(g’) = +, then P(h) > P(h’). 4.2 Describing Behaviors - Interstate Analysis RSIM+‘s interstate analysis is realized by so-called transi- tion rules in a similar way as in QSlM. Two types of transi- tions are distinguished: point transitions and interval transitions. A point transition is applied to states that describe the system at a certain time point. It infers infor- mation about the following time interval. An interval tran- sition works in the corresponding way. In contrast to absolute transitions, a relative interval transition can infer information about the duration to reach the next event. PQ transitions, like QSIM transitions, cover all possible combi- nations of values that amount and derivative of a parameter can take. On the P layer an exhaustive treatment of all possible combinations of P values does not seem necessary. Instead, some special but very useful transitions have been formulated. RSIM+ uses 12 point transitions and 19 interval transitions for PQ values and 2 point transitions and 14 interval transitions for relations between P values. The following sections describe how particular aspects of system behavior are solved by RSIM+ for our example problems and-they present some typical transitions. 4.2.1 Synchronization. A spring/block system with a too high mass has a longer period of oscillation. That is, the deviating and the reference system get out of phase. A strict pointwise comparison of both behaviors makes no sense. Instead, corresponding events and intervals should be compared with each other, i.e. the initial states, the intervals of approaching the rest position, the events of reaching the rest position, and so on. Therefore, a pointwise comparison must stop when the “faster” behavior reaches the next event. At this point, RSlM+ synchronizes both behaviors. This is done by interval transitions which infer information about the next event with a synchronization (the duration to reach the event is too low or too high) and without a synchronization (duration=N). In order to prevent discontinuous deviations, synchronization is triggered everytime when a parameter or its derivative reaches the basis landmark. The transition IAHDLNl (an attempt of a systematic acronym: Amount High, Derivative Low or Normal), for example, describes the case where a parameter is too high, i.e. too far away from 0, and is approaching 0 with a too low or just a normal velocity. Therefore, the duration to reach 0 is too high. IAHDLNl: pQ(f,(G,tj))=H A sign(f,(t.$$)=- A pQ(f’,($,tj>k {W) A signU’,@+ *I)=+ * (duration(t$.+At)=H A ((sign(f,tj+At)=O A P =N) v (sign($f,tj+At)=- h (f,%+At) A pQ(f,tj+Atk {LNJ)))) v (Sign(f,tj)=- A ((duration(t+t$E {L,N} A PQ(f,tj)=H) v (duration(ti,tj)=N A PQ(f,tj)=D))> Fig. 6a shows the first quarter of a period of RSM+‘s simulation output for the spring/block system with too high mass (concerning position, velocity, and acceleration of the block). It is deduced that reaching the rest position costs more time than normally. The interval transition IAHDLNl could be used for parameter x in both intervals. Notice, that in comparison to a pure absolute simulation, (as done by QSIM,) we have the additional event that the acceleration reaches “normal”. The behaviors of Fig. 6 can be derived unambiguously. In general, however, the degree of ambiguity of an RSIM+ simulation is significantly higher than that of the corresponding QSIM simulation. The projection of an RSIM+ behavior tree to absolute values results in the corresponding QSM tree. 4.2.2 Comparison of deviations. A spring/block system with a too high amplitude would have the same period as the reference system because of the linear dependency of position and acceleration. Without a comparison of devia- tions, it cannot be decided what happens if the block has to cover a higher distance with a higher velocity. With RSIM+, it can be deduced, that the period of oscillation does not change because of the equality of the P values of position, velocity and acceleration (Fig. 6b). The intrastate analysis for the initial state deduces that the P values of position, x, force, f, and acceleration, a, all are equal, i.e. they are too high by the same factor. The P value of the velocity, v, is not defined, since v and vref are both 0. The P transition P== deduces that in the following time interval the P values of x, v, and a must all be equal, if the P values of x and a are still equal: 1208 Qualitative Reasoning a) W ;$N $1 * sign(v) :0 w(v) :N sign a) pq(a ! it FqT; xl p* 01 I sign(v) ;; pq(v) sign a) :+ $$a I :L sign(v) it pq(v) sign a) :+ gq(a I :H , qval(tij mmmfOm ’ pq(x) :N sign(v) :+ pq(v) :L sign a) :0 pq(a \ :N duration : Fig. 6 mo deviating behaviors for the spring/block system, produced by RSIM+: a) the behavior for a too high mass b )the behavior for a too high amplitude. Events are indicated by rectangles, intervals by ovals. p== : (P(f,G)=P(f’,t$ v (PQ(f’,ti)=N A sign(f’,tj)=O)) A P(f,ti)=P(f”,ti) ~P(f,(ti,tj))=P(f’,(~,tj))=P(f”,(ti,tj) v P(f’ ,(ti,tj));ep(f,(ti,tj))#p(f’,(ti,tj)) While the equality of the P values of x and a always can be determined in the intrastate analysis, the equality of P(x) and P(v) is propagated from state to state by transition rules like P==. A more general interval transition states that if two P values are equal in a time interval (tip tj> they must still be equal at tja The information that the position must reach 0 in normal time is finally deduced by the interval transition IAHDH=-. This rule belongs to a group of 12 similar transitions that describe the case where a parameter is approaching 0 and both, amount and derivative, are too high or too low. In IAHDH=-, 0 is reached at the same time as-normally because amount and derivative are too high by the same factor. w=-:PQ(f,(ti,~))=PQ(f’,(ti,t))=H A Sigll(f,(c,t.))=- A sign(f ,(t,t))=+ A Ptf,(t.$.))=p(f’,(ti)=P(f,(tj t.n 3 (sign(f,t$=O A duiabon(G, (sign(f,$+At)=-A duration t .)=N A PQ(f,t$=Nj’v G,tj+At)=H) v (sign(f@=- A duration(G,t$E (L,N} A PQ(f,tj)=H) 4.2.3 Changes in the Behavioral Topology. A behavior can be characterized by a sequence of absolute transitions yi, -**, yk, i.e. the time points when a parameter reaches (or leaves) a landmark or its derivative reaches (or leaves) 0 (compare 10). Especially, we are interested in those absolute transitions PO, . . . . pi, {Pj) c CYi>, where a parameter or its derivative reaches (or leaves) the basis landmark. We call the pj basis transitions. Every behavior has a time function, T, which takes transitions to the time points when they occur. Weld defines the behaviors of two systems, S and &, as topologically equal if they have the same sequence of absolute transitions, ye, . . . . yk, and for 0 I i I k, QS(S,T(yi))=QS(Sref,Tr&yi)), i.e. the absolute qualitative states of both systems are identical (corresponding parameters have identical absolute values). If this is not the case, Weld speaks of changes in the behavioral topology. According to our discrimination of continuous and discontinuous deviations we distinguish continuous and discontinuous changes in the behavioral topology. We call a change in the behavioral topology ~o~~tinuo~s, if the behaviors still have the same sequence of basis transitions, PO, . . . . p1, and for 0 I j I 1 all deviations Of QS(S,T(Pj)) with respect to QS(Sref,Tref(Pj)) are continuous. Otherwise we call it discontinuous. The qualitative behavior of the heat exchanger is charac- terized by two transitions: the heat reaches the equilibrium temperature and the oil reaches the outlet. A certain refer- ence order of these transitions can change if the oil is passing the heat exchanger with a too high velocity. Both transitions are basis transitions, hence this is an example for a discontinuous change of topology. RSIIvI+‘s output for the heat exchanger with too high velocity is given by Fig. 7. As reference behavior, RSlM+ takes all possible absolute behaviors of the reference system. (Since devi- ating and reference system have the same absolute descrip- tion, these behaviors are generated implicitly.) With additional model information about the reference system, a special reference behavior and thus the corresponding devi- ating behaviors can be determined. Discontinuous changes of parameters are marked by a PQ value of D. This means: “Normally this parameter has a different sign for this time point/interval.” By a comparison with the other paths of the tree, it can be deduced which of them correspond (in their absolute descriptions) to possible reference behaviors. That is, possible changes of the absolute behavior (topology changes), resulting from an LGTN deviation, can exactly be determined. This includes an absolute description of the deviating and the reference behavior and relative (PQ and P) information for the deviating behavior. The deviating behavior of the spring/block system with too high amplitude (Fig. 6), on the other hand, is an example for continuous topology changes. The deviating behavior has a different set of transitions (e.g. landmark x2* is reached/left only in the deviating behavior), but it has the same order of basis transitions (reaching the rest position and the return positions). All deviations at basis transitions are continuous. 5 Related Work Relative descriptions are used in various approaches. (9) reasons about orders of magnitude, in (2) these concepts Simulation 1209 -~-__x__I___xII____I___xxI- ______x--~“ -~“ --,,“ ,“ ------~-~ Duration to reach the outlet is too low, oil at outlet is too hot. ‘1V” ---- Duration to reach the outlet is too low, duration to reach equilibrium temperature is normal. 7 All possible deviations of behavior under o high oil velocity. For a reference system ere equilibrium temperature is not reached, avior A is possible. If it is normally reached at outlet, behavior C is possible. If it is normally hed inside the heat exchanger, behaviors B, C A change of topology: the outlet has been reached, but the oil is still hot. A change of topology: equilibrium temperature is reached at the outlet. are used for fault diagnosis. The IQ analysis of (3) is a qualitative sensitivity analysis of a system’s steady state. Similar techniques that aim at fault diagnosis can be found in (4,5,6). Dynamic systems, on the other hand, are malyxxl in Weld’s DQ analysis and emrggerution (11). Both techniques predict the effects of differential changes as RSIM+ does. Input and output of RSIM+ and DQ analysis are similar, but DQ analysis cannot answer questions that require a comparison of deviations. Infer- ences in DQ analysis are based on the concept of perspec- tive , i.e. parameter deviations are not only described with respect to time but additionally relative to other parameters. In this way, a comparison of intervals of different length is possible. In RSIM+, this problem is solved by interval tran- sitions that perform a synchronization. DQ analysis sometimes produces no output. Due to this fact, topology changes can only be handled in an unsatisfying way (see 10, Section 4). RSIM+ always makes a prediction that contains all possible behaviors including changes in the behavioral topology. In (1) it is demonstrated how the comparative analysis problems that can be treated by DQ analysis can instead be solved by algebraic and qualitative manipulation of equations. Exaggeration answers concrete questions about the effects of a certain differential deviation on a target parameter. For this purpose it first exaggerates the given deviation, then simulates the exag- gerated system and finally rescales the exaggerated behavior by comparing it to a simulated normal behavior. Exaggeration always gives an answer that unfortunately can be wrong if not all relationships between parameters are monotonous. The idea of an exaggeration conflicts with a comparison of deviations because all deviations are mapped into the same set of extreme values. RSIM+‘s simulation techniques are similar to those of QSIM. But RSIM+‘s inferences have a more constructive character. RSlM+ does not use Waltz filtering. 6 Summary Relative descriptions are necessary to characterize certain kinds of system deviations and the resulting behavior. RSIM+ is a simulator that works with relative descriptions and is able to compare deviations with each other. The physical systems that can be described by RSIM+ corre- 1210 Qualitative Reasoning spond to those of QSIM. In RSIM+, the special properties of linear, overlinear and underlinear relationships between parameters are exploited to gain more accuracy $ the prediction of system behavior. Additionally, faulty M rela- tionships like TOO-FLATe+ can be express& RSIM+ predicts all changes to system behavior that can follow from LGTN deviations, i.e. changes in the behavioral topology are included. References (1) Chiu, C.; Kuipers, B. 1992. Comparative Analysis and Qualitative Integral Representations. In Faltings, B.; Struss, P. eds. Recent Advances in Qualitative Physics. The MIT Press. (2) Dague, P.; De&, P.; and Raiman, 0. Troubleshooting: When Modeling is the Trouble, AAAI-87, Seattle (1987) 590-595 (3) de Kleer, J.: Causal and Teleological Reasoning in Circuit Recognition, TR-529, AI-Lab., MIT, Cambrigde (1979) (4) Downing, K. L.: Diagnostic Improvement Through Qualitative Sensivity Analysis and Aggregation, AAAI-87, Seattle (1987) 789-793 (5) Gallanti, M.; Stefanini, A.; and Tomada, L.: ODS: A Diagnostic System Based on Qualitative Modelling Tech- niques, Conference on Artificial Intelligence Applications, Miami (1989) 142-149 (6) Kockskamper. S.; Neumann, B.; Josub, A.; and Miiller, H.: Die Anwendung modellbasierten SchlieBens bei der Diagnose schiffstechnischer Anlagen, in F. Puppe, A. Gtinter (eds.) Expertensysteme 93, Springer Verlag (1993) 14-27 (7) B. J. Kuipers: Qualitative Simulation, ArtijSciaZ Intelli- gence 29 (1986) 289-338 (8) Neitzke, M.: Modeling Physical Systems with Relative Descriptions of Parameters, in B. Neumann (ed.) ECAI-92, Vienna (1992) 683-684 (9) Raiman, 0.: Order of Magnitude Reasoning, AAAI-86, Philadelphia (1986) 100-104 (10) Weld, D. S.: Comparative Analysis, Artifkial Intelli- gence 36 (1988) 333-374 (11) Weld, D. S.: Theories of Comparative Analysis. (the MIT Press, Cambridge, 1990) | 1994 | 254 |
1,602 | Qualitative Reasoning r Automate r Chaos Toyoaki Nishida Graduate School of Information Science Nara Institute of Science and Technology 8916-5 Takayama, Ikoma, Nara 630-01, Japan nishida@is.aist-nara.ac.jp Abstract Chaos is ubiquitous in our everyday life and even a simple system may manifest chaotic behaviors. Chaos has been a challenge to the methodology of qualitative reasoning as well as classic science and engineering, due to unpredictability and complex- ity of behavior. In this paper, I claim that associating continuous domain with symbolic representation, a basic prin- ciple of qualitative reasoning, is vital for automat- ing analysis of chaos, as long as it is properly for- malized. As an empirical support to this claim, I present a computer program called PSX3 that can semi-automatically explore for chaotic behavior of a given system of piecewise linear ordinary dif- ferential equations with three unknown functions. The power of PSX3 originates from an ability of reasoning about smooth surfaces that implicitly exist in the phase space. PSX3 is im lemented using Common Lisp and Mathematics l? M. Introduction Chaos is ubiquitous in everyday life. Theoretically, it is known that even a simple system may exhibit chaos. Chaos has been a challenge to classic science. The source of difficulty is twofold: unpredictability due to sensitive dependence on initial conditions and com- plexity of geometry resulting from fractal structure. Huberman and Struss (Huberman and Struss, 1989) have taken chaos as a serious challenge to the whole methodology of qualitative reasoning, for the existence of chaos severely limits applicability of various filtering techniques and effect of landmark-based representa- tion, that have been popularly used in qualitative rea- soning systems. They propose to regard chaos rather a peculiar phenomenon and carefully separate them from commonsense and qualitative reasoning. In this paper, I show that associating continuous do- main with symbolic domain, a basic principle of quali- tative reasoning, is vital for analysis of chaos, as long as it is properly formalized. I claim that qualitative rea- soning techniques, with adequate generalization, pro- vide a powerful means for automating analysis of chaos. As an empirical support to this claim, I present a computer program called PSX3 that can semi- automatically explore for chaotic behavior of a cer- tain class of ordinary differential equations (ODES) and generate structural description of the behavior. The power of PSX3 originates from an ability of reasoning about smooth surfaces that implicitly exist in the phase space. PSX3 is implemented using Common Lisp and Mat hematicaTM . In what follows, I take a system of piecewise linear ODES that exhibits chaotic behavior and discuss issues related to analysis of chaos. Secondly, I describe how PSX3 analyzes chaotic behaviors. Thirdly, I character- ize reasoning about smooth surfaces as a generaliza- tion of conventional qualitative reasoning techniques. Finally, I discuss the strength and limitation of the current technique and suggest future direction. A Glimpse of Chaos In dynamical systems theory (Guckenheimer and Holmes, 1983), it is known that even a simple dynam- ical system manifests chaotic behavior. For example, Matsumoto and Chua (Matsumoto et al., 1985) have shown that a simple continuous dynamical system con- sisting of three subsystems of linear ODES with three unknown functions: -1.8x + 6.3~ - 2.7 dx dt= { (x < -1) 0.9x + 6.3~ (-15 2 _< 1) -1.82 + 6.33 - 2.7 (1 < Z) 5!2 g; 1 y;; -0.7y+z dt (1) exhibits chaotic behavior. Applied mathematicians study chaotic behavior, by investigating geometric and topological features of tra- jectories in the phase space spanned by a given set of unknown functions (or state variables). In the case of (l), Matsumoto and Chua have found that trajecto- ries (or orbits) tend towards a chaotic attractor with a “double scroll” structure, two sheet-like thin rings curled up together into spiral forms.’ Orbits approach ‘Roughly, an attractor is a dense collection of orbits that nearby orbits approach as t --) co. The reader is referred to (Guckenheimer and Holmes, 1983) for complete definition and detailed discussion. Simulation 1211 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Figure 1: A trajectory of Matsumoto-Chua’s equations (1) near the double scroll attractor reported in (Mat- sumoto et al., 1985) the attractor as time goes and manifest chaotic behav- ior <as they irregularly transit between the two rings, as illustrated by a sample trajectory shown in Figure 1. Investigation of chaos can be roughly divided into three stages. The first stage is search for a condi- tion under which a given dynamical system exhibits an interesting behavior. The second stage is qualita- tive analysis whose purpose is to identify the structure of the behavior in focus. The third stage is quantita- tive analysis, by applying known measurements such as Lyapunov exponents or fractal dimension (Moon, 1987) to obtain quantitative support of findings. Generally, as one proceeds to the later stages, the more well-studied, sophisticated mathematical tech- niques are available, some of which have been auto- mated. In contrast, the earlier stages depend on more general capability of humans, such as visual perception and spatial reasoning, as pointed out in (Yip, 1991b). Even mathematicians have to go through trial and er- rors in early stages of analysis. It is worth developing a computational model of earlier stages of dynamical sys- tems analysis, for (a) automated search does help both applied mathematicians in search for interesting phe- nomena and engineers who do not have ample knowl- edge about chaos, and (b) analysis and modeling of experts’ intellectual behavior as an integration of vari- ous cognitive processes are an important subject of AI research. Critical issues here are, (a) high-level representation of information such as topology and geometry of or- bits, and (b) its application to intelligently controlling nun+erical analysis. In (Nishida, 1993), I proposed flow mappings as a solution to the first issue. In this papers, I show that qualitative analysis of chaos can in fact be automated, using flow mappings as central represen- tation. I have implemented my theory as a program called PSX3. In the next section, I describe how PSX3 works. Then, I characterize my theory as an advanced formalization of a qualitative reasoning principle. Exploration for Chaos by PSX3 PSX3 takes a specification of system of piecewise linear ODES with three unknown functions and a region of analysis, and produces a qualitative and quantitative description of the behavior ranging from the regular to the chaotic, which can be used as a prescription for quantitative measurements. The procedure incorporated into PSX3 is roughly divided into local analysis, global analysis, and pre- scription generation for detailed quantitative measure- ments. Local Analysis In local analysis, PSX3 classifies trajectories in each intersection (cell) of region of analysis and a linear re- gion, into coherent bundles of orbit intervals. Roughly, a coherent bundle of orbit intervals is a collection of orbit intervals from/to a singly connected region of a cell surface or the same fixed point (Nishida, 1993). Figure 2a shows2 how PSX3 partitions the col- lection of orbit intervals contained in a cell cell-i: (-3 5 x 5 -1, -2 5 y 2 2, -3 < z < 3) made by in- tersecting a linear region (Z < -1) aid a given region of analysis (-3 5 x 5 3, -2 < y < 2, -3 5 z < 3). Figure 2b shows subsidiary partitioning on the surface of the cell, where each region of the cell surface is iden- tified by the attached number. Figure 2c shows several bundles of orbits that PSX3 has identified in cell-l. Orbits running through regions #83, #95, and #87 on the right side plane (x = -1) of cell-i are quali- tatively different with respect to this cell in the sense that they are running out of the cell from different sides of the cell (#77 on top plane (Z = 3), #66 on the rear plane (x = -3), and #94 on the right side (x = -l), respectively). PSX3 represents the result of partitioning as o {&}, where #i stands for either a fixed point or a two-dimensional region of the cell surface; and e a set of jlow mappings {4i + 4.j) which repre- sents the structure of flow (the collection of orbits), where a flow mapping $i + #j means that 4i (a two-dimensional region on the cell surface or a fixed point) is mapped to 4j (another two-dimensional re- gion or a fixed point) by the flow underlying the cell. Figure 2d shows a set of flow mappings for cell-l. Figure 3 shows results of local analysis for the remain- ing two cells in the given region of analysis. In order to obtain the partitioning, nontrivial amount of quali- tative and quantitative analysis is needed as described in (Nishida, 1993). Global Analysis After it has generated a set of flow mappings for each cell, PSX3 proceeds to global analysis and takes a col- ‘Although each surface pktitioning bundles of orbit intervals is approximated by triangulation, they are only for demonstration purpose and not used for reasoning. In order to reason about the flow, PSX only refers to regions on the cell surface such as region #95 in Figure 2b. 1212 Qualitative Reasoning (a) partitioning of the flow in cell-i: (-3~x~-1,-2,<g<2,-3<~<3) by a collection of smooth surfaces (4 bundles of orbit ktervals (1) #83 (2) #95 (b) resulting partitioning on the surface of cell-1 (3) #a7 (d) representation of the flow by flow mappings 61 -r+ 70 71 3 73 65 - 78 63 + 81 82 - 72 83 --* 77 80 d 85 76 * 86 62 --+ 89 90 --i 88 91 d 74 87 --) 94 95 4 66 97 * 92 79 * 98 99 --) 75 101 --P 68 84 4103 104 - 100 105 * 102 96 -106 107 + 67 69 4108 109 +64 93 --+ 110 Figure 2: Local analysis PSX has produced for cell-l Simulation 1213 (a) partitioning the surface of cell-2: L 2 0 E -2 -5 (b) flow map- (c) partitioning of the surface of cell-3: (d) flow map- pings for cell-2 (lItI3,-2~y<2,-352.~3) pings for cell-3: 113 - 117 123 + 111 114 - 124 126 + 118 112 -+ 127 125 + 129 132 - 135 136 + 120 140 + 116 121 - 141 115 + 142 144 -+ 134 145 - 138 119 - 147 148 - 133 149 + 143 151 --+ 146 128 + 152 153 + 130 131 --+ 154 137 + 155 156 --+ 122 157 + 150 139 - 158 Figure 3: Result of local analysis for cell-2 and cell-3 lection of flow mappings for each cell and looks for minimal sets of mutually transitioning flow mappings defined below. Definition 1 Given a set of frow mappings {& + q5j) and intersection relations {(fpm, &) 1 f& fl qSn # empty}, an extended set of flow mappings {&, --+* 4,) is defined as follows: (1) 4i ---f 4j * 4i --t* 4j (2) 4i --) 4j A 4k -+ 4711 A 4j fl4k # empty * 4i +* 4~7~ - (a) structural analysis (Transition 90 - 88 and 187 - 188 will eventuallv 168 + 167 174 - 159 169 + 177 179 + 163 170 -t 180 161 + 181 182 + 178 183 + 173 186 - 162 187 - 188 166 - 189 185 - 191 192 + 160 195 - 193 165 -t 196 197 - 175 200 - 164 184 - 201 202 - 198 203 + 199 176 + 204 205 -t 172 206 + 171 194 + 207 190 + 208 Definition 2 Given a set of flow mappings {q&, -+ 4j) and intersection relations {(4m, q&) 1 q& n C& # evW), @ = {4i + 4j) is a minimal set of mutu- ally transitioniny flow mappings ifl be removed at the prescription generation stage) - (b) envelope of the candidate of an attractor * I v(4i + 4j) E @ [4j +* 4i] 0 An algorithm for searching for a minimal set of mutu- ally transitioning flow mappings is implemented using a simple graph search algorithm. In the case of Matsumoto-Chua equations, PSX3 has found a minimal set of mutually transitioning flow mappings, as shown in Figure 4a. The predicted set of mutually transitioning flow mappings suggests that it is likely that the attractor is a composition of several recurrnt cycles, rather than a single cycle. As long as the phase space is partitioned into cells in such a way that each non-point attractor intersects more than one cell, mutually transitioning flow map- pings tell the approximate location and structure of the attractor. In other words, the surface of the union of bundles of orbit intervals corresponding to a minimal set of mutually transitioning flow mappings serves an envelope wrapping a candidate of a non-point attrac- tor, as shown in Figure 4b. Figure 4: Result of global analysis produced by PSX3 Prescription Generation for Quantitative Measurement Finally, PSX3 assembles a structured report on its find- ings as a prescription for further quantitative analysis. 1214 Qualitative Reasoning (a) PoincarC section (b) Poincark section (denoted with a dark color) and a characteristic orbit produced by PSS3 PoincarC map produced by PSXJ: it consists of about 3400 points recurrent orbit -2 Polncare section Figure 5: Prescription generation A critical information added at this stage is a Poincar6 section and mappings, which are popularly used by ap- plied mathematicians as a basis of quantitative anal- ysis. Poincar6 section is a plane that cuts across a recurrent orbit, as illustrated in Figure 5a. A Poincark map is represented as x(t) = xt H x(t + 1) = xt+l, where xi is the i-th point at which the recurrent orbit penetrates the Poincard section. It is possible to make preliminary diagnosis of a given recurrent orbit by ex- amining the shape of a Poincar6 map as a collection of points. The more diverged and fuzzier the Poincar6 map becomes, the more likely the orbit in question is cliaotic.3 PSX3 automatically generates a Poincar6 section by analyzing critical section of a minimal set of mutually transitioning flow mappings. PSX3 deter- mines where to start tracking an orbit, by intersecting the proposed Poincar6 section and the internal region delimited by an envelope wrapping a candidate of a non-point attractor. Figure 5b shows a Poincar6 sec- tion and an orbit that PSX3 has actually proposed and computed. Figure 5c shows a resulting Poincar6 map, which conforms to the one reported in (Matsumoto et al., 1985). Reasoning about Smooth Surfaces One of the fundamental principles of qualitative rea- soning is associating continuous domain with symbolic representation by aggregating coherent objects. The techniques embodied by PSX3 fit this schema. PSX3 aggregates orbit intervals (continuous geometric ob- jects) into bundles based on coherency relations defined with respect to a cell, associates each bundle with a flow mapping (symbolic representation), and uses the resulting set of flow mappings to set up a plan for more detailed quantitative measurements. PSX3 integrates qualitative and quantitative analysis for doing these. In particular, the success of PSX3 can be attributed 31 have not yet automated the evaluation of PoincarC map. Au- tomation could be possible using techniques pioneered by Yip (Yip, 1991a). to its ability of constructing representation of smooth surfaces implicitly existing in the phase space, by in- telligently controlling numeric and symbolic computa- tion. PSX3 combines numerical analysis and reasoning about smooth surfaces to establish delimiting surfaces in a cell. For example, when encountered with a set of fragmentary observations, PSX3 will consult a li- brary of smooth surface interaction patterns (Nishida, 1993), set up a hypothesis about the underlying ge- ometric structure, and try to verify it in subsequent analysis. Techniques incorporated into PSX3 can be regarded as an extension of conventional qualitative reasoning techniques in which real numbers are associated with a set of symbols, such as { -, 0, +}, by a set of land- marks. Although it has made various AI techniques such as GDE (de Kleer and Williams, 1987) applica- ble to continuous domains, the approach has flawed in several ways, especially in the case of reasoning about chaos. In contrast, my formalization is based on partition- ing the continuous domain by smooth surfaces. Rea- soning about smooth surfaces is more sophisticated and powerful, while more computationally expensive.4 Related Work and Discussion This work is considered to be an effort of devel- oping a computational model of dynamical systems theory (Guckenheimer and Holmes, 1983). Previous work in this direction involves: POINCARE (Sacks, 1991), PSX2NL (N is li a and Doshita, 1991; Nishida et 1 d al., 1991), Kalagnanam’s system (Kalagnanam, 1991), MAPS (Zhao, 1993), and Perfect Moment( Bradley, 1992). KAM (Yip, 1991b) is one of the frontier work, though it is for discrete systems (difference equations), as opposed to continuous systems addressed in this pa- per. Unfortunately, the techniques used in these sys- tems except MAPS (Zhao, 1993) and Perfect Moment 4However, it should be noted that the amount of redundant com- putation is significantly reduced for the sake of its expressive power. Simulation 1215 (Bradley, 1992) are severely limited to two-dimensional flows whose geometry is significantly simpler than those in three dimensional phase spaces. Indeed, con- tinuous flow in two-dimensional Euclidean phase space never exhibits chaos. In MAPS, the flow pipe model is used. A flow pipe represents a homotopy equivalence class of orbits and hence is essentially equivalent to a bundle of orbit intervals,5 despite some differences at the implemen- tation level.6 MAPS constructs the information struc- ture in a bottom-up fashion. Unfortunately, this is not enough for exploring for chaos. A guideline is needed to plan numerical computation for constructing a critical flow pipe which may serve as an envelope of a chaotic attractor. The method incorporated into PSX3 is a kind of exhaustive search. PSX3 partitions a given re- gion of analysis into a set of bundles of orbit intervals and searches for a candidate of an envelope of a chaotic attractor. Perfect Moment handles chaos with adaptive grids, which causes several problems due to discretiza- tion. Current implementation of PSX3 is limited in a cou- ple of ways. Firstly, PSX3 is specialized to flow in three-dimensional phase space. This is a rather seri- ous limitation, for most applications of practical in- terest are defined in higher dimensional phase spaces. The limitation might be overridden either by develop- ing a method of extracting a lower dimensional dynam- ics from a given system of ODES, or by taking a direct step towards generalizing the current method. The latter direction requires substantial efforts on reducing computational cost. Secondly, the subsystem for reasoning about smooth surfaces is “hard wired”: there is no separation be- tween a knowledge-base and a general reasoning en- gine. In developing PSX3, I have manually classi- fied geometric interactions among smooth surfaces and hand-crafted a reasoning algorithm. However, the same approach is intractable for more general classes of problems, namely hyper-surfaces in n-dimensional space. An interesting open problem is to develop a meta system which can generate a computational the- ory of reasoning about smooth surfaces in general n- dimensional spaces. Conclusion In this paper, I have shown that automated analy- sis of chaos can in fact be possible, and I have de- scribed PSX3 as an empirical support of the claim. The power of PSX3 originates from an ability of rea- soning about smooth surfaces that implicitly exist in the phase space. Acknowledgments I am grateful to Feng Zhao for useful comments. References Bradley, Elizabeth 1992. Taming Chaotic Circuits. Ph.D. Dissertation, M.I.T. de Kleer, Johan and Williams, Brian C. 1987. Diag- nosing multiple faults. Artificial Intelligence 32:97- 130. Guckenheimer, John and Holmes, Philip 1983. Non- linear Oscillations, Dynamical Systems, and Bifurca- tions of Vector Fields. Springer-Verlag. Huberman, Bernard A. and Struss, Peter 1989. Chaos, qualitative reasoning and the predictability problem. presented at 3rd International Workshop on Qualitative Physics, Stanford. Kalagnanam, Jayant 1991. Integration of symbolic and numeric methods for qualitative reasoning. Tech- nical Report CMU-EPP-1991-01-01, Engineering and Public Policy, CMU. Matsumoto, Takashi; Chua, Leon 0.; and Komuro, Motomasa 1985. The double scroll. IEEE Transac- tions on Ciruits and Systems CAS-32(8):798-818. Moon, Francis C. 1987. Chaotic Vibrations - An In- troduction for Applied Scientists and Engineers. John Wiley & Sons. Nishida, Toyoaki and Doshita, Shuji 1991. A geo- metric approach to total envisioning. In Proceedings IJCAI-91. 1150-1155. Nishida, Toyoaki; Mizutani, Kenji; Kubota, Atsushi; and Doshita, Shuji 1991. Automated phase portrait analysis by integrating qualitative and quantitative analysis. In Proceedings AAAI-91. 811-816. Nishida, Toyoaki 1993. Generating quasi-symbolic representation of three-dimensional flow. In Proceed- ings AAAI-93. 554-559. Sacks, Elisha P. 1991. Automatic analysis of one- parameter planar ordinary differential equations by intelligent numeric simulation. Artificial Intelligence 48:27-56. Yip, Kenneth Man-kam 1991a. KAM - A System for Intelligently Guiding Numerical Experimentation by Computer. The MIT Press. Yip, Kenneth Man-kam 1991b. Understanding com- plex dynamics by visual and symbolic reasoning. Ar- tificial Intelligence 51( l-3):179-222. Zhao, Feng 1993. Computational dynamics: Modeling and visualizing trajectory flows in phase space. An- nals of Mathematics and Artificial Intelligence 8:285- 300. 5These two models were independently developed and widely published in the summer of 1991. ‘The flow pipe model is implemented using (a) polyhedral ap- proximation for representing the shape of flow pipes and (b) re- lational graph representation for representing the topology of the phase portrait. 1216 Qualitative Reasoning | 1994 | 255 |
1,603 | Activity Analysis: ualitat ive Analysis of Stationary easonin Brian C. Williams Xerox Palo Alto Research Center 3333 Coyote Hill Road, Palo Alto, CA 94304 USA bwilliams@parc.xerox.com Abstract We present a. theory of a modeler’s problem de- composition skills in the context of opthal Tea- sowing - the use of qualitative modeling to strategically guide numerical explorations of ob- jective space. Our technique, called activity annl- ysl:s, applies to the pervasive family of linear and non-linear, constrained optimization problems, and easily integrates with any existing numeri- cal approach. Activity analysis draws from the power of two seemingly divergent perspectives - the global conflict-based approaches of combina- torial satisficing search, and the local gradient- based approaches of continuous optimization - combined with the underlying insights of engi- neering monotonicity analysis. The result is an approach that strategically cuts away subspaces that it can quickly rule out as suboptimal, and then guides the numerical methods to the remain- ing subspaces. Introduction and Example Our goal is to capture a modeler’s tacit skill at decom- posing physical models and its application to focusing reasoning. This work is ultimately directed towards the contruction of “self modeling” systems, operating in embedded, real time situations. This article ex- plores the modeler’s decompositional skills (Williams & Raiman 1994) in the context of optimal reasoning - the use of qualitative modeling to strategically guide gradient-based and other numerical explorations of ob- jective spaces. Optimal reasoning is crucial for embed- ded systems, where numerical methods are key to such areas as estimation, control, inductive learning and vi- sion. The technique we present, called activity analy- sz’s, applies to the pervasive family of linear and non- linear, constrained optimization problems, and easily integrates with any existing numerical approaches. Activity analysis is striking in the way it merges together two styles of search that are traditionally viewed as quite disparate: first is the more strategic, conflict-based approaches used in combinatorial, satis- ficing search to eliminate finite, inconsistent subspaces (e.g., (de Kleer & Williams 1987)). The second is the Jonathan Cagan Department of Mechanical Engineering Carnegie Mellon University Pittsburgh, PA 15213 USA cagan+@cmu.edu rich suite of more tactical, numeric methods(Vander- plaats 1984) used in continuous optimizing search to climb locally but. monotonically towards the optimum. Activity analysis draws from the power of both per- spectives, strategically cutting away subspaces that it. can quickly rule out as suboptimal, and then guiding the numerical methods to the remaining subspaces. The power of activity analysis to eliminate large sub- optimal subspaces is derived from Qu.aZitatiz(e KC!‘, an abstraction in qualitative vector algebra of the foun- dational Kuhn-Tucker (KT) condition of optimization t.heory. The underlying algorithm achieves simplicity and completeness, by introducing the concept of gener- ating prime implicating assignments of linear, qualitat- ice vector equations. This process of ruling oub feasi- ble, but suboptimal subspaces in a continuous domain, nicely parallels the use of conflicts and prime implicant generation for combinatorial, satisficing search. The end result is a metehod that achieves parsimonious de- scriptions, guarantees correctness, and maximizes the filtering achieved from QKT. Finally, activity analysis can be thought. of as au- tomating the underlying principle about monotonicity used by the simplex method to examine only the ver- tices of the linear feasible space. It then generalizes and automatically applies this principle to nonlinear programming problems. Figure 1: Hydraulic Cylinder Simdation 1217 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. To demonstrate t*he task consider the design of a hydraulic cylinder, a classic optimization problem, in- troduced by Wilde (Wilde 1975) to demonstrate the related technique of monotonicity analysis. The cylin- der (figure 1) delivers force f, through input pressure p. Weight is modeled as inside diameter (i) plus twice the cylinder thickness (t), force (f) as pressure (p) times cylinder area, and hoop stress (s) as pressure times diameter acting across the thickness. The task is to find a parametric solution that minimizes cylinder weight, while satisfying constraints including positiv- ity of variables (i, s, f, p, f > 0), maximum pressure (P) and stress (S), and minimum force (F) and thickness (T) (design variables are in lowercase, fixed parameters in uppercase, and equality and inequality constraints are labeled h, and g2, respectively): Minimize i + 2t, subject to: s - pf! = f- 4; 0, (ha =O) : T-t < 0, (92 5 0) = 0, (ha x(-J): P-P 2 0, (93 5 0) F-f < 0, (g1 5 0) : s-s < 0, (94 5 0) Given this symbolic formulation, activity a.nalysis uses qualitative arguments to classify regions of the design space where optima might lie and where they cannot. After eliminating suboptimal regions, each re- maining region identifies the solution as possibly lying on the intersection of one or more constraint bound- aries. Each region reduces the dimensionality of the problem by the number of intersecting boundaries, thus significantly increasing the ease with which a solu- tion can be found. In particular, for the cylinder prob- lem activity analysis concludes there are two subspaces of the design space that could contain the optima, one subspace in which g1 and 94 become strict equalities, and a second in which all but g4 become strict equal- ities. The new problem formulation finds the optima of the two spaces and combines the results as follows (where “arg min” returns a set of optima): Given: vector x = (istpf)T , 1. Let Y = argminx(i + 2-t), subject to: (hl = 0) (sl = 0) (93 5 0) (h2 = 0) (g;? 5 0) (g4 = 0). 2. Let Z = arg minx(i + 2f), subject to: (hl = 0) (Sl = 0) (93 = 0) (h = 0) (92 = o) (g4 5 0). 3. Return arg minx{ i + 2-t), subject to: XEYUZ. Originally, the problem has a 3 dimensional space to be explored (3 degrees of freedom - DOF) resulting from 5 variables, 2 equality constraints. The reformulated problem rules out the interior and boundaries, except some intersections. The first remaining subspace corre- sponds to a line (1 DOF) produced by the intersection of the 91 and 94 constraint boundaries with the h,. The second remaining space is a point (0 DOF) produced by the intersection of 91, gz, g3 and the h,. Thus find- ing a solution to the first, problem involves a single, one dimensional line search, and the second involves solving the system of equalities to find the unique so- lution. Using parameter values F=lOOO lbf, T=.05 in, S=30000 psi, T=lOOO in, applying matlab to the orig- inal problem took 46.3 seconds. The optimal solution lies iI1 Z, which took only 8.1 seconds to run; no feasi- ble solution exists in Y for these parameter values. Activity analysis draws inspiration from monotonic- ity analysis (MA) (Papalambros PC Wilde 1979; Pa- palambros 1982). Monotonicity analysis began as a set of principles and methods used by modelers to identify ill-posed problems and to partially solve them, based on monotonic arguments alone. These principles were encoded in several rule-based implementations (Azram & Papalambros 1984; Choy & Agogino 1986; Rao SC Papalambros 1987; Hansen, Jaumard, & Lu 1989), presented informally as heuristic methods. The problem activity analysis addresses is similar in spirit to that of MA; nevertheless, the approach is quite different. First, activity analysis operates di- rectly on an abstraction (QKT) of the Kuhn-Tucker (KT) conditions of optimization t*heory. While much easier to apply, QKT and KT are equivalent for the task, given only knowledge of monotonicities. Sec- ond, activity analysis provides a precise formulat,ion of the problem in terms of minimal pstntionary cou- erings, that guarantees the solution is parsimonious, maximizes the filtering derived from QKT, and insures correctness. Finally, a mapping to prime assignments and the introduction of a simple but complete prime assignment engine guarantees that these three proper- ties are achieved. Stationary Points and Kuhn-Tucker For a point x* to be an optimum it is necessary that, the point be stationa.ry, that is any “down hill” direc- tion- is blocked by the constraints. Activity analysis exploits this fact to eliminate sets of points that can quickly be proven to be nonstationa.ry, using a con- dition we call Qu.aZitative Kuhn-Tucker (QKT). This section introduces the optimization problem, the con- cept of stationary point, and the traditional algebraic, (Kuhn-Tucker) condition for testing stationary points. Activity analysis applies to the pervasive family of lin- ear and non-linear, constrained optimization problems 01 = (x, f, g> h): Find XI = arg min f(x) subject to: g(x) 5 0 h(x) = 0, where column vectors are denoted in bold (e.g., x, x*, g(x) and h(x)), f(x) is tl ie objective function, g(x) is a vect,or of inequality constraints and h(x) is a vector of equality constraints. A point. x E $2” is feasible if it satisfies the constraints, and fea.sibZe space 3 C_ W 1218 Qualitative Reasoning denotes all feasible points (represented 3 = (g, h)). A feasible direction s’from a feasible point is one through which a non-zero distance can be moved before hitting a constraint boundary. f(x) is decreasing at x in di- rection s’if vf(x) . s’ < 0. Finally, a point is stationary (denoted x*) if any direction that decreases the objec- tive is infeusible. The Kuhn-Tucker (KT) conditions (Kuhn & Tucker 1951) p rovide a set of vector equa- tions that are satisfied for a feasible point x* exactly when that point, is stationary: vf(x*) + XT v h(x*) + /.L~ v g(x*) = OT (KTl) subject to pTg(x*) = OT, P 2 0. fxj - T ;.A transposes column vector ,X to a row. Gradients ‘~g and vh denote Jacobian matrices. of is a row vector s . . . a;c ( i!l- . (3) and (&), n > vg and vh are matrices respectively, where (a,,) denotes a matrix whose element in the ith row and jth column is aa3, for all i and j. For example, KTl and KT2 are equivalences between row vectors, and KT3 is a relation between column vectors. In KTl the - v f term denotes directions of de- creasing objective from x*, the term (AT v h(x*) + ,LL~ v g(x*)) denotes infeasible directions from x*, and the equality says the decreasing directions are all in- feasible; hence, x* is stationary. More specifically, s’ decreases the objective if it has a component in the - ~7 f direction (s’ e of < 0). A direction is infeasible with respect to inequality constraint. gi(x*) if x* lies on the constraint. boundary (gi(x*) = 0) and it has a com- ponent in the + v gi(x*) direction. A direction is in- feasible with respect to equality constraint hj(x*) if it has a component in either the -v h, (x*) or $7 hj (x*) direction. Most importantly, if x* lies on multiple con- straint boundaries, then an infeasible direction has a component which is a linear, weighted combination of the above gradients for these constraints. The weights are p and ,\, (called Lugrunge multipliers), and the combination is pT’Jg + XTvh subject to KT2 and KT3. Hence all decreasing directions are infeasible when - v f equals one of these linear combinations (KTl ). Figure 2 shows an example of of and ‘(;7g gradient vectors, and the combined weighted vector, which exactly cancels of. A key property of KT is that it identifies active in- equality constraints. Intuitively, a constraint [g2] is active at a point x when x is on the constraint bound- ary and the direction of decreasing objective, of, is pointing into the boundary. When this is true pZ is positive. The basis of our approach is to conclude, by looking at signs of CL, that the stationary points lie at the intersection of the constraint boundaries. One or more constraints have been identified as active, hence the name activity analysis. vg2 CL2 vg2 Figure 2: Example gradient vector diagram for KT. ualitative KT Conditions Quulitutive KT (QKT) is an abstraction of KT that is a necessary, bub insufficient, condition for a point being stationary. It is the means by which activ- ity analysis quickly rules out suboptimal subspaces. Qualitative properties used by QKT to test a point x include whether each constraint is active at x, and the quadrant of the coordinate axes each: gradient of, vg and vh lies within. These properties can be ex- tracted quickly and hold uniformly for large subsets of the feasible space, and parameterized families of op- timization problems. QKT, its proof (see (Williams 1994)), and manipulations by activity analysis rely on a matrix version of SRl - a hybrid algebra com- bining signs and reals. This algebra behaves as one expects given a familiarity with (scalar) sign algebra and traditional matrix algebra (see (Williams 1994; 1991)). Derived from KT, QKT states that a feasi- ble point x* is stationary only if (QKTl): bf(x*)l + blT [vh(=)] + [plT [vg(x*)] > oT, subject to [plT[g(x*)] = OT, and (QKT2) [PiI # -k vwT3) where [v], called a sign vector, denotes the signs of the elements of v, such that [zfi] E (2, 0, ?}. Recall KT said that to be stationary there must exist a weighted sum (+C) of v’g and vh that exactly cancels of (note v?i is a row vector). QKT says a point, is nonstution- ury unless there exists a G that lies in the quadrant diagonal from that which contains v f. For example, in figure 2 v f lies in the upper left quadrant; thus, a Jii must exist that lies in the lower right. The sign vector [v] denotes the quadrant containing a vector v, and each component [uz] describes where v lies relative to the v, = 0 plane. For example, [*I = ( $ ^ ) indicates that +? is in the lower right. Using this alge- braic representation, the condition on diagonal quad- rants becomes -[v f] = [\i;]. Using only knowledge of the quadrant each con- straint’s gradient lies within and whether each con- straint is active (indicated by the signs of the lagrange Simulation 1219 multipliers [p] and [A]), we know from KT that the quadrants G may lie within are a subspace of those described by [p]*[og] + [XIT[vh]. Thus, -[of] = [G] & [/LIT[og] + [XIT[vh] (i.e., QKTl). For example, in figure 2 since vgl (= ( $ -& ) ) lies in the upper right and vg2 (= ( ^ fl ) ) lies in the lower left, it is possible for a G to lie in the lower right; thus, any x satisfying these conditions may be stationary. But sup- pose vg1 is replaced with og’,, which lies in the upper left for points in some subspace 31 c 3. Then G may lie in the upper or lower left, but not the lower right; thus, all points in 31 must be nonstationary. That is, evaluating -[v f] = [plT[og] for vgl and then 09:: ( -I- -) r(f ?) =(+ +) k t but i ) ( -i- -q gI(I P) =(q- j-) i t It is this second type of conclusion, made from only qualitative properties, that activity analysis uses to eliminate feasible subspaces of nonstationary points. Next, to instantiate QKTl on optimization problem OP s (x, f, g, h): 1. Compute Jacobians of, vg and vh by symbolic differentiation. 2. Compute signs of Jacobians. For each element, (a) replace real operators with sign operators, using properties [a + b] & [a] + [b], [ab] = [a][bJ, [a/b] = [a]/[b] and [-a] = -[a]. (b) Substitute for sign variables [al using positivity conditions ([a] = -q), and perform sign arithmetic (e.g., [5] * 4-, (-) + (I) 3 ^). 3. Expand QKT 1 by expanding matrix sums and prod- ucts. Returning to the hydraulic cylinder problem from the introduction, recall that x is the vector (itfs~)~, the objective f(x) is i + 2t, and the constraint vectors are: ( T h ZZ s-g f-E.&) , e; = (F-f T-t p-P s-S).~ The following shows [vh] after steps 2a (middle) and 2b (right): Repeating for [of] and [vg], and inserting into QKT: Expanding matrix operations for step 3 results in equations QKTl( l)-( 5): Q E (+)-[~,I-[~21 (1) 0 c [P41+[~11 (4) 0 c (i) -b21+ IAll (2) 0 c b3l - [AlI - iA21 (5) 0 E 4~11 -I- 1x21 (3) Note that the computation of sign matrices in step 2 is extremely simple, but suprisingly adequate for many problems. The symbolic algebra system Minima (Williams 1991) provides a general tool for deducing the signs of sensitivities (e.g., [ 1 9 ) subject to x sat- isfying the equality and inequality constraints. Having achieved an easily evaluable condition that is sufficient for testing the suboptimality of infinite subspaces, we turn to its use for strategically focussing optimization. Activity Analysis and Prime Assignments Activity analysis reduces an optimization problem to a set of simpler subproblems by “cutting” out feasi- ble subspaces that are suboptimal. These subspaces contain all and only those points that are provably nonstationary by QKT (see (Williams 1994)). The output of activity analysis is a concise description of the remainder, called a minimal pstationary covering (“p-” stands for “possible” according to QKT). It is a set of feasible subspaces (and corresponding optimiza- tion problems), at least one of which is guaranteed to contain the true optimum. What is key is that the descriptions are parsimonious, they maximize the “fil- tering” achievable from QKT, and are always correct (these three properties are theorems, stated precisely in (Williams 1994)). Th is section states and demon- strates the activity analysis problem, and a sound and complete solution algorithm. The core is a mapping between minimal pstutionary subspaces and prime us- signments, and a general prime assignment engine for arbitrary systems of linear sign equations. To start we say a point is pnonstutionury if it fol- lows from QKT that it is nonstationary; otherwise, it is pstutionury. A feasible subspuce is pstationury if all its points are pstationary, and pnonstutionary if all its points are pnonstationary. Activity analysis maximizes its use of QKT while preserving correct- ness by eliminating exactly the pnonstationary sub- spaces from its description of the feasible space. This description is built from a set C whose elements re- sult from strengthening one or more of the inequality constraints gi 5 0 to strict equalities gi = 0; that is, C is the powerset of constraint boundary intersec- tions. The description (called a minimal pstutionury covering), covers the pstationary points by collecting all pstationary subspaces that are maximal under su- perset. These cover every pstationary subspace. The 1220 Qualitative Reasoning activity analysis problem is then: girren optimi,-ation problem OP = (x, f, g, h) and instnntdation of QKT (=Qh’T(OJ’)), construct the minimal pstationary cov- ering C. Mapping QKT(OP) to C relies on two observations: First, from QKT2 (G [pu2(x)][gt(x)] = 0) it. follows that [Pi(X)] = T + gz(x) = 0 (d enoted Rl). That is, any point where [pi] = 4 must be on the gZ = 0 constraint boundary. Thus, when activity analysis shows that a subspace of pstationary points makes [pZ] = 4 for one or more gi’s, it concludes that these points lie along the intersection of the gL boundaries. Second, a par- ticular set of variable assignments for QKTl, called prime (implicating) assignments, directly maps to the minimal pstationary covering by applying the first ob- servation. The key here is that achieving parsimony, maximum filtering and correctness reduces to generat- ing complete prime assignments. The following properties, stated informally here, are given as definitions and theorems in (Williams 1994). First, a (partial) assignment to [x] is a set CY which as- signs each [;r,] at most one value, cy C {[x8] = s 1 [~:i] E x,s E (2,o,-?-}}. w e are interested in the consistent assignments to QKTI, where the [x] to be assigned is a vector of lagrange multipliers ( [plT [XIT) T. Addition- ally, the consistent assignments must also satisfy the restriction of QKT3 ([p] # L). Note that each con- sistent assignment C has a corresponding subset S of feasible space, produced by applying Rl to the assign- ment and then adding the resulting active constraints to the original constraint set. S has the property that every point in S satisfies C. Next, an implicating assignment y is a consistent as- signment to QKTl, such that whenever an extension to y satisfies restriction QKTS, it also is consistent with QKTl. That is, assignmenh y implies QKTl under restriction QKT3. An implicating assignment has the important, property that every point in its correspond- ing subspace S satisfies QKT. Thus S is a pstationary subspace. Finally, a prime assignment P is an implicating as- signment no proper subset of which is also an implicat- ing assignment. Thus P’s corresponding S is a maxi- mal pstationary subspace. Conversely, every maximal pstationary subspace is the corresponding subspace of some prime assignment. Thus the set of subspaces cor- responding to all prime assignments is a minimal psta- tionary covering. To produce all primes for’ QKTl, our prime assign- ment engine first computes the primes P, of each scalar equation in QKTl, then combines them using mini- mal set covering. Pulling this all together, the activity analysis algorithm is: Given problem OP = (x, f, g, h): 1. Instantiate QKTl (given earlier) --+ QKTl(OP), 2. Compute prime assignments P, of each QKTli(OP) E QKTl(OP), Compute minimal set covering of P, --+ P, deleting inconsistent assignments, Extract minimal sets of [p2] = $ assignments from P ----t IT, Map each element of U t,o a maximal pstationary subspace by applying [p,(x)] = $ --+ g,(x) = 0, producing a covering. Formulate and return a new optimization problem from this covering. Step one was demonstrated in the previous section. For steps two and three we note that QKTl is an instance of a linear system of sign equations (denoted L( [xl)) and solve the prime assignment problem for arbitrary L([x]). That is, L([x]) in vector form is 0 2 [B] + [A][x], with [A] and [B] being sign constant matrices, [x] an n vector, [A] an n by ?n matrix and [B] an m vector. The ith scalar equat,ion of L([x]) (denoted L,([x])) is of the form: For QKTl, xT is (F~XT)~, [B] = [of], and [A] is the matrix (vg oh). Additionally, we generalize the set of restrictions given by QKT3 (i.e., [pi] # L), to arbitrary sets of restrictions R( [xl) C {[z,] # sls, E x, s E (2, 0, $1). For the cylinder (table, end of QKT section), QKTl has 5 L,([x])‘s, with x = (p1w3p4~wdT. For ease of reading we wrot,e terms +[z~] as [a,], -[z~] as - [;r,], and eliminated ter$s,O[a,l. *Tile cy!@der R([x]) is {[PI] # ^, [PZ] # -7 lP3J # -1 lP41 # -1. For step 2, the prime assignments of each L,( [xl) are constructed from-three sets bf scalar assignments, con- sistent, with R([x] i : th ose restricting one of the equa- tion’s terms ([a,,] z,]) to be positive ( Pz), those mak- ing a term zero ( ZZ), and those making a term negative (N,), respectively: R 3 -M = bv3 I hl # 07 (b4 # bvl> sr wm-~ z = -GJl = 0 I I%?1 # 03 kJ1 # 0) e W[xl>> and = -M = -bvl I [%?I # 0, ([%I # +,I) sr Wm. Justifying P,, for example, we know in general that [c] # 0 --+-[cl’ = 4. This [u,~][x~] = 4 if [z3] = [a,]] and [u,j] # 0. The derivation of 2, and N, is similar. Constructing the prime assignments for the cylinder Li( [xl) uses: Next, recall that the prime (implicating) assign- ments for L, ([xl) must imply L, ([xl). That is, they guarantee that it holds, given R([x]), independent of Simulation 1221 additional consistent assignments. This is true if the right hand side of Li ([ x is 1) g uaranteed to be a superset of 0 (i.e., it is either 0 or 3). The form of the assign- ments that achieve this for syrne-L, ([xl) depends on the value of [bi], where [bi] = [gj for QKTl. Suppose [bi] = &, then the right hand side must become ?. This holds exactly when at least one of the [u,j][lpj] terms is negative (since 0 C (^) + (4) = ?‘). For example, in the cylinder QKT equation (2), X1 = ^ guarantees that the equation is satisfied. The only other assign- ment that guarantees this is ~2, = $. Thus the prime assignments for (2) are (A1 = -} and (~2 = 41. The treatment of [b,] = ^ is analogous. Next, suppose [bi] = 0, then to imply L,( [x]) the prime assignment can make the right hand side either 0 or ?. The first holds exactly when all terms are 0. The second holds when at least one term is positive and the other is negative. For example, cylinder QKTl(3) : 0 2 -[PI] + [AZ]. Thus, ‘the prime assignments are {X2 = 0, ~1 = 0) and (X2 = $,,ul = 4). Note that (X2 = ^, ~1 = -} is not acceptable, since by restriction [pi] # II. To summarize, the prime ;$yme$s of L, ([xl) are 1) Ni if [b,] = &, 2) P, = -, and 3) [bi] G 0 (where p {Zi} U {{p, n}lp E Pz, n E Ni} if an d n in (p, n> do not contradict eazh other). Completing step two for the table of cylinder equations QKTl( 1) - (5) produces: {A, = 4}, (A, = 4) P(l) {A, = l}, (p2 = $1 P(2) (X2 = 0,/-h =0}{/+=$-,p1=~} P(3) {X1=O,p4=0}, (x,=^,p4=+} P(4) (A1 = 0, x2 = 0, p3 = O}, {A, = i-, A:! = 2,) {A, = -F, p3 = $1 {Al = II, A2 = +), (A2 = i-, p3 = $} P(5) The fourth step, extracting the minimal sets of [pL] = 4 assignments results in {[,Y~] = $, [p4] = q} and {[PI] = -‘F, [pz] = $-, [p3] = G-}. The fifth step uses [pi] = 4- - g,(x) = 0 t. o map these sets to the equiv- alent minimal pstationary covering. The sets tell us that g1 and g4 must be active, or 91, gz and g3. The resulting cover is: FI = ((g2,g3},{hl, b,gl,g4}) and Fz = ({94},(~l,~2,91r92,93))r where (g, h) is a space defined by inequality g and equality h constraints. ,Tl and Fz denote the line and point highlighted in the introduction to the cylinder example. The final step, formulating a new optimiza- tion problem, produces: Given: S Z {x* 1 x* = arg minxe7 f(x),F E {31,F2}}, Find: minxE.s f(x). The first. part finds the minimum of each suhspace in the covering. The second part selects from these the global minimum. A more expanded form was given in the introduction. Thus through this example we have demonstrated activity analysis’ capability of par- tially solving constrained optimization problems from monotonicity constraints, and for synthesizing special purpose optimization codes. Discussion As we mentioned in the introduction, activity anal- ysis builds upon a large body of work from the me- chanical engineering community on monotonicity anal- ysis( Wilde 1975; Papalambros & Wilde 19i9; Papalam- bros 1982), a method that uses derivative informa- tion to address the boundedness and global opt,imal- ity of optimization problems. Monotonicity analysis provides two rules that test the boundedness of a for- mulation: Rule 1: If the objective function is monotonic with respect to a variable, then there exishs at least one ac- tive constraint that bounds the variable in the direction opposite of the objective function. The third step, constructing the composite primes for L([x]), is based on: Rule 2: If a variable is not contained in the object,ive function then it must be either bounded from both above and below by active constraints or not actively bounded at all (i.e., in the latter case any constraint The left hand side is a disjunction of the L( [x] ) prime assignments, and the right hand side is an expression in terms of the primes of L,( [xl), just computed. Thus, the desired primes result from reducing the expression on the right to minimal, disjunctive normal form. For this specialized case, this step is equivalent to comput- ing minimal set covering of the P( L, ( [xl)) and then removing inconsistent assignments (see a standard al- gorithm text, or (Williams 1994) for our algorithm). For the cylinder, the minimal covering of P( 1) - (5) produces just two prime assignments, that is monotonic with respect to that. variable must be inactive or irrelevant). Both of these rules can be derived from the Kuhn- Tucker Conditions. They also follow as an inst,ance of QKT and are embodied within activity analysis. The result of monotonicity analysis (exhaustive ap- plication of the rules) are several sets of const,raints one of which must be active for a problem to be well bounded. Various levels of rule-based imple- mentations of monotonicity analysis have been de- scribed in (Michelena & Agogino 1988; Rao SC Pa- palambros 1987; Azram & Papalambros 1984; Hansen, ({[h] = -$,I = +J/h]= i-&4] = -i-)9 Jaumard, Qi Lu 1989), which guide numerical opt.imiza- {[Xl] = O,[Az] = -L[p1] = -i-&2] = L[P3] = i&4] = O}}. tion codes. Choy and Agogino (Choy SC Agogino 1986) 1222 Qualitative Reasoning and Agogino and Almgren (Agogino & Almgren 198i) incorporate symbolic algebraic methods to aid in the evaluation of monotonicities and the solution of the optima. Cagan and Agogino (Cagan Sr: Agogino 1987) apply monotonicity analysis to identify topological changes to designs that improve performance. While these systems address the optima.1 reasoning problem, they do not present algorithms proven to be sound and complete (each of these implement.ations has been described as “heuristic” (Rao & Papalambros 1987; Hansen, Jaumard, & Lu 1989)). Activity analysis provides the following contribu- tions: it formalizes the strategic way in which a mod- eler focuses optimization, as the process of generat- ing minimal pstationary coverings. It. introduces QKT as a powerful condition for quickly eliminating large, suboptimal subspaces. Finally, it exploit,s t#his con- dition through a novel problem reformulation based on the prime, implicating assignments of linear sign equations. The activity analysis algorithm is sound and complet*e with respect to classifying the design space into pstationary and pnonstationary subspaces. The method of pruning suboptimal subspaces pro- vides a continuous analog to the conflict-based a.p- proaches prevalent in combinatorial satisficing search (such as those used in model-based diagnosis (de Kleer & Williams 1987)). Activity analysis automates the in- tuitions about monotonicity exploited by the simplex method to examine only the vertices of the linear feasi- ble space, most importantly, extending its application to nonlinear problems. Act.ivity analysis has been demonstrated on several engineering problems. The implementation is in Franz Lisp running on a Spare 2. The problem reformulation is passed to Matlab’s Optimization toolbox, where a wide variety of nonlinear gradient methods are avail- able. (W 11 i iams 1994) describes an extension to ac- tivity analysis for cases where monotonicities are only partially known. Activity analysis is currently being pursued in the context of visual 3D matching prob- lems and other embedded, realtime problems. Activity analysis can also be extended to provide explainable optimizers, ones that use QKT to provide common- sense explanations about optimality. Activity analy- sis is one of several techniques being developed that capture a modeler’s expertise at. strategically guiding numerical codes. References Agogino, A. M., and Almgren, A. S. 1987. Techniques for Integrating Qualitative Reasoning and Symbolic Computation in Engineering Optimization. Engineer- ing Optimization, 12: 117-135. Azram, S., and Papalambros, P. 1984. An Automated Procedure for Local Monotonicity Analysis. Trans. ASME, Journa.1 of Mechanisms, Transmissions, a.nd Automation in Design 106:82-89. Cagan, J., and Agogino, A. M. 1987. Innovat,ive De- sign of Mechanical Structures from First. Principles. AI EDA&? 1(3):169-189. Choy, J. K., and Agogino, A. M. 1986. SYMON: Au- tomated SYMbolic MONotonicity Analysis System for Qualitative Design Optimization. In Proceedings of ASME 1986 International Computers in Engineer- ing Conference, 305-310. de Kleer, J., and Williams, B. C. 1987. Diagnosing Multiple Faults. Artif. Intell. 32:97-130. Hansen, P.; Jaumard, B.; and Lu, S. H. 1989. An Automated Proceedure for Globally Opt,imal Design. Trans. of the ASME, Jou.rnal of Mechanisms, Trans- missions, a.nd Automation in Design 361-367. Kuhn, H. W., and Tucker, A. W. 1951. Nonlinear Programming. In Neyman, J., ed., Proceedings of the Second Berkeley Symposium on Mathematical Statis- tics and Probability. Berkeley, CA: Universit,y of Cal- ifornia Press. Michelena, N., and Agogino, A. M. 1988. Mul- tiobjective Hydraulic Cylinder Design. J0urna.l of Mechanisms, Transmission and Automation in De- sign 110:81-87. Papalambros, P., and Wilde, D. J. 1979. Global Non-Iterative Design Opt.imizat’ion Using Monotonic- ity Analysis. Trans. ASME, Journal of Mechanical Design 101(4):645-649. Papalambros, P. 1982. Monotonicity in Goal and Geometric Programming. Tmnsa.ctions of the ASME, Jou.rnal of Mechanical Design 104:108-113. Rao, J. R., and Papalambros, P. 1987. Implementa- tion of Semi-Heuristic Reasoning for Bounded Anal- ysis of Design Optimization Models. In Advances in Design Automation, proceedings of the ASME Design Automation Conference, 59-65. Vanderplaats, G. N. 1984. Numerical Optimiza- tion Techniques for Engineering Design With Appli- cations. New York: McGraw-Hill. Wilde, D. J. 1975. Monotonicity and Domi- nance in Optimal Hydraulic Cylinder Design. Trans of the ASM’E, Journal of Engineering for Industry 94( 4): 1390-1394. Williams, B. C., and Raiman, 0. 1994. Decomposi- tional Modelling through Caricatural Reasoning. In AAAI. Williams, B. C. 1991. A theory of interact,ions: unify- ing qualitative and quantitat,ive algebraic reasoning. Artif. Intell. 51. Williams, B. C. 1994. Charact,erizing Act,ivit#y Anal- ysis. in progress. Simulation 1223 | 1994 | 256 |
1,604 | Intelligent Automated Grid Generation for Numerical Simulations Ke-Thia Yao Computer Science Department Rutgers University New Brunswick, NJ 08903, kyao@cs.rutgers.edu (908) 932-5263 USA Abstract Numerical simulation of partial differential equations (PDEs) plays a crucial role in predicting the behavior of physical systems and in modern engineering design. However, in order to produce reliable results with a PDE simulator, a human expert must typically ex- pend considerable time and effort in setting up the simulation. Most of this effort is spent in generat- ing the grid, the discretization of the spatial domain which the PDE simulator requires as input. To prop- erly design a grid, the gridder must not only consider the characteristics of the spatial domain, but also the physics of the situation and the peculiarities of the nu- merical simulator. This paper describes an intelligent gridder that is capable of analyzing the topology of the spatial domain and predicting approximate phys- ical behaviors based on the geometry of the spatial domain to automatically generate grids for computa- tional fluid dynamics simulators. Typically gridding programs are given a pcsrtitioning of the spatial do- main to assist the gridder. Our gridder is capable of performing this partitioning. This enables the grid- der to automatically grid spatial domains of arbitrary configurations. Introduction Numerical simulation of physical systems plays a cru- cial role in engineering design. Unfortunately, getting simulation results with acceptable accuracy is a time- consuming and labor-intensive process. Although the amount of computational time needed to execute the numerical code is considerable, it may not be the dom- inant factor. In PDE simulations of physical systems with complicated geometries, the most time consum- ing portions are rather setting up the numerical simula- tion, verifying the correctness of the simulation results, and modifying the setup if the results are not within expect tolerances. Partial differential equation solvers require a grid, a discretization of the spatial regions of interest. Usually in computational fluid dynamics, the spatial regions of interest are the areas of the surface that contact the fluid. The quality of the grid strongly affects the ac- curacy and the convergence properties of the resulting simulation. Generating a proper grid involves reason- Andrew Gelsey Computer Science Department Rutgers University New Brunswick, NJ 08903, USA gelsey@cs.rutgers.edu (908) 932-4869 ing about the geometry of the regions of interest, the physics of the situation and the peculiarities of the nu- merical analysis code. To deal with the complexities of gridding, the current trend in the gridding field is to- ward interactive gridding (Remotique, Hart, & Stokes 1992, Kao & Su 1992). Interactive gridding more read- ily taps into the spatial reasoning abilities of the hu- man user through the use of a graphical interface with a mouse. However, this approach is not acceptable for automated design systems. We are working in the physical domain of fluid dynamics, in particular potential flows modeled by Laplace’s partial differential equation. The potential flow solver we use is PMARC, a product of NASA Ames Research Center. The input PMARC requires is a panelization - a discretization of an object’s wetted surface as a grid of surface patches, where each surface patch is an array of approximately planar quadrilateral panels. This array of panels is represented in PMARC as a matrix of corner points. See Figure 1 for a grid of a yacht automatically generated for PMARC by our gridding program. The yacht in Figure 1 consists of three input com- ponents: an ellipsoid hull, the Star & Strips keel, and the Star & Strips winglet. ’ The wake sheets attached to the rear of the yacht are the vortices shed by the yacht. Discussions on how to attach wakes and how to determine the shape of the wakes are beyond the scope of this paper. The Star 43 Strips winglet attached to the bottom of keel is considered a major innovation in the field of racing yachts, and the success of the Star & Strips was in part due to its winglet. Current au- tomated gridding programs should be but are not able to handle this kind of innovative topological change in design without human assistance. In this paper we de- scribe an automated gridder that is capable of gridding geometries of arbitrary topological configurations. The input to the gridder is expressed in a language we have developed called Boundary Surface Represen- tation (BSR). F g i ure 2 graphically depicts the BSR input for this yacht example. We shall use this yacht ‘The Star & Str+s is the yacht that won the 1987 Amer- ica’s Cup Competition. 1224 Qualitative Reasoning From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Figure 1: Yacht (consisting of three components hull, keel, and winglet) with wake sheets. example throughout this paper. Both BSR and the in- put will be discussed in much more detail later. For now we’ll point out that BSR input consists of two major parts: geometrical and topological. The geomet- rical part represents the detailed features of the yacht, which are the three input surface mappings (shape) in the figure. The topological part contains information on the adjacency of the input surfaces. The adjacency information is represented by dotted lines in the figure. Why is automated gridding hard? Steps to gridding We divide gridding into three steps. The first step is to partition the input surface into griddable surface patches. That is, this step finds the appropriate bound- ary lines (or partitioning lines) for the surface patches. As we’ll see this step is often the most difficult, be- cause it involves significant physical and geometrical reasoning. Step two, for each surface patch, reparumetrize it by defining two families of approximately orthogonal grid lines. A formal definition will be given later when BSR is defined. But, intuitively suppose a surface patch is laying on the zy-plane, then {z = constant, y = constant} is one possible parameterization, and {Z + Y = constant, x - y = constant} is another. The last step is to determine how many grid lines to lay down on each of the surface patches, and in partic- ular where to lay them down. This step corresponds to picking the constants to instantiate the equations in step two. The intersections of these grid lines form corner points of the array of panels, which is the in- put to PMARC. This step we shall call the grid line distribution step. The distribution of grid lines can make grids with the same reparametrization look dif- ferent and may make the numerical simulator behave differently. For example, using the equal-distance dis- tribution scheme, x = i/10, where i = 0,. . . , 10, may make the numerical simulator converge slower than a cosine distribution scheme, x = (1 - cos &/10)/2, where i = 0,. . . , 10. Evaluation criteria Gridding as defined by the three steps above is un- constrained. The ultimate test for a grid is to check how sound the resulting simulation is, and how well it resolves the physical features of the domain. Short of feeding the grid to a simulator, there are ways of checking the goodness of a grid. Through our discussion with hydrodynamicists we have formulated a list of grid evaluation criteria and constraints. On the basis of the geometric properties of the grid, these evaluation criteria attempt to pre- dict the soundness of PMARC’s output. We divide this list into four levels, ranging from constraints that absolutely must be satisfied to heuristic advice based on experiences of our experts. 1. Simple connectedness constraint: surface patches must be simply connected, i.e., no holes. 2. Coverage constraint: patches must not overlap or leave gaps. 3. Planarity criterion: panels must be approximately planar. 4. Heuristic criteria: o following streamlines: grid lines should follow the streamlines of the fluid flowing over the body. e orthogonality: grid lines should intersect at right angles. 0 expansion ratio: the area of the adjacent panels should not increase by more than a fixed ratio. Difficulties of part it ioning Much work has been done on the problem of auto- mated gridding (Thompson, Warsi, & Mastin 1985), and many gridding programs have been developed. However, most of these efforts concentrate on develop- ing new methods of reparametrization and new distri- bution schemes. The choices of which reparametriza- tion method and which distribution scheme to use are usually left to the human expert. Almost no work has been done on automated partitioning. Most of the programs rely exclusively on the human expert to do the partitioning. He is expected to do the partitioning by either writing batch commands, or more recently by using an interactive graphical inter- face. In either case, the partitions created only apply to the one particular problem at hand. More recently, (Schuster 1992) has b een trying to revive batch mode gridding by writing more general batch commands. However, his program is only able to grid a small, fixed set of airplane topologies. One of the fundamental problems with the current gridding programs is that they do not make use of topology. All the topological information has been distilled away by either having the user provide the partitions or by fixing the possible topologies. The programs can only work on individual surface patches. Another problem is that programs have neither the Simulation 1225 Figure 2: BSR input knowledge of physics nor the knowledge of numerical analysis needed to generate grids that will lead to good simulations. One manifestation of the lack of physical knowledge is as follows. A closer examination of the surface area near where the hull and keel meet reveals that the keel actually protrudes into the hull, and the hull has an extra surface area where the keel is. Surfaces given to the gridding program often contain fictional surface areas, areas that should not be gridded. Fictional sur- face areas are useful because they allow the hull and keel to be modified independently while still remaining in contact. However, an automated gridding program must be able to distinguish between the real and fic- tional areas in order to satisfy the coverage constraint. Recall that PMARC represents each patch by a ma- trix of corner points. This type of representation does not allow for holes in patches, i.e., the patches must be simply-connected. If the gridding program has knowl- edge of the underlying numerical analysis program, it would realize that once it removes the fictional surface area from the hull, it must break the hull in half to “cut” out the hole. This cut can be performed in lim- itless ways, but how it is done affects how easily the reparametrization and distribution steps can be per- formed to satisfy the evaluation criteria. In the following sections we present a geometric language, Boundary Surface Representation (BSR), which is capable of representing geometrical informa- tion, topological information as well as associating at- tributes of the physical domain to the geometry. Also, we present a principled method of solving the parti- tioning, reparametrization, and distribution problems based on reasoning about physics of the flow domain. We call this method streamline-based gridding. Boundary Surface Representation(BSR) Surfaces are basically two dimensional objects that reside in three dimensional space. So they are nat- urally represented parametrically as a mapping from parametric space, (u, w) = ([0, . . . , 11, [0, . . . , l]), to 3D Cartesian space, (z, y, z). Our gridding system pro- 12% Qualitative Reasoning vides a mapping facility to represent this shape map- ping, see Figure 2. No assumption is made about what mathematical form the mappings may take. Each map- ping is treated as a “black box”. The advantage of using a black box representation is that it provides greater flexibility by hiding the implementation details from the gridder. In our example, the hull is defined using algebraic formulae, and the keel and winglet are defined using B-spline surfaces. This mapping facility is not limited to defining shapes. Other geometric and physical values may also be defined. For example, the outward normals of a surface may be defined as a normal mapping from the parametric space, (u, v), to 3D vector space. Then in turn based on the shape and normal mappings, our gridding program can approximate the stream vectors on the surfaces as a ~IOUJ mapping by projecting the free stream vector, (1, 0, 0), onto the surface. The free stream vector is the direction the water would flow if the yacht were not present. Notice the boundaries of each surface are represented explicitly by directed edges, arcs. The arcs in turn are bounded by nodes. Explicit representation of the boundary is useful in that it allows for implicit rep- resentation of surfaces. That is, a closed sequence of arcs in parametric space can be used to denote the por- tion of the surface it encloses. The program adopts the counter-clockwise rule. A counter-clockwise, closed se- quence of arcs denotes the area bound by the arcs. A clockwise, closed sequence of arcs denotes the area out- side of the arcs. This implies the area on the “left-hand side” of an arc is “inside,” and area on the “right-hand side” is “outside.” Arcs are also useful in expressing topological infor- mation. In our notation two arcs are connected by a dotted line if they are the same line when mapped us- ing shape into zyz-space, even though they are distinct in parametric space. For example, in Figure 2 the keel parametric arcs h (ukeer = 0) and f (ukeer = 1) are connected by a dotted line, because both of these arcs map to the trailing edge of the keel. Thus in zyz-space it is possible to travel just in the direction of increasing ukeel and end up at your starting point. This dotted line together with the dotted line connecting arcs d ( Ukeel = [O,. . .,0.5]) and e (Ukeer = [0.5,. . ., 11) im- plies the topology of the keel is similar to that of a cylinder with one end closed or a “cup.” Notice that the hull parametric arcs b (uhurl = 1) and d (uhuli = 0) are connected to themselves. This is used to show that arcs b and d are degenerate, i.e., they each map to one point in zyz-space. The arc d maps into the trailing point of the hull; the arc b maps into the leading point of the hull. Also, notice each of the arcs on the winglet is con- nected to some other arc. This means that in zyz-space the winglet surface does not have any boundaries. Of the three components the winglet is the only one that actually encloses some finite volume in zyz-space. BSR provides a set of surface patch manipulation operations, such as intersection of surfaces, and divi- sion of patches into sub-patches. Figure 4 depicts the patches after the partitioning step. Reparametrization and distribution operations also are supported, see Fig- ure 5. Now, we can formally define reparametrization as a mapping from a unit square, defined in a new parametric space, say (s, t), to a surface patch in (u, V) parametric space. Streamline-based reasoning The solution to Laplace’s equation depends neither on the current state of the flow nor on time, so the ge- ometry of the object determines the solution. Since streamlines are key characteristics of the solution, an- alyzing how streamlines interact with geometry pro- vides key insights to qualitative behaviors of Laplace’s equation. These insights enable us to determine the topology of streamlines. In turn this topology provides natural boundaries for patches in grids. The most immediate reasoning problem we en- counter in streamline-based reasoning is how to get the initial set of streamlines, since we have not yet run PMARC to generate the solution from which stream- lines are extracted. We have experimented with var- ious methods of predicting the streamlines a priori. However, we have found the simple projection of the free stream vector onto the body surface to be a good approximation of the true streamlines. This the flow mapping defined earlier. Object classification Analyzing the pattern of streamlines on the surface of different objects, we define two object classes. This first is the source/sink node class. Streamlines on ob- jects from this class all originate from one point on the surface, the source node, and all flow to and terminate at another point on the surface, the sink node. Spheres, ellipsoids and other simple bodies of revolution are ob- jects of this class. These objects have axial-symmetry, so there can only be one source node and one sink node. The second is the source/sink line class. This class is like the previous class, except that the streamlines appear to originate and terminate at lines instead of nodes. For instance, the leading edge of a keel is source line, and the trailing edge is Sink line. All the stream- lines flow from the leading edge to the trailing edge. Any wing shaped object belongs to this class. Using only these two object classes, one can al- ready construct complex, geometric objects, such as the yacht in this paper. The yacht consists of a source/sink node object (hull), and two source/sink line objects (keel and winglet). New classes can always be defined as the need arises. Application to gridding Based on the following-streamline heuristic for grid- ding, it is reasonable to grid a source/sink node object as a single surface patch, since all the streamlines are flowing in one direction, from the source node to the sink node. A source/sink line object should be grid- ded as two surface patches with the source line and sink line acting as partitioning lines. Although the stream- lines still flow from the source line to the sink line, the streamlines take two different routes. For example, one set of streamlines flows to the sink from the right side of the keel (u > 0.5), and the other set flows from the left side (u < 0.5). The source/sink lines separate these two flow regions. Streamlines are also useful in reparametrization. Streamlines can be defined as one family of grid lines. Lines orthogonal to the the streamlines can be defined as the other family. For example, on a sphere these two families correspond to the two spherical coordinate di- rections, 0 and 4, where x = cos 8, y = sin 4 cos 8, z = sin 4 sin 0. Streamlines have constant 6 and the orthog- onal lines have constant 4. The sources and sinks provide guidelines on how to distribute the grid lines. The key to distributing grid lines is to highlight the physical features of the domain. That is, put more grid lines in regions where interest- ing physical changes occur. In the flow domain, the most interesting change is the change in direction and velocity of the flow. This change typically occurs most dramatically around the sources and sinks. So, the grid lines should be distributed more densely around them. The above discussion deals with idealized objects. In the yacht example, there is a keel attached to the hull, and a winglet attached to the keel. The following sections show how to deal with the topological changes in these idealized objects by going through the three gridding steps in more detail. Partitioning We break the partitioning step into three sub-steps: 1) Determine the surface partitioning lines, 2) Partition surfaces into surface patches, and 3) Determine real surfaces patches. Simulation 1227 -....---.- b' i ,-....-....--.- ,.- -.-. m-w.---. i L i -q -ji -+ : I i 1 i i I -.-...--.-.-.-.-.- I i .-.--.-._._.-. --I i-.--.-.-.-.-.-.-.-i =) ;.- .-Y._..-. - I 1 f i‘ --.--. ----. I .-m-V """"T i ! i i a-.---.-- .-.-.-._ i ( 1 i i-".. II Ii .i ! -.--.-.- .-.-.-.-I Figure 3: Partition lines: a) intersection lines, b) streamlines to “cut” holes out, and c) source/sink lines. part it ioning lines The partitioning lines that we use can be divided into three categories: surface intersection lines, streamlines, and source/sink lines. Intersection lines provide the boundary between real and fictional surface areas, so they must be present. See Figure 3a for examples. Notice that the hull-keel intersection line introduces a hole on the hull surface. This hole needs to be cut out, because of the simpZy-connected constraint. Using streamline-based reasoning, the logical way to “cutn out the hole is by cutting along streamlines. We search for a leading point and-a trailing point along the in- tersection. I?rom the leading point-we trace astream- line backward along the hull surface. From the trailing point we trace a streamline forward along the hull sur- face. These two streamlines are shown in Figure 3b. Source and sink lines are definitely needed, but all the sink lines turn out to be redundant. The source lines are shown in Figure 3c. Notice that source/sink nodes in xyz-space may become source/sink lines in uw parametrii space, as in the hull. . part it ion the surface patches We shall not go into detail on how BSR accomplishes the actual partitioning. Basically BSR 1) gathers all the partition lines of a particular surface, 2) intersects the partition lines with each other and with the bound- ary lines of the surface, 3) breaks all the lines at in- tersections, 4) forms a wire frame from the broken lines, and 5) forms the surface patches based on the I wire frame. The surface patches after partitioning are shown in Figure 4. BSR updates the topological in- formation after the partitioning process. The shaded surface patches are fictional and will not be gridded. determine the real surface patches Real and fictional surface patches can be distinguished by reasoning using the outward normal mappings, the counter-clockwise rule, and intersection lines. For ex- ample, the surface patch Keell, Figure 5, has inter- section lines in common with the hull surface (arc 6) i : Figure 4: Surface patches after partitioning. Dotted lines across uv-space are not drawn to reduce clutter. Omitted dotted lines would show Keel1 connected to Hulll, Wing1 and Wing3, and would show Keel2 con- nected to Hu112, Wing2 and Wing3. and the winglet surface (arcs 2 and 3). The hull out- ward normaIs along the hull-keel intersection generally point in the negative z-direction. The inward direction of arc 6 as defined by the counter-clockwise rule is in the negative l&eel direction, which corresponds to the negative z-direction in xyz-space. This implies that Keel1 is outside of the hull. Similar reasoning using arcs 2 and 3 shows Keel1 is outside of the winglet. Since Keel1 is on the outside of all its neighbor sur- faces, KeeZl is a real surface patch. If a surface patch is on the inside of one or more of its neighbors, then it is a fictional patch. Reparametrization Our gridding program uses two reparametrization methods, but here we only discuss transfinite interpola- tion. Given a quadrilateral, transfinite interpolation is a well known mathematical technique that maps a unit square on to a quadrilateral by interpolating against opposite edges of that quadrilateral. This method re- quires the surface patch to be reparametrized to have exactly four sides. But, surface patches tend to have more than four boundary edges. In order to use transfi- nite interpolation, we describe a heuristic, streamlined- based method of grouping the boundary arcs of the surface patches into four groups. See Figure 5. We can classify each arc as either parallel or orthog- onal with respect to the streamlines. For example, the patch Keel1 is bounded by six arcs. Arc 1 is a sink line. Arc 5 is a source line. So, by definition they are orthogonal to the streamlines. Arc 4 is a boundary arc from the original input surface. Arcs 2, 3 and G are in- tersection lines. These four arcs are neither completely parallel nor completely orthogonal to the streamlines. But, by sampling different segments of these arcs we can approximately classify arcs 2, 4 and 6 as parallel, and arc 3 as orthogonal. So, six groups are formed, {(l), (2), (3), (4), (5), (6)). But, unlike the graphical depiction in Figure 5, arc 3 is very short when com- pared to its neighbors, arc 2 and 4. So, heuristically merging arc 3 with its neighbors, we get four groups, w, (27 3,417 (5)7 WI. Our grouping method works well, because the 1228 Qualitative Reasoning u keel Figure 5: Reparametrization and Distribution boundary arcs of the surfaces patches tend to be par- titioning lines: intersection lines, streamlines, and source/sink lines. Classification of streamlines and source/sink lines are straightforward. In practice in- tersection lines tend always to be parallel, because an orthogonal intersection line causes too much drag, and would not be used in properly designed yachts. This heuristic method may fail to group the bound- ary arcs into four groups. Failure indicates that the geometry of the surface patch is too complicated, and additional partitioning lines may be needed. So far we have not encountered such a case. Distribution According to streamline-based reasoning, grid lines should be concentrated more densely around sources and sinks. Sources and sinks tend to be at the ends of the surface patches (in Figure 5 arc 1 and arc 5) in our streamline-based gridding method. So, compli- cated distribution schemes usually are not needed. We have experimented with cosine and hyperbokic tangent schemes, which distribute more grid lines at the ends and yet distribute them smoothly enough as not to violate the expansion ratio constraint. Both schemes work well, but if many grid lines are laid out, cosine tends to place grid lines too densely at the ends. This leads to numerical truncation error. Beside resolving physical features, distribution must also resolve geometric features. For example, one Skeel = constant grid line must be laid out at the intersection of arc 2 and arc 3, and another one grid line at the intersection of arc 3 and arc 4. Grid lines that must be laid out are shown as heavy, dotted lines in Figure 5. The node at the intersection of arc 3 and arc 4 touches three surface patches, Keell, KeeZ2, and Wing3. Not laying a grid line at that node would cre- ate a gap there so the three patches would not meet. Computational Results Our gridding algorithms have been implemented in a working program. Figure 6 shows the results of a con- vergence study in which our gridding program gener- ated a series of grids for PMARC. A convergence study is a series of simulations using grids with the same partitioning and reparametrization, but with increas- ingly denser grid lines. As the grid becomes denser and grid spacing decreases, output quantities computed by PMARC should converge to their correct values. The output quantity we are most interested in is effective draft, a measure of the efficiency of a sailing yacht’s keel. Figure 7 shows how effective draft converges as grid spacing is reduced in our convergence study. Other values in Figure 6 can also be used as checks on the soundness of the simulation. For example, the maximum Cp (pressure coefficient) should approach 1 as the grid is refined, and the minimum Cp should not become too negative, as very large negative values usu- ally indicate flaws in the grid. (Gelsey 1992) discusses automated evaluation of simulation output quality. Panels 100 362 1378 5460 Effective Lift Drag 2.014 0.198 -I- 2.081 0.242 2.202 0.283 2.230 0.308 Draft 1.805 1.688 1.651 1.604 Figure 6: Convergen Draft min Cp -1.655 -1.126 -1.798 -2.632 e study 1.8 1.75 1.7 1.65 1.6 1.55 0 12 3 4 5 6 7 8 Grid Spacing Figure 7: Convergence as spacing is reduced Future Work This work can be extended in various directions. One is to add feedback and local refinement capabilities to the gridder. The streamlines predicted by PMARC may be fed back into the gridder to improve the grid. Also, the gridder can be extended to detect and correct local flaws in the grid based on intermediate values, such as the coefficient of pressure. Another direction is to ex- tend the gridder to other physical domains where PDE simulators are needed. We believe our methodology of identifying key physical features of the domain and of reasoning about how they interact with the geometry is quite general and extensible. For example, in the ingot casting problem of heat transfer the temperature profile seems to be the key feature (ky Ringo Ling, Steinberg, & Jaluria 1993). Temperature profiles tend to change the fastest near sharp corners and in ap- pendages (regions where the surface area to volume Simulation 1229 References Chao, Y. C., and Liu, S. S. 1991. Streamline adaptive grid method for complex flow computation. Numeri- cal Heat Transfer, Part B 20:145-168. Chung, S. G.; Kuwahara, K.; and Richmond, 0. 1993. Streamline-coordinate finite-difference method for hot metal deformations. Journal of Computational Physics 108:1-7. Dann&hoffer, J. F. 1992. Automatic block- structured grid generation - progress and challenge. In Kant, E.; Keller, R.; and Steinberg, S., eds., AAAI Fall Symposium Series: InteZZigent Scientific Compu- tation, 28-32. ratio is large). This suggests that isotherms should be useful as grid lines, and they should be distributed more densely near corners and appendages. Related Work Using streamlines is a natural idea. (Chung, Kuwa- hara, & Richmond 1993) defines a 2D finite-difference method based on streamline-coordinates, instead of Cartesian coordinates. (Chao & Liu 1991) applies streamline-based gridding to 2D flow problems consist- ing of a single patch. Many geometric modeling sys- tems have been developed, such as Alpha1 by (Riesen- feld 1981) and SHAPES by (Sinha 1992). (Requicha 1980) provides a good survey. Most of these systems are intended for modeling mechanical components, and provide little support for gridding, like representation of parametric space objects for reparametrization and distribution, and algorithms to manipulate these ob- jects. Previous AI work in gridding includes (Dannen- hoffer 1992), and (Santhanam et al. 1992). In the 2D planar flow domain, Dannenhoffer’s program is able to do partitioning by merging tempkates of previously- solved cases. So, the set of shapes it can handle is lim- ited. Santhanam identifies several key parameters to modify and improve grids in 1D Euler domain. (Gelsey 1994) describes automated setup of numerical simula- tions involving ordinary differential equations. Conclusion Numerical simulation of partial differential equations is a powerful tool for engineering design. However, human expertise and spatial reasoning abilities are needed in order to form the spatial grids which PDE solvers require as input. We have developed a geo- metric modeling language, BSR, capable of expressing geometrical, topological, and physical aspects of the gridding problem, and we have used BSR as a basis for an intelligent automated system for generating the grids required for numerical simulation. The grid gen- eration process involves analyzing the topology of the spatial domain, predicting and classifying the interac- tions of physics and geometry, and reasoning about the peculiarities of the numerical simulator. Acknowledgments The research was done in consultation with Rut- gers Computer Science Dept. faculty member Gerard Richter. We worked with hydrodynamicists Martin Fritts and Nils Salvesen of Science Applications In- ternational Corp., and John Letcher of Aero-Hydro Inc. Our research benefited significantly from inter- action with the members of the Rutgers AI/Design group. Thanks to Ringo Ling, Steven Norton, and Mark Schwabacher for proofreading and commenting on the paper. This research was partially supported by NSF grant CCR-9209793, ARPA/NASA grant NAG2- 645, and ARPA contract ARPA-DAST 63-93-C-0064. Gelsey, A. 1992. Modeling and simulation for au- tomated yacht design. In AAAI Fall Symposium on Design from Physical Principles, 44-49. Gelsey, A. 1994. Automated reasoning about ma- chines. Artificial Intelligence. to appear. Kao, T. J., and Su, T. Y. 1992. An interactive multi- block grid generation system. In Smith, R. E., ed., Software Systems for Surface Modeling and Grid Gen- eration, number 3143 in NASA Conference Publica- tion, 333-345. Ling, S. R.; Steinberg, L.; and Jaluria, Y. 1993. MSG: A computer system for auotmated modeling of heat transfer. AI EDAM 7(4):287-300. Remotique, M. G.; Hart, E. T.; and Stokes, M. L. 1992. EAGLEView: A surface and grid generation program and its data management. In Smith, R. E., ed., Software Systems for Surface Modeling and Grid Generation, number 3143 in NASA Conference Pub- lication, 243-25 1. Requicha, A. A. G. 1980. Representations for rigid solids: Theory, methods, and systems. Computing Surveys 12(4):437-464. Riesenfeld, R. F. 1981. Using the oslo algorithm as a basis for CAD/CAM geometric modeling. In Proc. NCGA National Conf., 345-356. Santhanam, T.; Browne, J.; Kallinderis, J.; and Mi- ranker, D. 1992. A knowledge based approach to mesh optimization in CFD domain: 1D Euler code exam- ple. In Kant, E.; Keller, R.; and Steinberg, S., eds., AAAI Fall Symposium Series: Intelligent Scientific Computation, 115-l 18. Schuster, D. M. 1992. Batch mode grid generation: An endangered species ? In Smith, R. E., ed., Software Systems for Surface Modeling and Grid Generation, number 3143 in NASA Conference Publication, 487- 500. Sinha, P. 1992. Mixed dimensional objects in geomet- ric modeling. In New TechnoZogies in CAD/CAM. Thompson, J. F.; Warsi, Z. U. A.; and Mastin, C. W. 1985. Numerical grid generation : foundations and appZications. North-Holland, Amsterdam. 1230 Qualitative Reasoning | 1994 | 257 |
1,605 | Estimating Reaction Plan Size Marcel Schoppers Robotics Research Harvesting, PO Box 2111, Redwood City, CA 94063 Abstract The Shannon/Ginsberg circuit size estimate, by assum- ing independence of Boolean inputs, is not usable as a plan size estimate. By re-estimating circuit size as a function of the number of combinations w of Boolean inputs, I show that a reaction plan over w world states should grow as O(w/log w), on average. However, in a Blocks World containing N blocks and w z N N world states, actual Universal Plans grow only as O(N3). This difference is shown to be attributable to the Uni- versal Plans’ use of dynamically bound object vari- ables. Finally I obtain the general domain-independent result that for a domain containing w world states, the expected size of a reaction plan with variables is ww/10g 4 ll~og~P+(wJ)) where p is the number of preconditions per operator, v is the number of those preconditions that introduce an unbound variable, and b is the number of possible bindings per variable. The exponent is < 1 and allows this formula to predict plan size reductions of many orders of magnitude. Review of Plan Size Arguments Reaction plans are a relatively new representation for controlling embedded agents. As argued in (Schoppers 1989b), they mitigate the cost of run-time replanning by functioning as caches of responses to possible situa- tions, thus trading time against space. Predictably, the increased space requirements have led to criticisms that for domains of any “reasonable size”, a reaction plan could only prescribe reactions to arbitrary situations by being a “very large” plan indeed. This argument was made most forcibly by (Ginsberg 1989), who formal- ized domain size as the number of atomic propositions (or ground literals) in the vocabulary of the domain’s representation, formalized plan size as the number of gates in a hardware implementation of a reaction plan, and employed a version of (Shannon 1949)‘s circuit size estimate to argue that the vast majority of reaction plans for domains having n ground literals would re- quire 0(2n/4n) gates for their hardware implementa- tion, thus implying that reaction plans would in general be too large to be practical - unless they contained a reaction that invoked a planner, in which case a reason- able plan size would be obtainable only if the reaction plan “passed the buck” to planning nearly all the time (so why have the reaction plan at all). Ginsberg’s arguments were accompanied by two re- buttals. (Chapman 1989) exhibited a reaction plan of fixed size that was capable of building block tow- ers of arbitrary height (without resorting to planning). (Schoppers 198913) argued from common sense: Gins- berg’s arguments imply also that production systems’ are “impractical in general” because needing an ex- ponential number of rules. Yet the AI field deems the hand-building of production systems a worth-while effort; how then can the automatic building of sim- ilar functionality be deemed impractical? Although those rebuttals should have cast some doubt on Gins- berg’s argument, many subsequent papers have cited him as proving conclusively that reaction plans are “im- practical in general” (Doyle & Wellman 1990, p.34) (Ingrand & Georgeff 1990, p.284) (Kaelbling 1990a, p.437) (Drummond & Bresina 1990) (Christensen 1990, p.1006) (Godefroid & Kabanza 1991, p.640) (Chrisman & Simmons 1991, p.761) (Bonasso 1991, p.1225) (Lyons & Hendriks 1992, p.154). Before proceeding with the main argument, we must clarify the meaning of “all possible situations” as the range of situations a reaction plan should have reason- able responses for. It might mean “all physically pos- sible situations” but then, if one cannot expect SIPE (for example) to build a plan that pushes a meddle- some baby out of the way when SIPE’s domain model does not distinguish meddlesome babies, neither can one fault reaction plans for having the same limitation. If one replies that domain models must be dynamically refinable and that SIPE, given a refined model that includes meddlesome babies, could simply build new plans that deal with such babies, then similarly, both (Kaelbling 1988) and (Schoppers 1989a) describe how to automatically (re)construct reaction plans from do- rIn a production system the choice of rule to be fired amounts to a reaction to the contents of the system’s work- ing memory. If the rule firing engine carries any “state” from one firing to the next, that state exists solely for efficiency purposes, and makes no difference to the rule/reaction selected. 1238 Robotics From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. main models. From this point, the only fair arguments about reaction plan size are those that hold even under fixed domain models. Said differently, fair size argu- ments will hold even when “all possible situations” is reduced to “all situations distinguishable within a given domain model.” This paper isolates a false assumption that invalidates Shannon’s circuit size estimate as a predictor of reaction plan size; develops an improved predictor of reaction plan size; exhibits a small reaction plan that defies even the improved predictor; mathematically attributes the unexpectedly small plan size to the plan’s use of dynamically bound ob- ject variables; finds an expression for the expected size of reaction plans containing dynamically bound object variables; tests the expression on reaction plans for block stack- ing, and gets results that are many orders of magni- tude better than previous estimates. Importance of the Independence Assumption The circuit size argument proceeds as follows. 1) There are 22” Boolean functions of n Boolean variables; 2) With g = 2n/4n gates it is possible to build at most 2w 7 n2g (<< 2”“) Boolea n functions (Shannon 1949; Ginsberg 1989); h ence 3) The vast majority of Boolean functions on n inputs require more than 2n/4n to gates to implement them. This argument presupposes (and Ginsberg explicitly requires) that the n Boolean inputs are independent. If they are not independent, then there are < 2” possible combinations of input values, hence there are << 22n Boolean functions on those n inputs, hence 2n/4n gates may be more than enough, hence the argument collapses. It follows immediately that the circuit size argument cannot be used to predict reaction plan size unless the independence assumption holds of the ground literals being tested by the plan. There are not many planning domains in which the independence assumption is satisfied. In particular, flu- ents give rise to as many ground literals as the fluent has possible values, but those ground literals are not inde- pendent. To see how quickly fluents invalidate size esti- mates, observe that in an N-Blocks World, each block can sit on N things, thus generating at least N2 ground literals, and leading to the naive conclusions that the number of world states is 2N2 and the number of gates needed is > 2N2/4N 2. With N = 10 this predicts 103’ world states and > 3x 1O27 gates when in fact there are only 6 x lo7 world states (see Derivation 1 of the Ap- pendix). This huge discrepancy arises solely from the fact that what’s-on(Block) and what’s-under(Block) are fluents. Hence, we can now conclude that the Shan- non/Ginsberg argument works only in domains that contain no fluents. Common examples of fluents include the amount of fuel remaining, the distance travelled, the positions of things, and the current time. Since the world is full of fluents, the circuit size estimate is generally worthless as an estimate of plan size. We can however salvage something of the circuit size estimate as follows: e There are 2” Boolean functions on w combinations of Boolean values. e With g binary gates it is possible to build at most (16(g+n+2)2)g B oo 1 ean functions on n inputs (Shan- non 1949; Ginsberg 1989). e If we happen to set g = w/(2 log,w) and use n << g we can build circuits for at most P4W2 l%2w)2)g = (g$;2y (2 > log,2w 2g 2h2w + l)(Wll%,W) = (log2w)Q = (log,w)(“~‘“g2w) 2w+wog24 = (~og2w)(w/log2w) = 2w x w”g2w) w lb2w Boolean functions, which provides for less than half of the 2w possible functions whenever w > 7. Consequently, a planning domain containing w >_ 7 world states will (on average) require a reaction plan of size > w/(210g2w). The Appendix (Derivation 2) shows that in the N- Blocks World w is Q( NN), so our improved plan size estimate is 0 (N N-1/ log N). This estimate is shown in Table 1 under the heading “improved number of gates”. Also shown, under the heading “size of random parti- tion,” is a size estimate based on the expected number of equivalence classes in a randomly selected partition on w world states (see Derivation 3). This estimate too is O(w/log w) (Haigh 1972). These estimates of plan size are already much less devastating than Ginsberg’s, but might still-be interpreted as damaging to the (fully- explicit) reaction plans enterprise. However , the next section ‘undermines the circuits analogy completely. Importance of Object Variables I begin by calculating the actual size of a Universal Plan needed to build a tower of N blocks from any initial configuration of N blocks. Two action descriptions are required for a Blocks World that does not model the robot arm: puton(X,Y) -- on(X,Y> <+ clear(X), clear(Y). putoff (Y,X> -- clear(X), ontable <+ on(Y,X> ? clear(Y). The action name comes first, followed by “--“, then the action’s postconditions, then “<+“, and finally the action’s preconditions. The preconditions preceding a “?” are filters or qualifiers on the applicability of the Reactive Control 1239 blocks number of world states 3 13 4 73 5 501 6 4051 7 37633 8 394353 9 4596553 10 5.89 x lo7 15 6.56~10~~ 20 3.28~10~' 25 5.10x 1o27 number of gates number of gates random partition UP size UP size UP size w/o vars w vars w vars 14 3.7 6.4 10 9 6.1 1024 12.2 23 35 22 9.6 3.36x lo5 58.2 107 192 45 16.0 4.77x108 352 629 1393 81 26.0 2.87~10~~ 2576 4480 11834 133 40.8 7.21x10-' 22078 37450 112635 204 62.5 7.46 x102r 216136 359000 1181120 297 94.0 3.17x1o27 0.22x lo7 o.39x107 1.35x107 415 140 5.99 x 1o64 1.48~10~~ 2.30~10~~ 8.03~10~~ 1485 958 1.61~10~~~ 0.50~10~' 0.75~10~' 2.09x101' 3630 6324 5.57 x 1o184 0.58x 1O26 0.85 x 1O26 1.72 x 1O26 7225 41581 Table I: Sizes of Blocks World Reaction Plans. action: If they are false, the action does not apply, and its other preconditions should not be achieved. The preconditions that come after a “?” should be achieved if they are false and the action applies. When there is no explicit “?” there is no applicability filter. These action descriptions, when fed into a Univer- sal Plans planner, cause the planner to autonomously discover the goal conflict associated with the Sussman Anomaly problem, and to resolve that goal conflict by generating “confinement” rules. How that is done for the S-blocks world is described in (Schoppers 1989a). The most general confinement rule is on(Y,Z) < above(X,Y) <++ labove(Z,X) (where the above(X) Y) relation is defined as the tran- sitive closure of the on(X,Y> relation). This rule informs the Universal Plans interpreter that when- ever there exist bindings of X, Y and Z such that on(Y, Z)Aabove(X,Y) is implied by the current goals and on(Y,Z> is false, then we must first make iabove (Z, X) true, after which the two goals can be achieved in the given order. The above three rules are sufficient to drive a Uni- versal Plans interpreter. They may also be fed into a Universal Plans compiler, to produce a fully ex- plicit Universal Plan for a given number of blocks, as follows. For convenience, let blocks be designated by numbers rather than letters, and consider a con- junctive goal of the form on( i ,2) A on(2,3) A.. . A on(N-1 ,N) . The confinement rule reorders the con- juncts as on(N-1,N) < . . . < on(2,3) < on(l,2) and further requires that the achievement of each con- junct should be “confined” to circumstances in which each block yet to be placed is not under the tower being built. Thus, the compiled Universal Plan would be a decision tree that has the confinement rule built in as follows (.I, X, Y and Z are block numbers): 1240 Robotics subplan TWR-READY( J) { J52? t: - finish top 2 bloclcs - on(1,2) ? t: NO-OP f: ACHIEVE-ON( 1,2) f: - tower is ready from base to J - on(J-1,J) ? t: - J-l is in place too, go up - TWR-READY( J-l) f: - J-l not in place, unbury 1.. J-2 - crl-ready( J-2, J-l, J) ? t: crl-ready( J-3, J-l, J) ? . t: . . . . t: crl-ready(l,J-1,J) ? t: - not burying l..J-2 - ACHIEVE-ON( J-l, J) - unbury each of 1.. J-2 - f: ACHIEVE-NOT-ABOVE( J,l) . . f: :CiIIEVE-NOT-ABOVE( J ~-3) I f: ACHIEVE-NOT-ABOVE( J, J-la) condition crl-ready(X,Y,Z) { on(W) - confinement not needed - or not above(Z,X) - confinement achieved - 1 subplan ACHIEVE-NOT-ABOVE( Z,X) 1 ACHIEVE-CLEAR(X) subplan ACHIEVE-CLEAR(X) { NEW VARY; Y := the-block-on X; clear(Y) ? t: PUTOFF(Y,X) f: ACHIEVE-CLEAR(Y) 1 subplan ACHIEVE-ON(X,Y) { clear(X) ? t: clear(Y) ? t: PUTON(X,Y) f: ACHIEVE-CLEAR(Y) f: ACHIEVE-CLEAR(X) 1 An important point: while above (2, X) is a relatively complex test whose presence might allow an unfair size reduction, it turns out to be dispensible: this plan would work even if NOT above (Z, X) was replaced with clear(X). Observe that the plan is encoded as a few functions which invoke each other recursively; the Summary sec- tion comments further. For now we treat the above as macros and pretend that they generate a monolithic Universal Plan. The size of this plan is calculated in the Appendix (Derivation 4), and comes out to be (N-1)3 + N for N blocks. This size is shown in Table 1 under the heading “actual UP size with vars”. Let us put this size in context. The Shan- non/Ginsberg circuit size estimate was O(2N2/N2). My improvement thereon, allowing for dependence among literals, was Q(NN-‘/ log N) (taking u/ M NN from Derivation 2). The actual plan size is 0( N3). I claim that the actual Universal Plan is so much smaller than the predicted sizes because it uses vari- ables to refer to “whatever block is on top of the block to be moved”. To verify this, Derivation 5 calculates how big the plan would have been if block-variables had been disallowed, and comes out with the sizes shown in Table 1 under the heading “actual UP size with- out vars”. Observe that replacing block-variables with block-constants makes the plan larger than both my improved circuit size estimate and the partition size estimate. Consequently it is safe to say that the re- markably small size of the Universal Plan with vari- ables can be completely attributed to the utility of the block-variables. Expected Size of Plans Containing Variables In this section I obtain a general domain-independent result: the size of a reaction plan containing variables as a function of the size of an equivalent plan without variables. Throughout, the size of a plan is equated with the number of leaves of the equivalent binary de- cision tree (which is one greater than the number of decision nodes). The expected size of the decision tree is calculated using a recurrence relation on a number of construction operations r, where each operation adds an action operator/schema instance to the tree. Let the “average” operator instance have p(> 1) pre- conditions, of which ~(2 0,s p) contain exactly one unbound variable (other preconditions containing none) and let all unbound variables range over b( > 1) possible bindings. For simplicity we assume that the subplans being used to achieve each of a given operator instance’s preconditions all have the same size, and conceptually we assemble the decision tree from its leaf nodes toward its root. Then the expected size of the decision tree is given by s&9 = 1 psv+ 1) + : ; ‘, ; ; because for each tested precondition (with or without variables) a false outcome leads to the subplan of size &(r-1) for achieving the precondition, and a true out- come leads to testing the next precondition, until all p preconditions come out true; then the last 1 is for exe- cuting the operator instance’s primitive action. Thus, svw = I r:p=l (pr+l - l)/(p- I) : p > 1 Now suppose that the w variables in the average op- erator’s preconditions can not be bound dynamically. Then the decision tree must explicitly test each pos- sible binding to see if it matches the actual situation. Figure 1 shows an example from the Blocks World: the on(X, a) test, applied when block towers are disman- tled, expands into one case in which a is already clear (no binding for X) and multiple cases in which a is un- der one of a number of possible blocks, with each block now requiring a separate subplan for its removal. on(K es (move a) (remove X) . . . on(xb,a)? A no yes (move a) (remove xb) Figure 1: Plan Expansion to Eliminate Variables. Accordingly, the size of an equivalent decision tree without variables is s(r) = i l:r=O {w b + (p-v)} S(r-1) + 1 : r > 0 (wherein S has no subscript). Writing the term in braces as K and simplifying: Reactive Control 1241 Since K: = 1 requires both l/b 5 p 5 1 and o = (l- p)/(b-1), we ignore this case in what follows. If the reaction plan without variables should distin- guish S classes of world states, the appropriate number of tree construction operations is r = log,{(/,+l)S + 1) - 1 (K > 1). Using this same number of construction operations build the equivalent decision tree with variables: to s, { log,{(+l)S + 1) 1 - : p = 1, K > 1 = (pm2wP+13 - l)/(p - 1) : p > 1, K > 1 The case p = 1 (one precondition per operator) reveals clearly that variables can reduce a reaction plan’s size to the logarithm of of its variable-free magnitude. For the case p > 1 we use log,a: = logpx/logpK: to simplify: s zJ= {(+l)S+ l}1’10gp6 - 1 : p > _I K; > ~ P-1 ? Let us check this last formula numerically. For S we use the known sizes of Universal Plans without vari- ables. (In other d omains, estimate 20, then estimate S from SSMew-l, see Derivation 3.) Assuming that the Universal Plan consists of equal numbers of the put on and putof f operators shown in Section 3, we find p = 1.5 and v = 0.5, and we set b = N - 1, so K = (N + 1)/2. Th e resulting plan size estimates are shown in Table 1 under “est. UP size with vars”. The results reveal that our general formula is inaccurate, under-estimating for small N and over-estimating for large N. Indeed, a little algebra (with w x N0.8N, S =:‘2w/log,w, and l/log,K: --+ logNp) shows that S, is O(P’.‘~) and hence remains exponential, where the actual plan grows as N 3. Nevertheless, our formula is clearly a very large improvement on previous plan size estimates. It is worth noting that, using the values of p and v just given, the the exponent simplifies to 0.585/log2{(N+1)/2}. When N = 25 this is M 0.158 and is responsible for re- ducing the estimated plan size from 1O26 to 104. While the exact reduction clearly depends on the values of p, v and b being used, the example demonstrates the power of a fractional exponent and promises similar ef- fectiveness in other domains, since the general form of the exponent is domain-independent. Summary This paper has demonstrated that Shannon’s circuit size ‘estimate cannot be used as an estimate of reac- tion plan size, for two reasons. First, Shannon’s circuit size estimate relies on an assumption that the inputs to the circuit are independent. The penalty for failing to observe the independence assumption is a massive over-estimate; the reward for observing it is the realiza- tion that virtually all planning domains contain fluents, which falsify the assumption. Second, most approaches to building reaction plans allow the plans to contain variables that are bound at execution time - a feature for which the circuit size estimate has no analog. To drive the point home in a constructive way, I showed that the small size of a Universal Plan for Blocks Worlds was completely accounted for by the presence of dynamically bound variables in the plan, and found that in any domain, the expected size of reaction plans containing variables was 0 ((w/log w) l’logAp+(bl I’)), where w is the number of world states and the ex- ponent encodes the power of dynamically bound vari- ables. The new formula was empirically tested on Blocks World plan sizes and improved on previous esti- mates by many, many orders of magnitude. More gen- erally, the new formula’s fractional exponent was shown to be very effective indeed at keeping plan size under control. (Whether the new formula accurately predicts actual plan sizes is less important than the fact that the formula is based on domain-independent considerations and shows variables to be very effective.) The fully explicit block-stacking circuits produced by other approaches will be even smaller than the sizes es- timated for fully explicit Universal Plan. Those sav- ings are generally obtained by one of two means: (1) the hand-coded “plans” may be iterative because they are built by hand, whereas Universal Plans are recur- sive because they are built automatically; (2) the hand- coded plans may use internal data (“state bits”) to con- trol reaction plan execution, whereas the Universal Plan analyzed above was assumed to be completely sensor- driven. Finally, bear in mind that reaction plans are usu- ally not fully explicit. The Universal Plans interpreter, given just the three rules required for block stacking (see Section 3), can back-chain recursively (without searching) to dynamically construct exactly the same decision sequence as the plan analyzed above. The PRS (Georgeff et al 1987) and RAPS (Firby 1987) inter- preters similarly back-chain recursively to dynamically instantiate arbitrarily large plans implicit in a small number of “knowledge sources”. The GAPPS compiler (Kaelbling & Rosenschein 1990b, set 3.3.2), when made part of a situated automaton, could dynamically in- stantiate only the relevant parts of GAPPS programs. When fast execution-time re-assembly and disassembly of relevant plan parts is supported, the size of fully ex- plicit reaction plans becomes entirely irrelevant. Beyond combating an ugly rumor about reaction plans, this paper also contributes to analyses of the space complexity of solutions to entire problem do- mains. Such solutions include production systems and many ordinary hand-written programs - the latter may be construed as reacting to input data and the states of CPU and memory. Appendix: Derivations Derivation 1: Number of World States 1242 Robotics of ways N blocks can be stacked calculated An alternative formulation of c(w) is in The number three steps: 1. find all possible combinations of tower sizes, under the assumption that blocks are identical and interchangeable, 2. for each allowed combination of tower sizes, make blocks non-interchangeable and find all ways of permuting them such that the resulting world states are distinct, 3. find the sum, over all possible combinations of tower of the number of distinct block permutations. sizes, N list of partitions - 1 1 2 2,1+1 3 3,2+1,1+1+1 4 4, 3+1, 2+2, 2+1+1, l+l+l+l 5 5,4+1, 3+2, 3+1+1,2+2+1, 2+1+1+1, 1+1+1+1+1 To generate the partitions of N+l from those of N, add 1 to each component of each partition of N, store the resulting partition if it has not been encountered before, and finally add a partition consisting of N+l 1s. For Step #2 we represent each partition as consisting of ni is (e.g. a partition of 5 as 1 3s and 2 Is), then count N!/ n.n;! distinct states under the given partition. The denommator factors out states that differ only by a posi- tional interchange of towers of the same size. Step #3 sums the results of Step #2 over all the partitions of N. The above calculation was implemented as a C program. The results for N<25 are shown in Table 1 under the heading “actual world states”. Derivation 2: Approximate Number of States N!, which appears in Derivation 1, is a lower bound on the number of N-Blocks World states. A loose upper bound may be found by noting that the N things possibly under a given block can be distinguished with log,N bits, so that it takes only N log, N bits to encode what’s actually under each of the N blocks in a given state, thus allowing at most $‘J%N = NN possible states in the N-Blocks World. Em- pirically we find that (N N)0.8 is a very good approximation. Derivation 3: Size of Random Partition Let Sp) denote a “Stirling number of the second kind” (Knuth 1968, p.65); th ese numbers indicate how many ways w objects can be partitioned into m non-empty subsets. Let a(w) be a “Bell number”; these numbers indicate how many ways a set of w objects can be partitioned. Let c(w) be the cardinality of a randomly chosen partition of w objects. Then, using a well-known identity, c(w) = c”= is!“) ‘f?;w) t wtl w+l qw+q = x siw+l) = >(iSf”’ + sp,’ ) i=o i=o = (c(w) + 1) B(w). (1) w-l c(w) = - 44 i-o cc wY~l;)tct4 + ww Here we define c(w) by adding the new wth element to any subset out of a partition on w - 1 elements. A set of w- 1 elements contains (,“--;L,) possible subsets of size w - 1 -i. For each such subset, the remaining i elements can be parti- tioned in f?(i) ways, and for each such partition the expected number of equivalence classes is c(i)+1 (the additional 1 ac- counts for the class containing the new wth element). Now, making heavy use of Equation 1, we obtain w-l c(w) = C( W- 1 y%+1) w-l-2 i=o e4 w-l = C(“$g.$ JZO w-l l+CL w-l w-2 W-3 = 3=1 j! c(w-1) + 1 c(w-2) + 1 *** +-J-.9 + l Raising both sides to the power c(w- c(w-1) + 1, and taking logarithms: 1) + 1, using 44 < ctw> c(w-l)+l < ew-l c(w)c(w) < ew--l c(w)ln c(w) < w - 1 An over-estimate ? of c(w) can now be obtained very effi- ciently by iterating 2 = (w-l)/ In t. Derivation 4: Size of Actual U.P. The size of the monolithic Universal Plan (with variables) for building a tower of N blocks is the number of decision nodes, which (in any binary tree) is one less than the num- ber of outcomes. To get that number we need to replace the macros “ACHIEVE-<goal>" with explicit decision trees containing only the puton and putoff actions. The plan for constructing a tower of N blocks num- bered from 1 (at the top) to N (at the bottom) is just an instance of TWR-READY(N), which incorporates an in- stance of TWR-READY (N-l), and so on recursively, down to TWR-READY2. For J > 3 TWR-READY(J) incorporates J-2 instances of ACHIEVE-NOT-ABOVE(Z,X),toensure thatthetowerisnot being built on top of blocks 1 through J-2. Unrolling the plan recursively as in the previous item, the plan incor- porates N-2 + N-3 + . . . + 1 = (N-l)(N-2)/2 instances of ACHIEVE-NOT-ABOVE(Z,X).Similarly, the planincorpo- rates N-l instances of ACHIEVE-ON(J-1,J). In general, ACHIEVE-NOT-ABOVE (Z,X> could be achieved by dismantling the tower on top of Z, then mov- ing Z to the table. Since the plan must provide for the worst case in which Z is directly on top of X and all the other blocks are stacked on top of Z, Reactive Control 1243 ACHIEVE-NOT-ABOVE{2 ,X) must be prepared to disman- tle the whole tower on top of X. Moreover, every- thing above X must be dismantled in any case, prior to moving X. Hence we simplify the analysis by equating ACHIEVE-NOT-ABOVE(Z,X) with ACHIEVE-CLEAR(X).Then each occurrence of ACHIEVE-NOT-ABOVE (Z ,X) unfolds as a series of calls to PUTOFF(Y 1, one for each next higher block in the tower. Since there can be at most N- 1 blocks on top of X, the (N-l)(N-2)/2 occurrences of ACHIEVE-NOT-ABOVE(Z ,X> select from a total of (N-l)*(N- I)( N-2)/2 outcomes. By virtue of the structure of TWR-READY(J) we know that the ACHIEVE-ON(J-1, J> subplan only occurs when the tower below J has been completed. Therefore, the ACHIEVE-CLEAR(J-1) and ACHIEVE-CLEAR(J) sub- plans incorporated within ACHIEVE-ON (J-l, J) need only cope with the J-2 and J-l blocks (respectively) that are not already in the partially completed tower. Conse- quently, to dismantle the worst-case towers above blocks J-l and J, each ACHIEVE-ON(J-1,J) subplan must un- fold as (J-2)+(J-1) calls to PUTOFFO , plus one call to PUTON (J-i, J> . Summing over J from 2 to N we find a to- tal of Nx(N-1) outcomes within the ACHIEVE-ON subtrees. Thus the total number of outcomes of the decision tree is (N-l)(N-l)(N-2)/2 + N(N-1) + 1 = (N-1)3 + N. (The last 1 is for the NO-OP in TWR-READY(21.) This num- ber is shown in Table 1 under the heading “actual UP size with vars”. Derivation 5: Size of U.P. Without Variables Recall that the actual block-stacking plan incorporated (N-l)(N-2)/2 instances of ACHIEVE-NOT-ABOVE(Z ,X), each of which may have to remove up to N-l blocks. Inability to use variables would force each such instance to cope with (N-l)! possible permutations of blocks in each tower, for a combined size of (N-l)! x (N-l)(N-2)/2 outcomes. Similarly, the N-l instances of ACHIEVE-ON(J-1,J) each incorporate two subplans ACHIEVE-CLEAR(J) and ACHIEVE-CLEAR(J-I), which may have to remove all permutations of J-l or J- 2 blocks, respectively. From those subplans we get a size contribution of -g, ((J-l)! + (J-2)!) = 1+ (N-l)! + 2 x;-” Ic!. Adding a further N-l cases in which ACHIEVE-ON(J-1,J) does not require block-removal, and the 1 case in which no action at all is necessary, we get the total sizes shown in Table 1 under the heading “est. size of UP without vars”. References Bonasso, R.P. 1991. Integrating reaction plans and layered competences through synchronous control. Proc 12th IJCAI: 1225-1231. Chapman, D. 1989. Penguins can make cake. AI Mag- azine lO(4): 45-50. Chrisman, L. & Simmons, R. 1991. Sensible planning: focusing perceptual attention. Proc AAAI Nat’1 Conf on AI: 756-761. Christensen, J. 1990. A hierarchical planner that gen- erates its own hierarchies. Proc AAAI Nat’1 Conf on AI: POO4-1009. 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1,606 | Structured Circuit Semantics for Reactive Plan Execution Systems Jaeho Lee and Edmund H. Durfee* Department of EE and CS University of Michigan Ann Arbor, MI 48109 {jaeho,durfee}@eecs.umich.edu Abstract A variety of reactive plan execution systems have been developed in recent years, each attempting to solve the problem of taking reasonable courses of action fast enough in a dynamically changing world. Comparing these competing approaches, and collecting the best features of each, has been problematic because of the diverse representations and (sometimes implicit) con- trol structures that they have employed. To rectify this problem, we have extended the circuit seman- tics notion of teleo-reactive programs into richer, yet compact semantics, called structured circuit seman- tics (SCS), that can be used to explicitly represent the control behavior of various reactive execution sys- tems. By transforming existing systems into SCS, we can identify underlying control assumptions and begin to identify more rigorously the strengths and limita- tions of these systems. Moreover, SCS provides a basis for constructing new reactive execution systems, with more understandable semantics, that can be tailored to particular domain needs. Introduction The realization that agents in dynamic, unpredictable environments should consider the evolving state of the environment when making decisions about actions to take to pursue their goals, has led to a plethora of systems for reactive plan execution, including PRS (In- grand, Georgeff, & Rao 1992), Universal Plans (Schop- pers 1987), Teleo-Reactive Programs (Nilsson 1992; 1994), and RAPS (Firby 1989; 1992), among others. The challenge faced by a researcher who needs to incor- porate a reactive plan execution system into a larger endeavor is determining how to decide among these candidate systems. For example, in a project to de- velop a system for controlling and coordinating out- door robotic vehicles (Lee et al. 1994), which reactive plan execution system is right for the job? A primary difficulty in answering this question is that many of the fundamental capabilities of and as- sumptions behind reactive plan execution systems are *This work was sponsored, in part, by ARPA under con- tract DAAE-07-9%C-R012. 1232 Robotics not easily discernible, being tied up in descriptions of procedures and interpreters, which are in turn ex- pressed in system-specific ways. One goal of the work we describe here, therefore, is to develop a means for formally specifying reactive plan execution systems so as to cast a variety of these systems into a single framework, thereby allowing us to more readily identify and compare the capabilities and assumptions of each. With such tools in hand, moreover, we are working toward devising an interpreter for our formalism that will allow us to easily implement appropriate reactive plan execution systems with precisely the characteris- tics needed by a particular domain. Our new formalism, called Structured Circuit Seman- tics (SCS), extends the Circuit Semantics of Teleo- Reactive Programs to be powerful enough to encom- pass the representation capability of many reactive planning systems. In this paper, we briefly review cir- cuit semantics as a starting point for our extensions, and point out some limitations of circuit semantics that make it inappropriate for a task like that of controlling outdoor robotic vehicles. We then present our SCS for- malism to overcome these limitations, and demonstrate the power of SCS through a simple assembly problem that demands reactive and robust plan execution. Fi- nally, we analyze SCS as a general reactive plan specifi- cation language by comparing SCS with other reactive plan execution systems. We conclude this paper with discussions on implementation issues and extensions to applications involving multiple agents. Circuit Semantics When executing on a computational system, a pro- gram is said to have circuit semantics when it produces (at least conceptually) electrical circuits that are in turn used for control (Nilsson 1992). In particular, a teleo-reactive (T-R) sequence is an agent control program based on circuit semantics, combining no- tions of continuous feedback with more conventional computational mechanisms such as runtime parame- ter binding and passing, and hierarchical and recur- sive invocation structures. In contrast with some of the behavior-based approaches, T-R programs are re- From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. sponsive to stored models of the environment as well as to their immediate sensory inputs (Nilsson 1994). In its simplest form, a T-R program consists of an ordered set of production rules (from (Nilsson 1994)): K1 + al; KS + a2; ---; Ki -+ a;; e*-; Km -+ a,; The Ki are conditions, and the ai are actions. The in- terpreter scans the T-R sequence from the top until it finds a satisfied condition, and then executes the corre- sponding action. However, executing an action in this case might involve a prolonged activity instead of a dis- crete action. While the condition is the first true one, the action continues to be taken, so the T-R program can be continuously acting and evaluating whether to continue its current action (if it still corresponds to the first true condition) or to shift to another action (if the current action’s condition is no longer satisfied or a condition earlier in the program becomes satisfied). The actions, ai, of a T-R sequence can be T-R se- quences themselves, allowing hierarchical and recursive nesting of programs, eventually leading to actions that are primitives. In an executing hierarchical construc- tion of T-R programs, note that a change of action at any level can occur should the conditions change. That is, all T-R programs in a hierarchy are running concur- rently, in keeping with circuit semantics, rather than suspending while awaiting subprograms to complete. Limitations of the T- While T-R programs capture circuit semantics for re- active control in a very compact way, their compact- ness comes at the cost of representativeness for other domains. For example, in the outdoor robotic vehicle domain, suitable reactive execution appears to require a language with a richer circuit semantics than is em- bodied in T-R programs (or in many other reactive execution systems, for that matter). Execution Cycle In an ideal reactive system with circuit semantics, the conditions are continuously being evaluated and, when appropriate, their associated actions are continuously being executed. Real electrical circuits, however have a natural, characteristic frequency that leads to cycles of execution, and these same cycles occur in reactive execution systems, corresponding to the perception- cognition-action cycle. Traditionally, reactive systems have concentrated on increasing this frequency by, for example, reducing the time needs of cognition, but this cycle cannot be completely eliminated. Circuit semantics represents two different kinds of actions- energized and ballistic. Energized actions are those that must be sustained by an enabling condi- tion to continue operating; ballistic ones, once called, run to completion (Nilsson 1992). We argue that the energized actions can be implemented using ballistic actions by making the perception-cognition-action fre- quency higher than or equal to the characteristic fre- quency of the agent’s environment. In fact, if the agent is to be implemented using conventional computer sys- tems, the energized actions must be mapped down to the ballistic actions anyway. Our definition of atomic actions to be described later is based on this argument. Clearly defining an execution cycle, therefore, goes hand-in-hand with defining atomic actions. Without a characteristic execution cycle, a continuously running system could take control from any of its actions, even if those actions are incomplete. For example, consider a T-R program whose conditions are to be evaluated both against sensory input and on stored internal state information. While executing an action that is sup- posed to make several changes to the internal state, an earlier condition in the T-R program is satisfied, and the original action is abandoned, possibly rendering the internal state inconsistent. In pathological cases, the system could become caught in an oscillation between zero (when “wedged”) or more actions. Of course, such interruptions could be avoided by augmenting the con- ditions such that they will not change truth value at awkward times, but this implicitly institutes an exe- cution cycle and atomicity, which should be more effi- ciently and explicitly represented. Non-Deterministic Behavior In a T-R program, the condition-action pairs are or- dered strictly and statically. However, generating a to- tal ordering on the actions at design time might be dif- ficult and can lead to overly rigid runtime performance. For example, actions that appear equally good at de- sign time will have an order imposed on them nonethe- less, possibly forcing the system into repeatedly taking one action that is currently ineffective because it hap- pens to appear earlier than a peer action. Instead, the system should be able to leave collections of actions unordered and try them non-deterministically. The do any construct in our formalism to be de- scribed in the following section can specify multiple equally good actions for the situation. One of the ac- tions is chosen nondeterministically at run time and executed. If the chosen action fails, another action within the construct is again nondeterministically se- lected and tried until one of them succeeds. We can imagine a circuit component with one input and n out- puts, which energizes one of its outputs whenever the component is energized. Note that, with work, this nondeterminism can be forced into T-R programs by, for example, having the condition of each equally good action include a match against some randomly assigned state variable that is randomly reassigned upon each action failure. However, once again, such machinations serve to implicitly implement a capability that should be explicit. Best-First Behavior One of the reasons for demanding reactivity is to be sensitive to the way utilities of actions vary with spe- cific situations and to choose the applicable action that Reactive Control 1233 is best relative to the others. Since which action is best relative to the others depends on the runtime situation, the selection cannot be captured in the static ordering of actions. Let’s consider a simple three line example T-R program: available( airplane) + fly; available( car) + drive; True + walk; Suppose that the airplane is not available initially. The agent thus chooses to rent a car and drive. After driv- ing 10 hours, the agent needs to drive only 30 more minutes to get to the destination; however, it discovers that it is passing an airport which has a plane avail- able. According to the above T-R program, the agent switches to the flying action, even though it could be that, between dropping off the rental car, boarding the plan, taxiing, and so on, flying from here will take much longer than just completing the drive. If the agent is to accomplish its goal in a timely way, the T-R program above needs additional conditions for taking the airplane to avoid this inappropriate transi- tion. The question is where to put what conditions. For this three line program, it is not terribly hard to devise additional conditions. If we assume, for sim- plicity, that the function tt (travel-time) returns the time needed to get to the destination from the current situation, the T-R program becomes: available( airplane) A tt (airplane) < tt (car) A tt(airplane) < tt(foot) -+ fly; available(car) A tt(car) < tt(foot) + drive; True + walk; But what if there are ten different ways to get to the destination? The lefthand side conditions of the T-R program might have to mention all the ways of travel- ing. Moreover, if a new way to travel were discovered, it could not be introduced into this T-R program with- out possibly affecting the conditions for other actions. A more general answer is to introduce a decision layer above the circuit layer. The decision layer dynami- cally makes utility-based (cost based in dual) selec- tions among candidate actions, conceptually energiz- ing the “best” circuit. In SCS, the do best serves this purpose. Each action in the do best construct has an associated utility function as well as an energizing con- dition. Each action with a satisfied condition competes (or bids) by submitting its (expected) utility, and the highest bidder is selected. ’ This scheme is very similar to blackboard control mechanisms where each knowl- edge source proposes its utility, but differs from many blackboard systems in that the conditions and utili- ties for the actions are checked every cycle, as dictated by the circuit semantics. Using the do best construct, ‘Tie-breaking is done similarly to the nondeterministic selection of actions. In fact, the do any construct is just a special case of the do best where the utility calculations always return identical values. the above example will be represented as follows ttu is a utility function of the travel time. where do best { available(airplane) [ttu(airplane)] -+ fly; available( car) [ttu(car)] + drive; True [ttu(foot)] -+ walk; } Note that, in keeping with circuit semantics, we can map the decision layer into real circuitry as well, be- ing realized as a circuit that controls other circuits which evaluate themselves dynamically. By having some number of decision layers (about decision layers), we can get the meta-levels of other reactive systems such as PRS. Failure Semantics The success of an action can be measured in terms of whether it had the desired effect at the desired time on the environment. As was argued previously, because of the characteristic frequency of the system, even sus- tained actions (such as keeping a vehicle centered on the road) can be viewed as sequences of atomic ac- tions (such as repeatedly checking position and cor- recting heading). Thus, since an atomic action might have a desired effect on the environment, determining whether that effect was achieved is important in con- trolling the execution of further actions. Effects can be checked for in the energizing conditions associated with an action, such that failure naturally leads to the adoption of a different action. However, because there might be a variety of subtle effects on the environment that an action would cause that would indicate failure, and because embedding these in the energizing condi- tion could be inefficient and messy (non-modular), it is useful to allow actions to return information about success and failure. In T-R programs, if an action fails without changing any of the program’s energizing conditions, the same action will be kept energized until the action eventu- ally succeeds. If actions can return failure information, constructs can respond to this information, allowing a broader range of reactive (exception handling) behav- ior. In SCS, several different constructs encode differ- ent responses to action failures to provide a variety of reactive execution behaviors. Structured Circuit Semantics The basic unit in the structured circuit semantics is an action, ai. Every action is atomic; it is guaranteed to terminate within a bounded time and cannot be interrupted. As argued previously, sustained actions are typically repetitions of an atomic action. Once all actions are defined, we can limit the (up- per and lower) bound for the perception-cognition-action cycle. Atomic actions can also be grouped to form other atomic actions, as in (al; . . . ; a,). In this case, all actions in the group are executed in sequence with- out being interrupted. Execution of an action usually 1234 Robotics changes the environment and/or internal state (includ- ing the world model) and returns either success or fail- ure. The semantics of success and failure are important in some constructs such as do any, do best, and do all. For generality, we can loosely define a condition as a function which returns true of false, and when true can generate bindings for variables expressed in the condition.2 We can then define various control con- structs and their semantics. Some concepts are bor- rowed from the semantics of the Procedural Reason- ing System (PRS) and a PRS implementation (UM- PRS (Lee et al. 1994)). B ecause of space limitations, we cannot describe the PRS architecture in detail here, but interested readers can refer to (Ingrand, George& & Rao 1992). The purpose of most of the constructs is to wrap the actions and attach energizing conditions to collections of actions, corresponding to the conditions (I-() in T-R programs. As in the T-R programs’ circuit semantics, the conditions are durative and should be satisfied during the execution of the wrapped actions. The difference is that the conditions are checked only between atomic actions rather than continuously, pro- viding us with clear semantics for the execution and feedback cycles, and avoiding the potential oscillation problems mentioned previously. The constructs can be nested, and the attached con- ditions are dynamically stacked for checking. When- ever an atomic action is finished, the stack of condi- tions is checked from top to bottom (top conditions are the outmost conditions in the nested constructs). If any condition is no longer satisfied, new choices of action at that level and those below are made. A step is defined recursively as follows. In the con- struct descriptions below, Ki, ai, Si, Vi, 1 5 i 5 n are conditions, actions, steps, and utility functions, respec- tively. o ai is an step composed of a single atomic action. An action returns either success or failure and so does the step. 0 (al;- ; a,) is an atomic step composed of atomic actions. The step fails if any of the actions fails. odo {S1; S2; se-; S,} is a step that specifies a group of steps that are to be executed sequentially in the given order. The overall do step fails only as soon as the one of the substeps fails. Otherwise it succeeds. do* {a . +} has the same semantics as those of do except that, whenever a substep fails, it retries that substep until it succeeds. Thus do* itself never fails. This construct allows us to specify persistent behavior, and is partic- ularly useful within the do all and do any constructs explained below. odoall {S,; S2; e-e; S,} is a step which tries to execute all steps in parallel (at least conceptually). If the agent 2More specifically, for our implementation we assume a pattern matching operation between condition patterns and specific relational information in the world model. The details of this are beyond the scope of this paper. can do only one step at a time, it nondeterministically chooses among those as yet unachieved. If any one of the steps fails, the whole do all fails immediately. This is similar to the semantics of the AND branch of the Knowledge Area in PRS. do* all is a variation of do all which tries failed substeps persistently, yet nondeterministically until all of them have succeeded. o do any (27,; S2; . - .; S,} is a step which selects non- deterministically one 5’; and executes it. If that step fails, it keeps trying other actions until any of them succeeds. If every step is attempted and all fail, the do any step fails. This construct corresponds to the OR branch of the Knowledge Area in PRS. do* any is a variation of do any which keeps trying any action including the already failed steps until any of them succeeds. o do first {K1 + S,; . . .; K, + S,} is a step which behaves almost the same as a T-R program. That is, the list of condition-step pairs is scanned from the top for the first pair whose condition part is satisfied, say Ki, and the corresponding step Si is executed. The en- ergizing condition Ki is continuously checked (at the characteristic frequency) as in T-R programs. The dif- ference is that, if a step fails, the whole do first fails. To persistently try a step with satisfied conditions even if it fails (as in T-R programs), the do* first construct can be used. o do best {Kl [Ul] + S1; . . a; K, [U,] + S,} is a step which evaluates Ui for each TrueKi (1 5 i 5 n), and selects a step Si which has the highest utility. If several steps have the highest utility, one of these is selected by the do any rules. The failure semantics is the same as that of the do any construct. The do* best step is similarly defined. 0 repeat {S,; $7; -. -; S,} works the same way as do does, but the steps are repeatedly executed. The repeat* step is also similarly defined. The do, do all, do any, do first, do best, repeat, and their *-ed constructs may have following optional modifiers o while Ko : specifies the energizing condition Ko to be continuously checked between each atomic action. The associated step is kept activated only while Ko is true. For example, do while Ko {. . .} does the do step as long as Ko is true. Note that Ko is an energizing condition of the associated step. Thus, if the energizing condition is not satisfied, the step does not fail, but just becomes deactivated. until Ko is shorthand for while -- lKo. o when KO : specifies that the condition Ko must be true before the associated step is started. That is, Ko is only checked before execution, but not checked again during execution. For example, do* all when Ko while K1 {. . a} is a step which can be activated when Ko is true, and all substeps of which will be persistently tried while K1 is true. unless KO is shorthand for when lK0. Reactive Control 1235 free( 1) A free(2) A available(B) + Lplace(B,2); free(3) A free(a) A available(B) + Rplace(B,2); free(l) A free(3) A available(A) + place(A,l); free(3) A free(l) A available(C) + place(C,3); free(l) A lfree(2) A available(A) + place(A,l); free(3) A lfree(2) A available(C) + place(C,3). Figure 1: T-R Program We have described SCS as a general semantics for re- active plan execution systems. As a matter of fact, the semantics can be directly transformed into SCS Lan- guage (SCSL) which is interpreted and executed by an interpreter. We are currently implementing the SC’S Reactive Plan Execution System in C++. The system consists of the SCSL interpreter and the world model. The SCSL has numerous other built-in actions includ- ing arithmetic operations, world model match and up- date, etc. In the SCSL, a step can be defined using the construct define with a list of arguments (local vari- ables) that are bound when the step is called: define step-name($zi, $22, ..., &cm) step. The defined step can be called, and expanded accordingly at run time. Example: BNL Problem To briefly illustrate how SCS can help clarify the im- plicit control semantics of a plan execution language, we here consider a simpler example than what we have encountered in the robotic vehicle domain, but which still exemplifies concerns in reactive and robust plan execution. In the BNL (B Not Last) problem (Drum- mond 1989), we are given a table on which to assemble three blocks in a row: block A on the left, at location 1; block B in the middle, at location 2; and block C on the right, at location 3. The blocks are not ini- tially available for placement, and each block can be placed on the table once available (the exact means for moving blocks is immaterial). The only constraint on assembly is that block B cannot be placed last: once A and C are down, there is not enough room to squeeze in B since it must be swept in from the left or the right. We assume that a block, once placed, cannot be moved away again. As in (Drummond 1989), we assume three pred- icates: free, at, and available; and four ac- tions: place (A, 1) (place block A at location 1), place (C ,3 ) (place block C at location 3), Lplace (B, 2 ) (sweep B in from the left), and Rplace (B, 2 ) (sweep B in from the right). The ex- ample in Figure 1 is an T-R program that we generated to solve this problem. 3 This program solves the prob- lem, but contains some implicit ordering preferences for placing B from the left and placing A first when A and C are both available. By translating the T-R 31n (Nilsson 1992), a similar T-R program is presented, but it is for a simpler variation of the BNL problem. 1236 Robotics do* first { free(l) A free(2) A available(B) -+ Lplace(B,2); free(3) A free( 2) A available(B) + Rplace(B,2); free(l) A free(3) A available(A) + place(A,l); free(3) A free( 1) A available(C) -+ place(C,3); free( 1) A lfree(2) A available(A) + place(A,l); free(3) A Ifree(2) A available(C) + place(C,3) } Figure 2: Direct Translation to SCS repeat while free( 1) V free(2) V free(3) { do any { do while free(2) A available(B) { do any { do when free(l) { Lplace(B, 2) }; do when free(3) { Rplace(B, 2) }; }} do while free( 1) A free(3) ( do any { do when available(A) { place(A, 1) }; do when available(C) { place(C, 3) }; }} do while lfree(2) { do any { do when available(A) { place(A, 1) }; do when available(C) { place(C, 3) }; }}}}} Figure 3: SCS Program for the General BNL Problem program into SCS (figure 2), and comparing it to our own solution in SCS (figure 3), the implicit control or- dering of T-R programs is explicitly seen,” highlighting how T-R programs cannot capture, in an explicit way, nondeterminism, which has been captured in the richer semantics of SCS. elate rk and Future Work Because SCS embodies circuit semantics, previous comparisons (Nilsson 1992; 1994) between T-R pro- grams and reactive plan execution systems such as SCR (Drummond 1989), GAPPS (Pack Kaelbling 1988), PRS (I n g rand, Georgeff, & Rao 1992), and Uni- versal Plans (Schoppers 1987), are applicable here as well. In this section, therefore, we concentrate on com- parisons more specifically with SCS. As illustrated in the previous section, the do first construct and the capability of defining a step covers the circuit semantics of T-R programs. Universal Plans also fit easily within SCS through the nested use of the do when construct. The real power of SCS over T-R programs or Universal Plans are manifested when the simple SCS constructs interact in various ways. Situated Control Rules (SCR) are constraints for plan execution that are used to inform an indepen- dently competent execution system that it can act without a plan, if necessary. The plan simply serves to increase the system’s goal-achieving ability. In other words, SCR alone is not a plan execution system, and its rules are not executable. This does not preclude, however, developing an integrated system where one 4The SCS constructs can often allow multiple such map- pings. Thus, while program equivalence cannot always be detected syntactically, the implicit control information can be captured and compared explicitly. component generates SCRs which, in turn, are auto- matically compiled into a SCS program to execute on another component. The semantics of SCS would make such compilation possible, although the SCR formula- tion has weaknesses that must be overcome, such as (1) it does not consider variable binding, (2) it has no hierarchical execution structure (function call or recur- sion), and (3) it has no run-time reasoning. The RAP system (Firby 1989; 1992) is very sim- ilar in flavor to SCS. RAP’s intertwined conditional sequences enable the reactive execution of plans in a hierarchical manner. As with other systems, its basic difference with SCS is that it lacks circuit semantics, as well as several features of SCS including: failure semantics (when a RAP method fails, it assumes the robot is in the same state as before the method was attempted) and the ability to enter a method from the method’s middle. SCS has clear failure semantics and specifies what to do and where to start. Another limi- tation of the RAP interpreter is that methods lack run- time priority information, which is expressed by util- ity functions in SCS do best. RPL (McDermott 1992) extends RAPS by incorporatingfluents and a FILTER construct to represent durative conditions, but these are much more compactly and intuitively captured in scs. The central system of Sonja (Chapman 1990) uses a circuit description language, MACNET and ar- bitration macrology. Although it supports circuit semantics at the (boolean) gate level, the arbitra- tion macrology allows only compilation time arbitra- tion in a non-structured manner because it compiles down into MACNET circuitry just before the system runs. SCS can more generally capture reactive be- havior required for applications such as playing video games (Sonja (Chapman 1990) and Pengi (Agre & Chapman 1987)) and for the traffic world scenario (CROS (Hendler & Sanborn 1987)). PRS deserves special mention, because a major mo- tivation in developing SCS has been our need for for- mally specifying the PRS plan representation and its execution model. A formal specification of a reactive plan is essential for us to be able to generate it, reason about it, and communicate about it among multiple agents. In the PRS perspective, SCS can be inter- preted as a formalism for the PRS execution model using circuit semantics. In particular, the meta-level reasoning capabilities of PRS introduce a wide variety of possible execution structures. So far, we have been able to express much of PRS’s utility-based meta-level decision making in SCS using the do best construct. Note that these constructs can be nested to arbitrary depth, corresponding to multiple meta-levels in PRS choosing the best method for choosing the best method for achieving a desired goal. Decisions at lower levels can affect higher-level decisions through failure seman- tics and changes to the internal state, while utility cal- culations guide choices from higher to lower levels Encouraged by the ability of SCS to capture explic- itly the control structures of various plan execution systems, we are implementing SCS Reactive Plan Execu- tion System in C++. This effort is directed at supplant- ing our previous implementation of PRS with a more general execution system that can be tailored to the control needs of our application domain. Toward this end, we are currently working on rigorously capturing in SCS the content of PRS meta-level knowledge areas. With this modified system, not only will we have a more flexible plan execution system, but also one with clear semantics to support inter-agent communication and coordination in dynamic environments. eferences Agre, P. E., and Chapman, D. 1987. Pengi: An implementation of a theory of activity. In AAAZ-87, 268-272. Chapman, D. 1990. Vision, instruction and action. Tech. Report 1204, MIT AI Laboratory. Drummond, M. 1989. Situated control rules. In KR’89, 103-113. Firby, R. J. 1989. Adaptive execution in complex dynamic worlds. Tech. Note YALE/DCS/RR #672, Dept. of Computer Science, Yale University. Firby, R. J. 1992. Building symbolic primitives with continuous control routines. In Hendler, J., ed., Ar- tiJicia1 Intelligence Planning Systems: Proc. of the First International Conference, 62-68. Hendler, J. A., and Sanborn, J. C. 1987. A model of reaction for planning in dynamic environments. In Proc. of the DARPA Knowledge-Based Planning Work- shop, 24.1-24.10. Ingrand, F. F.; Georgeff, M. P.; and Rao, A. S. 1992. An architecture for real-time reasoning and system control. IEEE Expert 7(6):34-44. Lee, J.; Huber, M. J.; Durfee, E. H.; and Kenny, P. G. 1994. UM-PRS: an implementation of the procedural reasoning system for multirobot applications. In Con- ference on Intelligent Robotics in Field, Factory, Service, and Space (CIRFFSS ‘94), 842-849. McDermott, D. 1992. Transformational planning of reactive behavior. Tech. Note YALEU/CSD/RR #941, Dept. of Computer Science, Yale University. Nilsson, N. J. 1992. Toward agent programs with circuit semantics. Tech. Report STAN-CS-92-1412, Dept. of Computer Science, Stanford University. Nilsson, N. J. 1994. Teleo-reactive programs for agent control. Journal OfArtificial Intelligence Research 1:139- 158. Pack Kaelbling, L. 1988. Goals as parallel program specifications. 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1,607 | Associative Memory in an Immune-Based System C.J. Gibert* and T.W. Routen Department of Computing Science De Montfort University Leicester LEl 9BH, United Kingdom twr@dmu.ac.uk *Current Address: Chemin de la Monnerie, Route de la Ville es Blais, 44 380 Pornichet, France. Abstract The immune system offers to be a rich source of metaphors to guide the exploration of the notion of an adaptive system. We might define a class of systems which are inspired by, but diverge from, descriptions of the immune system, and refer to them as immune-bused systems. The research reported here is motivated by a desire to explore the possibilities of such systems. Specifically, we attempt to construct an associative memory using immune system modelling as a starting point. I. Introduction The immune system and more particularly the immune network and the immune response have been compared with neural networks (e.g. Hoffmann, 1986) and classifier systems (e.g. Farmer et al., 1986). Although the immune system presents similarities with these systems, it also has interesting differences from both (Gibert, 1993). Farmer (1991) described some of these similarities and differences in identifying the computation performed by immune networks as a species of connectionism. One can indeed view the immune system as displaying parallel distributed computation. The coherency of the overall behaviour of the system is an emergent property of many local interactions. Farmer further suggested that aspects of the immune system make it more complicated than its sister connectionisms. It would seem therefore, that the immune system holds great potential for machine learning and offers to be a rich source of metaphors to guide the exploration of the notion of an adaptive system. An impressive amount of work has been done in theoretical immunology to model faithfully the behaviour of the immune system, or some of its components. These models are computationally very complex, although still simplified from an immunological point of view. For the purposes of artificial intelligence, we are not constrained by biological actuality just as those working on neural networks are not constrained by properties of real neurones. Since the immune system has interesting properties, the models of the immunologists might offer a good starting point from which to construct computational models which embody some of those properties and yet which are of practical use. We might define a class of systems which are inspired by, but can diverge from, descriptions of the immune system, and refer to them as immune-based systems. We believe that this class currently has few, if any, members. The research reported here is motivated by a desire to begin to explore the possibilities of such systems. The implicit role of the immune system is to defend the host from external entities which may lead to disease (called pathogens). It operates by being able to discriminate between inner (endogenous) and foreign (exogenous) entities. When an entity is recogniscd as foreign, several mechanisms leading to its destruction are triggered. The end of the immune response is normally marked by the absence of the foreign agent, or its reduction to a harmless quantity. Upon presentation of the same pathogen, a secondary response is normally generated. A secondary response is characterised by a speedier obliteration of the infectious agent. It is apparent from the differential responses that initial contact with the pathogen leads the immune system to adapt, in order better to be able to deal with the same pathogen subsequently. Thus, it is a form of memory, and it is a form of content-addressable memory since the secondary response can be elicited from a pathogen which is similar, although not identical, with the original one which established the memory (this is known as cross-reactivity). 852 Neural Networks From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. 2. Immune system Many different cells and molecules are involved in the immune response. For the sake of simplicity in this exercise, we only present and model some of these. 2.1. Recognition The basis of the immune system is in cellular and molecular interactions. Certain cells (B-lymphocytes, henceforth B cells) synthesise and carry on their surface molecules called antibodies. Molecules are three- dimensional structures with uneven surfaces made of projections and indentations. They therefore have shapel, which is referred to as specificity. If two molecules have complementary specificities, they bind to each other (in a chemical reaction); the strength of the bond depending on the degree of complementarity. A fundamental operation of the immune system is the binding of antibodies with other molecules (which are, in that case, called antigen) which serves to tag them for destruction by other cells. This process is referred to as antigen recognition. Antigen specificities are characteristic of the B cells which produce them, in the sense that all antibodies produced by any particular B cell have the same specificity. Therefore, we can speak of an antibody recognising the antigen, or of the cell recognising it. It is important, as will become evident later, that, in addition to antigen-antibody binding, there are also reactions between endogenous entities. Antibodies can themselves be ‘recognised’ by other antibodies. 2.2. B cells and the immune network When a B cell recognises an antigen, it may be stimulated, in which case it becomes enlarged and starts replicating (producing identical copies of itself). We refer to a set of identical cells as a clone. Since all cells in a clone are identical, a clone can be said to have a specificity. A clone also has a size, which is the number of cells in the clone. Whether a B cell actually is stimulated or not, depends on its affinity with present antigens and also with other clones in the system, and their respective sizes. The network formed by clones recognising other ’ This depends also on other factors such as electrostatic forces, hydrogen bonding, hydrophobic groups and Van der Waals forces. In the remainder of this text, the word shape will refer to the geometrical shape together with all these factors; some authors use the phrase generalised shape (Perelson, 1989). clones in the system is referred to as the immune network which was postulated by Jerne (Jerne 1973; 1974). This relationship is often formally expressed in terms of the field of the clone in many models in the literature. Whereas neural net models most commonly use threshold activation functions, considerable evidence (Coutinho, 1989) suggests that proliferation of a B cell is well approximated as a bell-shaped function of its general field, mutated by two thresholds, lower and upper, beyond and below which the cell is activated and proliferates. Below the lower threshold, the cell does not respond because too few of its antibody receptors are cross-linked, beyond the higher threshold, the cell stops responding (a phenomenon referred to as high zone tolerance); the cell is said to be suppressed. Since antibody binding depends on the affinity with antigen or other antibodies, B cells with high affinity are suppressed at lower concentrations than low affinity B cells (Male et al., 1991). 2.3. Mutation During an immune response, dividing B cells are subject to replication “errors”. These genetic errors, e.g. gene recombination and somatic mutation, generate cells which produce different antibody specificities. Some of these specificities are not functional in that they will not be able to bind to the present antigen, but others may have an even higher affinity with it. For an interesting exploration of the consequences of different mutation rates see (Weinand, 1990). 2.4. Meta-dynamics of the system The immune system is in a state of constant flux. New clones are produced by the bone marrow continuously. Populations of B cells show high turnover rates, of order of X5%-30% of the total pool per day (Kinkade, 1987; Coutinho, 1989). Since the total population of B cells is almost constant in the immune system a great number of them die each day. When a new clone is created by the bone marrow, if its affinity with other clones present in the immune network is not zero, the clone can proliferate and possibly survive longer that other clones. The immune network is self- organising, since it determines the survival of newly created clones. It also determines its own size (for a detailed discussion see De Boer and Perelson, 1991). This is referred to as the meta-dynamics of the system (Stewart and Varela, 1991; Bersini and Varela, 1991). Neural Networks 853 2.5. Memory Immunological research offers two main classes of hypotheses concerning the maintenance of the memory of a pathogen by the immune system. Firstly, cells which participate in a/primary response acquire “memory cell” characteristics which distinguish them from other “virgin”, cells. Memory cells are thought to decay more slowly or have an infinite life. They are not suppressed by high dose of antigen and proliferate faster. An alternative view is based on the immune network hypothesis, due to Jerne (1973,1974). As Farmer (1991) postulates “In an immune network a memory can potentially be modelled by a fixed point of the network. The concentrations at the fixed point are held constant through the feedback of one type to another type.” (p. 174). The dynamic maintenance of memory in immune network would seem to constitute an attractive approach for an adaptive system, since a particularity of memory in general is its limited capacity; adaptive systems need to be able selectively to forget. Localised memories due to network interactions are hypothesised to be stable memory states of the network (De Boer and Hogeweg, 1989b; Weisbuch, 1990; Weisbuch et al., 1990). 3. Engineering associative memory Thus, we have the bare bones *of a possible model of the immune system. The task we set ourselves was to harness this (albeit crude) model in an attempt to create a content-addressable auto-associative memory. Inputs to the system are black and white pictures of 64 by 64 pixels and are analogous to antigen. Our aim is to present these ‘antigen’, initiate a ‘primary response’ which creates the memory of the antigen, and then be able to observe the existence of the memory by prompting a secondary response via either a further injection of the same, or similar, antigen. 3.1. Equations The differential equations we use are discussed and justified in the immunology literature. The generic equation for computing the field fi, of a clone i, in a system containing n clones is as follows:- fi = ,taijxj (1) where au is the affinity with which clone i interacts with clone j and xj is the size of the clone j. It is worthy of note that this equation is isomorphic with the familiar weighted sum of artificial neural networks, where the affinities correspond with connection weights and the sizes correspond with activation levels. The bell-shaped activation function was first proposed by De Boer and Hogeweg (1989b) and can be produced as the product of two sigmoid functions as in equation (2):- f(h)=hx82 Ol + h 8, + h (2) This function has been studied extensively (e.g. De Boer and Hogeweg, 1989a, b; Weisbuch, 1990; De Boer and Perelson, 1991). If 01 c< 02 is chosen, the maximum value of the function is almost equal to unity, at each threshold the value is almost equal to 0.5. We can characterise the motion system in the following terms:- of a clone in the dX. $=mi+xi(l+b(fi)+b(Axaa)-d) (3) Here, xi is the size of clone i, m i is the daily production of cells in this clone by the bone marrow, d represents the decay of the cells in the system, b is the bell-shaped function (2) andfi is the field “seen” by the clone i at instant t. A describes the concentration of antigen, while aiA is the affinity of the clone i for the antigen (Parmer, 1991; Weisbuch, 1990; De Boer and Perelson, 1991). 3.2. Entities and affinity A basic requirement for an immune-based system is the development of a way of modelling the entities of the system along with a means for computing the affinities between them. In fact, we are interested not in representing cells and antibodies in all their complexity, but only representing those aspects relevant from the point of view of their interaction (more realistic models have been developed, e.g. Inman, I978 as described by Stewart and Varela, 1991 or Weinand, 1990). In immunological terms, we are interested in representing only their combining regions. These are called paratopes and epitopes and are best thought of as keys and locks. A cell has a key of a certain shape (its paratope) which can fit a lock of a certain shape (epitope) held by certain antibodies, and by other cells. We follow Seiden and Celada (1992; Celada and Seiden, 1992) who suggest an extremely simple fixed- length binary representation of the shape of paratopes and epitopes; a form of representation common to many investigations in current machine learning. The affinity a@, between a paratope and an epitope is then determined 854 Neural Networks by the number of complementary bits. When au = aji, the network is said to be symmetrical. Several models have used symmetrical networks (e.g. De Boer and Hogeweg, 1989a; Weisbuch, 1990) although this represents a simplification since non-symmetrical interactions occur in the immune system (De Boer and Perelson, 1991). Interactions are not symmetrical either when the affinity function does not produce the same affinity between reciprocal interactions, or when paratopes and epitopes are separately represented. Non- symmetrical networks are less stable that symmetrical ones (Hoffmann, 1986). 3.3. Output: defining the winner As Farmer et al. (1986) note that there is no clear analogue for output in the actual immune system, which simply seeks to remove antigen. We reasoned as follows. If there were an output of the immune system then it would surely be related somehow to the successful termination of the immune response. A natural assumption to make is that, if we can obtain interesting output from the system, it must surely be related to the clone which is, in some sense, the most relevant effecters of the destruction of the antigen. We shall refer to this clone as the winner of the response, and define output in terms of it. We shall see later that it is not straightforward to define the winner. This is not necessarily a disadvantage; many possibilities present themselves and suggest interesting avenues of investigation. 3.4. Simulation A constant and continuous production of clones by the bone marrow is simulated. At each time step, a certain number of randomly generated clones are inserted into the system. If a new clone has the same paratope and same epitope as an existing one, the size of the existing clone is increased by the size of the new one. The initial size of a clone is chosen so that no network activity is initiated. Since clones decay, the number of clones and the total population of cells are constant in the system. The parameters are chosen so that the number of clones is large enough for the probability of recognition of an antigen to be equal to unity. Therefore, the repertoire is complete, as in the real immune system. When an antigen (i.e. a pattern to be remembered by the system) is injected, all the clones present in the system follow equation (3). The clones which recognise the antigen start expanding. When the sizes of these clones reach a sufficient level, network activity is triggered. Anti-idiotypic clones are stimulated, proliferate, and then stimulate their own anti-idiotypic partners and so on. 3.5. Artificial idiotope assignment We experimented initially with a non-symmetrical model in which epitopes and paratopes were represented separately. Our idea was to to force the memorisation of an antigen. During the period when the antigen is present, the clones directed against that antigen (referred to as Abls) expand, exciting their anti-idiotypic partners (Ab2s). In the system, the idiotope of each Ab2 present in the system is assigned the same shape as the antigen and therefore represents an internal image of the antigen. Figure 1. The shape of the antigen becomes the idiotope of Ab2s present in the system. Therefore a loop is created between Abls and Ab2. The idea is forcibly to create recognition loops in the network to enable the maintenance by the network of the clones responding to the antigen. After the removal of the antigen, the size of Abls will be large (due to the immune response), so will that of Ab2s (due to stimulation from the expanded Abls). Abls and Ab2s suppress each other and start decaying until an equilibrium is reached, with Abl clones maintaining some Ab2 clones and vice-versa. Depending on their respective sizes at the end of the response, the equilibrium can be reached in a stimulatory state, where the size of the clones oscillate or in a suppressed state where they do not change. This is over-simplified and the memory state may not be stable, depending on the reciprocal affinity of Abls and Ab2s, and the presence of other cross-reactive clones. However, no stable state would be possible without the bell-shaped proliferation function. For a more detailed discussion, see Weisbuch (1990) or Weisbuch et al. (1990). Neural Networks 855 In this model, the winner is defined as the largest that there exist immunological interpretations for clone directed against the antigen upon its removel. The equation (4), although it is conceivable that antibody output of the system is taken as the idiotope of the feedback and other regulatory effects within the immune largest anti-idiotypic clone of the winner. system may have something like this effect. Patterns presented to the system were remembered through the maintenance, within the system, of the clones directed against them by the interactions in the network. However, the system was not stable. Should the field of a clone fall between the activation thresholds, it would proliferate continuously. Since the probability for inserting a new clone which would suppress the clone was small, the system would collapse. Suppression was not the dominant influence, as it is hypothesised to be in the real immune system. 3.6. Symmetrical network model Because symmetrical networks are known to be more stable, we decided to experiment with one. Since network interactions are symmetrical, it is assumed that, for a clone responding to an antigen, at least one anti- idiotypic clone is present in the system and therefore will proliferate as its partner proliferates. These interactions should maintain memory cells in the system. We have investigated ways of stabilising the dynamics of the model. If the field of a clone is modified according the size of the clone, the clone can be prevented from expanding. For example, if, in equation (3),fi becomes:- This time, in defining the winner of the response, we took into account the affinity of each clones with the antigen. The winner was chosen to be the clone for whom the product of size with affinity was greatest. This was thought desirable since we had observed that, although a high affinity clone proliferates faster than lower affinity clones, should its size have been low at the presentation of the antigen, it is not certain that its growth during the immune response would be sufficient to ensure that it be the largest clone at the termination of the response. This time, the output was chosen to be the complement of the shape of the winner (since we expect high affinity clones to win, and high affinity clones represent a close or perfect reproduction of the input pattern). On f w+xi” Ji (4) the system becomes stable. In equation (4), 6 ts a constant, Xi is the size of the clone i, fi is the field of the clone i and n is another constant. The constants are chosen according to the other parameters of the system. . . . . . . . . . . . . . . . . . . . . .... ........ . .......... 5.. ....... -4 .................. ......................... .......................... * .lOElQ I-----.---------.-----.-------r- Figure 2 According to equation (4), the function is plotted for 8 = 10000, and n = 2. Equation (4) can be interpreted as follows: when a clone grows large, the field seen by that clone becomes less and less significant. Experimentally, this seemed to stabilise the immune network, apparendy without modifying the properties of the system. It is not certain In this model, most clones in the network were suppressed. Memory cells were naturally maintained by the interactions in the immune network, but did tend to dissipate slowly and eventually disappear. The model provided stable network behaviour, but this is not really a surprise (e.g. see Weisbuch, 1990). However, the system did not show good quality outputs, particularly after secondary responses. Although memory cells expand faster than virgin cells, the output after a secondary response is of relatively poor quality. At the end of a primary response, the winner was usually the clone which showed the highest affinity for the antigen. Since many clones participated in the immune response, the winner, although having high affinity with the antigen, was not necessarily one which was well integrated in the network. Winners were not always maintained by the interactions of the network because of the absence of partners which could maintain them. Although the dynamics of this system showed better stability, it did not acquire the patterns we desired. There is possibly an analogy here with the ability of a neural network to ‘train’ apparently successfully, but in 856 Neural Networks fact have been learning a relationship other than the one intended by its designer. 4. Conclusions In our experiments, we found two requirements which we found difficult to satisfy simultaneously: remembering patterns, while maintaining system stability. The first model proved unstable, but offered the possibility of forcing the insertion of memory cells into the network. The second model proved stable, but did not allow that forcing and did not systematically maintain the clones we desired. It seems that interactions in the immune-based system can exhibit memory properties. Nevertheless, the clones which are maintained by those interactions still tend to disappear. It may well be that memory cells should have a slower decay rate, which would compensate for their observed decay. This solution should be experimented with, but we believe that it may well have consequences for the behaviour of the network, since interactions, although symmetrical in terms of affinity would be asymmetrical in terms of motion. Although we failed to arrive at a satisfactory model, we found our investigations exciting since they took place in an extremely rich, yet relatively unexplored design space: immune-based modelling. We hope that this paper increases the prospects of a wider exploration of that space. 5. References Bersini, H., and Varela, F. J. 1991. The immune recruitment mechanism: a selective evolutionary strategy. In: Belew, R. K. and Booker, L. B. (eds), Proceedings of the Fourth International Conference on Genetic Algorithms, San Mateo: Morgan- Kaufman, 520-526. Celada, F., and Seiden, P. E. 1992. A computer model of cellular interactions in the immune system. In: Immunology Today, 13(2): 57-62. Coutinho, A. 1989. Beyond clonal selection and network. In: Immunological Reviews, 110: 63-87. De Boer, R. J., and Hogeweg, P. 1989a. Unreasonable implications of reasonable idiotypic network assumptions. In: Bulletin of Mathematical Biology, 51: 381-408. De Boer, R. J., and Hogeweg, P. 1989b. Memory but no suppression in low- dimensional symmetric idiotypic networks. In: Bulletin of Mathematical Biology, 5 1: 223-246. De Boer, R. J., and Perelson, A. S. 1991. Size and connectivity as emergent properties of a developing immune network. In: Journal of Theoretical Biology, 149: 381-424. Farmer, J. D., and Packard, N. H. 1986. Evolution, games, and learning: models for adaptation in machine and nature. In: Physica D, 22: vii-xii. Farmer, J. D., Packard, N. H., and Perelson, A. S. 1986. The immune system, adaptation, and machine learning. In: Physica D, 22: 187-204. Farmer, J. D. 1991. A Rosetta Stone for connectionism. In: Forrest S. ted.), Emergent Computation, London: MIT Press, 153-187. Giber& C. J. 1993. The immune system and machine learning. M.Sc. Human-Computer Systems Project Report De Montfort University, Leicester. Hoffmann, 6. W. 1986. A neural network model based on the analogy with the immune system. In: Journal of Theoretical Biology, 122: 33-67. Jeme, N. K. 1973. The immune system. In: Scientific American, 229: 52-60. Jeme, N. K. 1974. Towards a network theory of the immune system. In: Annales d’lmmunologie (Institut Pasteur), 125C: 373-389. Kinkade, P. W. 1987. Experimental models for understanding B lymphocyte formation. In: Advances in Immunology, 41: 181-267. Male, D. Champion, B. Cooke, A. and Owen, M. 1991. Advanced immunology. Grower Medical Publishing: London, England. Perelson, A. S. 1989. Immune network theory. In: Immunological Review, 110: 5-36. Seiden, P. E., and Celada, F. 1992. A model for simulating cognate recognition and response in the immune system. In: Journal of Theoretical Biology, 158: 329-357. Stewart, J. and Varela, F. J. 1991. Morphogenesis in shape-space. Elementary meta-dynamics in a model of the immune network. In: Journal of Theoretical Biology, 153: 477-498. Weinand, R. G. 1990. Somatic mutation, affinity maturation and the antibody repertoire: a computer model. In: Journal of Theoretical Biology, 143: 343-382. Weisbuch, 6. 1990. A shape space approach to the dynamics of the immune system. In: Journal of Theoretical Biology, 143: 507-522. Weisbuch, G., De Boer, R. J. and Perelson, A. S. 1990. Localized memories in idiotypic networks. In: Journal of Theoretical Biology, 146: 483-499. Neural Netwdrks 857 | 1994 | 26 |
1,608 | esults on Controlling Action with rejective Visualization Marc Goodman* Cognitive Systems, Inc. Computer Science Department 234 Church Street New Haven, CT 06510 -Brandeis University Waltham, MA 02254 Abstract A projective visualizer learns to simulate events in the external world through observation of the world. These simulations are used to evaluate potential ac- tions on the basis of their probable outcomes. Results are given that indicate, 1). the error rate for projec- tive visualization is sub-linear as the system projects farther into the future, 2). the error rate is inversely proportional to the number of cases, 3). a simple do- main model can be used to reduce the effect of com- pounding error, and 4). projection can be used to increase the performance of an agent, even when this projection is imperfect. Introduction Projective visualization is a technique for controlling action. A system built with projective visualization learns to project situations into the future based on past experience. Potential actions are selected and re- jected based on an evaluation of the projected state. Previous work (Goodman 1993) presents the basic model for projective visualization and results indicat- ing that a limited form of projection can be used to build a system that performs as well as a reactive sys- tem, based on observation of the reactive system. It also offers preliminary results on the accuracy of pro- jection for increasing windows of projection. Projective visualization starts with a concrete rep- resentation of an observed process or activity. These observations are organized as a set of temporally linked cases. The system induces a large number of decision trees, using an algorithm akin to ID3 (Quinlan 1986), CART (Brieman et al. 1984), or Automatic Interac- tion Detection (Hartigan 1975). Each decision tree is responsible for projecting an individual feature of a sit- uation one step forward into the future. During pro- jection, a new, hypothetical case is created using these decision trees, and this hypothetical case serves as the basis for further projection. *Thanks to David Waltz and Richard Alterman for use- ful discussion. This work was supported in part by ARPA under contract no. DAAHOl-92-C-R376. Other work on the direct application of previous ex- perience to prediction has been presented (Rissland & Ashley 1988; Klein, Whitaker, & King 1988). Both of these works use a very restricted notion of prediction, however. It is assumed that there is only one value to be predicted and that that value is directly associ- ated with the retrieved case (i.e. there is no notion of a projection window, or of projecting an entire situation. Rather, prediction in this sense is akin to a classifica- tion task). Prediction in Battle Planning has also been treated as a classification task (Goodman 1989). The issues addressed in this pa,per are closely related to issues of simulation. Simulation has been framed in terms of a qualitative model of a domain (Kuipers 1986). The SIMGEN system (Forbus & Falkenhainer 1990) uses both qualitative and quantitative informa- tion to drive simulation of a physical systems, and introduces the notion of self-explanatory simulations. Both of these techniques require significant knowledge of the domain, in the form of qualitative relationships. One of the issues addressed by this paper is to what extent such models can be used to guide the induction process. This paper extends previous results (Goodman 1993). This paper presents details on the inductive algorithm used to generate the projectors used by the system and evaluates their performance. This paper also compares the accuracy of projection with and without interpretations, and with and without a simple domain model to guide induction. Finally, the effect of projecting farther and farther into the future on the ability of the system to act is evaluated. The target domain discussed in this paper is a simula- tion of personal combat between two gladiators armed with axes and shields, based on the video game The Bilestoud. The perceptual system of the agent in the combat simulation includes a visual system, a pain sense, a kinesthetic sense, a haptic sense, a sense of joint stress, and awareness of motor control signals which control the agent’s body. The personal combat simulation is a good domain for Learning Agents 1245 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. evalu .ating projection because: 1). data can be automatically created t: large amount of test the limits of the system, 2). the domain is inherently real-time, fo- cusing on very small changes in the state of the world at each time step, 3). the system must project rela- tively large distances into the future to evaluate the effectiveness of its actions, and 4). there are relatively large number of different actions that the agent can take at each step, which allows this work to examine both the accuracy of projection as well as the effects of projection on performance. How Projective Visualization Works Projective visualization manipulates a representation of a process or activity called a case. A case is defined as a snapshot of the state of the world, along with temporal links to previous and next cases. In effect, a case is like a single frame of a motion picture. In the personal combat domain, cases are gathered every ith of a second. Throughout this work, this paper will use the following terms: Field: A case is a collection of fields, each field defln- ing a particular value in the case. For example, in the personal combat domain, there is a field for the amount of damage to the left elbow of the agent, a field for the angle of the agent’s left elbow, and so on. Match fields are used to build a set of in- ductive indices for projecting individual features of a situation. Different sets of indices may have dif- ferent match fields. Outcome fields are used as a classifications or predictions by the system. Differ- ent sets of indices will have different sets of outcome fields. For example, one set of indices may be useful for projecting the angle of the agent’s elbow, while another set of indices is useful for projecting whether the agent will continue walking. Field value: A field value of a case is the value of a particular field for that case. For example, the field value for the angle between the agent’s head and its opponent’s axe might be 30”. Feature projector: A feature projector is a set of in- dices that is responsible for predicting the value of one or more outcome fields. Projector: A projector is a collection of feature pro- jectors that can be used to predict an entire future state of the combat simulation from current and pre- vious states of the combat simulation. Building and using the personal combat projector consists of two separate phases. In the first phase, in- dividual feature projectors are built off-line. In the second phase, the resulting projector is used to rapidly predict future states of the combat simulation. There is no reason, in principle, why learning and action could not be integrated. However, the computation resources required to perform learning and the real-time require- ments of action in the domain have mandated this sep- aration. How the Projector is Built A projector consists of a large number of feature pro- jectors, each of which is an inductively formed discrim- ination tree that indexes a set of cases. The algorithm for generating these indices, called PVClus, is sum- marized below: The Spearman’s Rho correlation between pairs of fields is used to cluster these fields into groups that have high correlation using a Leader algorithm (a variation of the K-means clustering algorithm (Har- tigan 1975)). Each group of correlated fields will serve as a set of outcome fields for an individual fea- ture projector. The reason for grouping such fields is that highly correlated fields may have common underlying factors that govern their behavior. The set of fields describing the combat simulation is enhanced by adding interpretations that capture temporal and other relationships between fields and values. For example, the system creates new fields that capture the first and second discrete derivatives of the existing fields. Each feature projector with associated outcome fields is used to build a discrimination tree. The leaves of this tree are sets of cases with similar val- ues for their outcome fields. The internal nodes of the tree are binary decisions. For example, an inter- nal node might check whether the agent’s shield is between the agent and its opponent’s axe. Such an internal node might separate cases where the agent was protected from damage from other situations. These discrimination trees are built as follows: (a) The set of field values associated with the out- come fields for the feature projector, the discrete first derivatives of these outcome fields, and the discrete second derivatives of these outcome fields are compared. The set of fields that minimizes the following equation is selected: Where each f; is the cardinality of the subset of cases that all have the ith field value for their out- come field, and f is the cardinality of the set of cases as a whole. This measure gives an indica- tion of the a priori error rate if the system were to use this set of fields as outcome fields. A more accurate measure of such error would be: Error = g 2 FieldValue --2 FieldValue i=O j=O Where ci represents the ith case in the set. There are two drawbacks to this form, however. First, it takes O(n2) time to compute whereas the first form is O(n), and second, it is only appropriate for comparing numerical values. The set of fields with 1246 Robotics (b) (4 (4 The purpose of this computation is to try and re- duce the complexity of the decision tree needed to accurately project a value. For example, consider a rocket tracking domain. Before firing, the rocket is at rest and the easiest way to predict its location at the next time step is to use its current location. When the rocket begins firing, its acceleration will be constant and easy to predict, whereas its veloc- ity and location start changing and become more difficult to predict. After the rocket engine cuts out, its X location will change, whereas its velocity will be constant (barring air resistance). Mean- while, its Y location and velocity will change, but its acceleration will still be constant due to grav- ity. A natural approach to solving this problem is to find some way for a given cluster of cases to predict which of these representations for the fu- ture state of the rocket is easiest to predict and to use this as the outcome for building the set of indices inductively. The algorithm gathers all the fields that describe the previous state of the combat simulation, and associated interpretations. For each such field, given a set of associated cases, all field values for that field are tested as possible discrimina- tors. Each discrimination divides the cases into two sets, those whose field values are less than or equal to the candidate field value, and those whose field values are greater than the candidate field value. The field value for a particular field that accounts for the largest degree of variance in the outcome fields for that feature projector is found. The winning field value is tested for statistical sig- nificance using the Mann-Whitney U Test. If the field value passes this test, the associated field is saved as a match field. If not, the field is ig- nored. The Mann-Whitney U Test is an appro- priate test for statistical significance because it is non-parametric, and, in general, the system can- not make assumptions about the distribution of values in particular fields. The best field value overall is used as an initial dis- crimination. The discrimination, A, is enhanced as follows: 1. For each match field and its associated field val- ues, each field value is used to form a candidate discrimination, B. minimum a priori error are used as the outcome fields for the discrimination tree. ii. Boolean conjunctions of features A&B, &!bB, A&B and &LB are t#ested. The conjunction of features that best accounts for variance in the outcome fields of the feature projector is selected. If the variance accounted for by the conjunc- tion is greater than the variance accounted for by A, then the addition of B is checked for sta- tistical significance using the Mann-Whitney U (4 Test. If adding B passes this test for statistical significance, then A is set to the conjunction of features, and the process repeats at item 3(d)i. If adding B fails the test for statistical signifi- cance, then the next best candidate discrimina- tor is tried. If no discriminator passes the test for statistical significance, or no discriminator improves the variance accounted for by A, then A is used as the basis for a parent node in the tree. This technique is essentially hill climbing to improve the discriminations in the tree. The chief advantage of such a technique is that it con- serves data. With all such discrimination tree learning algorithms, the more examples that are available at any given point, the more accurate is the credit assignment on individual features. By grinding as much information out of each dis- crimination in the tree, the system ends up with a short tree with relatively few leaves, measures that have been argued are particularly important (Fayyad & Irani 1990). The set of cases are partitioned based on the in- ternal node. The process repeats for each sub- set of cases at item 3a. The algorithm terminates when no new, statistically significant discrimina- tions can be added that improve the variance in out come fields. How the Projector is Used At run-time, a case is created that describes the cur- rent state of the combat simulation. For each feature projector, this case is used to traverse the associated discrimination tree of the feature projector. The mean values for the outcome field values in the leaf clus- ter are used to set the corresponding fields in a fresh case buffer. When each feature projector has been tra- versed, the system has a hypothetical case that de- scribes the predicted state of the combat simulation. This predicted state can then serve as the basis for further projection. Traversing each discrimination tree takes roughly O(log n) where n is the number of cases. The total time complexity for projection is therefore O(pm log n) where p is the projection window, or how far into the future the situation is projected, m is the number of feature projectors (which is effectively constant for any given system), and n is the number of cases. It is, therefore, possible to do projection very quickly. Learning with Domain There are two primary sources of domain knowledge available to the system. The first source of domain knowledge is a set of interpretations that can be de- rived from the raw case representation. For example, in the personal combat domain, the system may au- tomatically create representations of the spatial rela- tionships between objects in the world (such as the joints of the bodies of the agent and its opponent) Learning Agents 1247 90 a0 70 60 Error 50 40 30 20 **Row footurrr ..-Fmturrt,I~rpr~om,~nd Mods1 04:::::::::::::::::::““““” 1 3 5 7 9 I1 13 15 17 19 21 23 23 27 29 Projection Winded Figure 1: Error VS. Projection Window for Systems with and without Domain Knowledge based on Cartesian, deictic, and landmark reference systems (Miller & Johnson-Laird 1976). Automatically deriving new representations is similar to constructive induction (Callan & Utgoff 1991). The effect of these new, derived representations is two-fold. On the posi- tive side, it reduces the hypothesis space bias, defined as being a component of inductive bias that defines the space of hypotheses that are being searched (Bun- tine 1990). On the negative side, since the number of possible discriminations is drastically increased, the chance of beta error (accepting a discrimination as sta- tistically significant because the confidence interval is too loose) is also increased. This can actually decrease the overall performance of the system (Almuallim & Dietterich 1991). The second source of domain knowledge is a sim- ple model of qualitative influences between fields (or quala’tative model (Kuipers 1986)). The system uses such a model in conjunction with the inductive algo- rithm described in Section as follows: 1). the system determines the set of fields that are directly relevant to the outcome field using the qualitative model. 2). This subset of fields is used as the set of initial match fields by the inductive algorithm. The inductive algo- rithm terminates when it is unable to add any more discriminations that are statistically significant, based on these match fields. 3). The system determines the set of fields that are directly relevant to the previous set of match fields. Another pass of induction is per- formed. 4). The system continues to expand the set of match fields and perform additional induction phases until no new match fields can be added. At that point, a final pass of induction is performed with all available match fields. Hence, the model is used to create an applicution- specific bias (Buntine 1990). There is some similar- ity between this technique and the use of primary and secondary features for indexing cases in Explanation Based Indexing (Barletta & Mark 1988). esults Figure 1 shows the effect of the projection window (or how far the system projects into the future) on the error rate for projection. The data points in the chart were generated as follows: o Three projectors were built using 16K cases from ob- servation of two reactive agents battling each other in the combat simulation. The trend labeled “Raw Features” was built with only raw fields (164 differ- ent fields) and first and second discrete derivatives used as match fields (for a total of around 500 fields). The trend labeled “Features plus Interpretations” was built using interpretations as well as raw case fields (for a total of around 2000 fields). The trend labeled “Features, Interpretations, and Model” was built using both interpretations and a simple quali- tative model of the domain. a One at a time, each projector was integrated with the combat simulation. Whenever a combat situa- tion was detected, the system would begin project- ing. These projections were saved. At the next time step, the actual state of the world was compared to the previously projected states of the world. For each of the 164 fields describing the current situa- tion, the sum of the absolute value of the difference between the actual and projected situations was cal- culated. For each of the three projectors, 1,000 sim- ulations were observed, amounting to approximately 50,000 comparisons for each graphed point. e The maximum mean error for each field over the entire projection window was found. The corre- sponding field values for each of the error logs was then normalized by dividing the actual error over the maximum error. Hence, all errors for each field were normalized to the interval [O..l]. This was done so that the composite error for the projector overall would not be dominated by individual fields where the range of projection was much larger than other fields. For example, the value of a distance field could be anywhere from 0 to 4000, whereas the value of a pain field might only be in the range of 0 to 4. e the datapoints in the trends are the sum of the nor- malized error rates for all of the fields in the pro- jector. Hence, the maximum possible error rate is 164. Note that the error rate forms a kneed-over curve with respect to the projection window. This is because as the system projects farther and farther, more and more of its projections become no better than a guess based on the a ptiori distribution of values in the set of cases. As more and more of these projections “top off,” the sum of their errors becomes a kneed-over curve. As shown in Figure 1, the projector built without in- terpretation or model was the most accurate over all. This result is in keeping with other work (Almuallim & Dietterich 1991). However, as shown in Figure 2, pro- jectors built with interpretations were more accurate for complex or difficult to explain features. Figure 2 shows the results of projecting the angle of movement 1248 Robotics 6 T----‘- ____________.__________________c________---- 70 - T- - . . . . . ..-....-.................-..----.---------.--.---~------------- 0~;;;;;;;;;;:;:;;;:::;~:~::~~ 1 3 5 7 9 I1 I3 15 I7 19 21 23 25 27 29 Projrtlon Windw Figure 2: Error VS. Projection Window on a Com- plex Concept for Systems with and without Domain Knowledge 6 5 Error 4 3 2 0 .* Rev Foohma *Featurea plut lntsrprrtrilonr -*- Fe@turu, Interpretatlonr, and M&l Figure 3: Error VS. Projection Window on a Complex Concept with Inadequate Model of the agent, opponent, and devices in the simulation (a total of 18 different features). These features are particularly difficult to project accurately, because of interactions between the bodies of the agent and op- ponent (which may obstruct each other in a variety of complicated ways). Explaining these fields adequately requires the system to make use of higher-level in- terpretations. Also note that due to the difficulty in projecting this field accurately, the error rate tops off rather quickly. In both Figure 1 and Figure 2, the accuracy of the projector built with a simple model was greater than the performance of the system with interpretation but without a model. This is because the model helps the system to reduce the effects of compounding errors. Such a situation isn’t, however, guaranteed. Figure 3 shows the accuracy of the three projectors on how much pain the agent and opponent will be feeling in the future. Such a projection is very difficult to model directly, because it requires the model to explain when and under what circumstances the axe will come into contact with the agent’s body in the future. A com- plete model would involve virtually every field of the situation description. In this case, allowing the system 60 40 Error 30 0 4 : : : : : : ; ; ; :::I 12345678 9 10 I1 12 13 14 LogofthotdumberofCaws -Projection Wlrdw-1 ~Projetion Wlnev-2 e- Projection windDv=s +Pmjection Windw=lO * Pmjdon Windw=20 *Projection Wlndw-30 Figure 4: Error VS. Size of Training Set for Different Projection Windows _-_ _________________________________ ‘.4T - Rrlormna ~~~ 0.6 ________________________________________---------------- “. 1:::::~:::::::::.::::~::::~::::~:: 0 1 2 3 4 5 6 7 0 9 10 Projection Windov Figure 5: Performance of the Agent VS. Window *Brunch-C ?b M&l - Ermh-4, Ml *Branch-B, t'lobl Projection to select its discriminations purely on a statistical basis is more effective than guiding induction with a model. Figure 4 shows the effect of training set size on error rate for different projection windows. Separate pro- jectors were built with 256, 512, 1024, . . . . 16384 cases (these projectors were built with interpretations, but without a model). Error rates for each projector were generated as above. For small projection windows, the error rate falls roughly linearly in relation to the log of the number of cases in the training set. On the other hand, for larger projection windows, the effects of com- pounding error in projection (which can be considered a form of noise) grow to dominate the accuracy of the system. This supports the importance of reducing the effect of compounding error by using a model of the domain. Figure 5 shows the effect of projection on one facet of the performance of the agent, namely how much damage the agent is able to inflict on its opponent in each game. These trends were generated as follows: e The branching f&or defines how many randomly generated patterns of control signals were evaluated (see (Goodman 1993) for a discussion of generating more accurate control signals using action generu- ions). So, for a branch factor of 4, four different patterns of control signals are randomly generated, evaluated, and selected from. Learning Agents 1249 For each pattern of control signals, the system projects forward k steps. An evaluation of the projected situation k steps in the future is performed. For these tests, the simple difference between the sum of the damage to dif- ferent parts of the agents body and the sum of the damage to the opponent’s body was computed. The pattern of control signals with the best evalua- tion was determined and executed. At the end of the simulation, the total amount of damage to the agent’s and opponent’s bodies were logged. The mean values of the damage to the op- ponent’s body are shown in the graph. Three trends were generated. The first trend, “branch=4, no model” was generated using a projec- tor without either a model or interpretations. The sec- ond trend, “branch=4, model” was generated using a projector built with both interpretations and a sim- ple qualitative model, using a branch factor of 4. The third trend, “branch=8, model” was generated using the same projector as the previous trend, but with a branch factor of 8. Note that a projection window of 0 will result in the system evaluating all patterns of control signals as being identically effective. Hence, with a projection window of 0, the system is acting completely randomly. The significant result shown in this graph is that pro- jection does, in fact, help the system to perform more effectively, even when this projection is imperfect. Also note that the performance of the system continues to increase as the system projects farther into the future, until around 5 steps into the future where the perfor- mance levels off. This increase in performance is in spite of the compounding error shown in Figure 1. The performance of the system with a projector that was built using both interpretations and a model was significantly higher than the performance of the system without such domain knowledge. This may seem sur- prising, given Figure 1 which shows that the projector without domain knowledge was more accurate overall. However, most of the fields that are most directly rele- vant to controlling action, such as projecting damage, rely heavily on such domain knowledge. Figure 5 also shows that the performance of the sys- tem can be significantly increased by increasing the branching factor. Such a result, while not surprising, is good support for the usefulness of projection in se- lecting among actions. It also reaffirms the need for high-quality action generation (Goodman 1993). Conclusions This paper has demonstrated that it is possible to build systems that can project situations into the future us- ing previous experience. It has also demonstrated that the usefulness of such projections may be increased through the judicious use of domain knowledge (specif- ically interpretations of raw data and simple qualita- tive models). Finally, it has shown that projection, 1250 Robotics even imperfect projection, can be used to improve the performance of an agent taking action in the world. References Almuallim, H., and Dietterich, T. 1991. Learning with many irrelevant features. In Proceedings of the Ninth National Conference on Artificial Intelligence. Barletta, R., and Mark, W. 1988. Explanation based indexing of cases. In Proceedings of the First DARPA Workship on Case-Bused Reasoning. Brieman, L.; Friedman, J.; Olshen, R.; and Stone, C. 1984. Classification and Regression Trees. Wadsworth. Buntine, W. 1990. Myths and legends in learning classification rules. In Proceedings of the Eighth Nu- tionul Conference on Artificial Intelligence. Callan, J., and Utgoff, P. 1991. Constructive induc- tion on domain information. In Proceedings of the Ninth National Conference on Artificial Intelligence. Fayyad, U., and Irani, K. 1990. What should be minimized in a decision tree? In Proceedings of the Eighth National Conference on Artificial Intelligence. Forbus, K. D., and Falkenhainer, B. 1990. Self- Explanatory Simulations: An integration of qualita- tive and quantitative knowledge. In Proceedings of the 1990 American Association for Artificial Intelligence, 380-387. Lawrence Erlbaum Associates. Goodman, M. 1989. CBR In Battle Planning. In Proceedings the Second DARPA Workshop on Case Bused Reasoning, 312-326. Goodman, M. 1991. A Case-Based, Inductive Archi- tecture for Natural Language Processing. In AAAI Spring Symposium on Machine Leurning of Natural Language and Ontology. Goodman, M. 1993. Projective visualization: Learn- ing to act from experience. In Proceedings of the Eleventh National Conference on Artificial Intelli- gence. Hartigan, J. 1975. Clustering Algorithms. John Wiley and Sons. Klein, G.; Whitaker, L.; and King, J. 1988. Using Analogues to Predict and Plan. In Proceedings of the First DARPA Workship on Case-Bused Reasoning, 250-259. Kuipers, B. 1986. Qualitative simulation. Artificial Intelligence 29:289-338. Miller, G. A., and Johnson-Laird, P. N. 1976. Lun- guuge and Perception. Cambridge, Massachusetts: The Belknap Press of Harvard University Press. Quinlan, J. R. 1986. Induction of decision trees. Mu- chine Learning 1:81-106. Rissland, E., and Ashley, K. 1988. Credit Assignment and the Problem of Competing Factors in Case-Based Reasoning. In Proceedings of the First DARPA Work- ship on Case-Based Reasoning, 250-259. | 1994 | 260 |
1,609 | Learning to Select Useful Landmarks Russell Greiner Siemens Corporate Research Princeton, NJ 08540 greiner@learning.siemens.com Abstract To navigate effectively, an autonomous agent must be able to quickly and accurately determine its current location. Given an initial estimate of its position (per- haps based on dead-reckoning) and an image taken of a known environment, our agent first attempts to lo- cate a set of landmarks (real-world objects at known locations), then uses their angular separation to ob- tain an improved estimate of its current position. Un- fortunately, some landmarks may not be visible, or worse, may be confused with other landmarks, result- ing in both time wasted in searching for invisible land- marks, and in further errors in the agent’s estimate of its position. To address these problems, we propose a method that uses previous experiences to learn a se- lection function that, given the set of landmarks that might be visible, returns the subset which can reliably be found correctly, and so provide an accurate regis- tration of the agent’s position. We use statistical tech- niques to prove that the learned selection function is, with high probability, effectively at a local optimal in the space of such functions. This report also presents empirical evidence, using real-world data, that demon- strate the effectiveness of our approach. 1. Introduction To navigate effectively, an autonomous agent R must be able to quickly and accurately determine its cur- rent location. R can obtain fairly accurate estimates of its position using dead-reckoning; unfortunately, the errors in these estimates accumulate over long dis- tances, which can lead to unacceptable performance (read “bumping into walls” or “locating the wrong of- fice”). An obvious way to reduce this problem is to observe the environment, and use the information in these observations to improve our estimate of R’s po- sition; ~5, the work using Kalman filters (Kosaka & Kak 1992; Cox & Wilfong 1990) and other techniques (Smith & Cheeseman 1987; Kuipers & Levitt 1988; Fennema et al. 1990; Engelson 1992) We will model the environment using only a set of “landmarks”, each a (potentially visible) real-world object at a known loca- tion; these objects could be doors, corners and pictures when specifying the hallways within building, or major Ramana Isukapalli Department of Computer Science Rutgers University ramana@cs.rutgers.edu buildings, junctions and prominent signs when speci- fying the streets within a city.’ Given an initial esti- mate of its position (perhaps based on dead-reckoning) and an image taken of a known environment, R can first attempt to locate a set of possibly visible land- marks, then use their angular separation to obtain an improved estimate of its current position. Landmark-based position estimation is a popular technique in robot navigation (Case 1986; Sugihara 1988; 1987; Levitt & Lawton 1990). Many of these landmark-based methods assume that all landmarks can be found reliably. Unfortunately, some landmarks may not be visible; for example, certain corners may always be in shadow and so are difficult to see, or some hanging pictures may have been removed after the floor-plan was released. These can force R to waste time, searching in vain for invisible landmarks. Worse, some landmarks may be easily confused with others; e.g., door A may be mistaken for door B, or some land- mark A (say the convex corner of two walls) may be occluded by another object B (say the convex corner of filing cabinet) that looks sufficiently similar that R might think that B is A. As this can cause R to believe that A is located at B’s position, these mis-identified objects can produce further errors in R’s estimate of its position.2 It therefore makes sense to search for only the subset of the potentially visible landmarks that can be found ‘Notice thi s i nformation is essentially the same as the information required for the navigation task itself, to spec- ify the destination or some required intermediate points. N.b., we assume that this set of all possible landmarks is known initially; this contrasts with other systems that also attempt to learn the set of landmarks from the observa- tions; cf., (Kuipers & Byun 1988) and others. 2Another possible complication is that R may identify a wide landmark correctly, but mistakenly refer to the wrong position within that landmark. Also, R’uses a set of identi- fied landmarks to locate its position; depending on the ge- ometric positions of these landmarks, small errors in land- mark location may lead to quite large errors in R’s posi- tional estimate. We of course prefer landmarks sets that provide position estimates that are relatively insensitive to errors in landmark identification. Learning Agents 1251 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. reliably, which are not confusable with others, etc. Un- fortunately, it can be very difficult to determine this good subset a priori, as (1) the landmarks that are good for one set of R-positions can be bad for another; (2) the decision to seek a landmark can depend on many difficult-to-incorporate factors, such as lighting conditions and building shape; and (3) the reliability of a landmark can also depend on unpredictable events; e.g., exactly where R happens to be when it observes its environment, how the building has changed after the floor-plan was finalized, and whether objects (per- haps people) are moving around the area where R is looking. These factors make it difficult, if not impos- sible, to designate the set of good landmarks ahead of time. This report presents a way around this problem: Section 2 proposes a method that learns a good “se- lection function” that, given the set of landmarks that may be visible, returns the subset which can usually be found correctly. We also use statistical techniques to prove that this learned selection function is, with high probability, effectively at a local optimum in the space of such functions. Section 3 then presents empir- ical results that demonstrate that this algorithm can work effectively. We first close this section by present- ing a more precise description of the performance task, showing how R estimates its position: Specification of Performance Task: At each point, R will have an estimate 2 of its current position z and a measure of the uncertainty (here the covariance ma- trix). R uses the LMs( x > algorithm to specify the subset of the landmarks that may be visible from each position x; we assume LMs ( jt > is essentially the same as LMs ( x > . (I.e., we assume that R’s estimate of its position is sufficient to specify a good approximation of the set of possibly appropriate landmarks.) R also uses an algorithm Locate( jE, 6, img, lms ) that, given R’s estimate of its position jE and uncertainty &, an image img taken at R’s current position and a set of landmarks lms, returns a new estimated position (and uncertainty) for R. To instantiate these processes: In the current RAT- BOT system (Hancock & Judd 1993), the LMs pro- cess uses a comprehensive “landmark-description” of the environment, which is a complete list of all of the objects in that environment that could be visible, to- gether with their respective positions. This could be based on the floor-plan of a building, which speci- fies the positions of the building’s doors, walls, wall- hangings, etc.; or in another context, it could be a map of the roads of a city, which specifies the locations of the significant buildings, signs, and so forth. The Locate( ?, c?, img, lms ) process first attempts to find each landmark ai E lms within the image img; here it uses ji and (3 to specify where in the image to look for this Zi. It will find a subset of these landmarks, each at some angle (relative to a reference landmark). Locate then uses simple geometric reasoning to obtain a set of new estimates of R’s position; perhaps one from each set of three found landmarks (Hancock & Judd 1994)) or see (Gurvits & Betke 1994). After removing the obvious outliers, Locate returns the centroid of the remaining estimates as its positional-estimate for R, and the variance of these estimates as the measure of uncertainty; see (Hancock & Judd 1993). As our goal is an eficient way of locating R’s po- sition, our implementation uses an inexpensive way of finding the set of landmarks based on simple tests on the visual image; n. b., we are not using a general vision system, which would attempt to actually identify spe- cific objects and specify particular qualities from the visual information.3 2. Function for Selecting Good Landmarks While many navigation systems would attempt to lo- cate a/l of the landmarks that might be visible in an image (i.e., the full set returned by LMs( 2 )), we ar- gued above that it may be better to seek only a subset of these landmarks: By avoiding “problematic” land- marks (e.g., ones that tend to be not visible, or con- fusable), R may be able to obtain an estimate of its location more quickly, and moreover, possibly obtain an estimate that is more accurate. We therefore want to identify and ignore these bad landmarks. We motivate our approach by first pre- senting two false leads: One immediate suggestion is to simply exclude the bad landmarks from the cata- logue of all landmarks that LMs uses, meaning LMs( .> will never return certain landmarks. One obvious com- plication is the complexity of determining which land- marks are bad, as this can depend on many factors, in- cluding the color of the landmark, the overall arrange- ment of the entire environment (which would specify which landmarks could be occluded), the lighting con- ditions, etc. A more serious problem is the fact that a landmark that is hard to see from one R position may be easy to see, and perhaps invaluable, from another; here, R should be able to use that landmark when reg- istering its location from some positions, but not from others. We therefore decided to use, instead, a selection function Se1 that filters out the bad landmarks from the set of possibly visible landmarks, lms = LMs( ii >: Here, each selection function Se& returns a subset Se& ( lms, 2, C? > = lmsi E lms; R then uses this subset to compute its location, returning Locate( 2, 6, img, lms; ). We want to use a selection function Seli such that Locate( 2, +, img, lmsi ) is reliably close to R’s true position, x. To make this 3Figure 3 shows, and describes, the actual “images” we use. Also, this articles does not provide pseudo-code for either LMs or Locate, as our learning algorithm regards these process as black-boxes. 1252 Robotics more precise, let Err( Se&, (x, ji,6, img) ) = 11 x - Locate( 2, 6, img, Seli(LMs(ji), 2,6) ) ]I be the error4 for the selection function Seli and any “situation” (x, 2, &, img), and let AveErr( Seli ) = Et x,g,s,img) [Err( Seh, (x, %h img) > I be the expected error, over the distribution of situa- tions (x, ?, &, img), where E. [.I is the expectation oper- ator. Our goal is a selection function Sel+ that min- imizes this expected value, over the set of possible se- lection functions. The second false lead involves “engineering” this op- timal selection function initially. One problem, as ob- served above, is the difficulty of determining “analyt- ically” which landmarks are going to be problematic for any single situation. Worse, recall that our goal is to find the selection function that works best Ozler the distribution of situations; which depends on the dis- tribution of R’s actual positions when the function is called, the actual intensity of light sources, what other objects have been moved where, etc. Unfortunately, this distribution of situations is not known a priori. We are therefore following a third (successful) ap- proach: of learning a good selection function. Here, we first specify a large (and we hope, comprehensive) class of possible selection functions S = {Se&). Then, given “labeled samples” - each consisting of R’s posi- tion and uncertainty estimates, the relevant landmark- set and image, and as the label, R’s actual position - identify the selection function Se& which minimizes AveErr ( Se& ). Space of Selection F’unction: We define each selec- tion function Sell, E S as a conjunction of its partic- ular set of “heuristics” or “filters”; Filters(Selectk) = {fl'...' fm}, where each filter fi is a predicate that ac- cepts some landmarks and rejects others. Hence, the Selectk( lms, 2, & > procedure will examine each e E lms individually, and reject it if any fi filter re- jects it; see Figure 1. While we can define a large set of such filters, this report focuses on only two parameterized filters: BadTypeK3 (.4!, 2, &) : Reject e if Type( ! ) # Ka TooSmallk,,k:,(!, %, 6) : Reject ! if ]]Posn(e) - 211 > k1 and AngleWidth 2) < Jc:! 4As we are also c onsidering the efficiency of the overall process, we will actually use the slightly more complicated error function presented in Section 3 below. This is also why we did not address the landmark-selection task using robust analysis: Under that approach, our system would first spend time and resources seeking each landmark, and would then decide whether to use each possible correspon- dence. As our approach, instead, specifies which landmarks should be sought, we will gather less data, and so expend fewer resources Sel, ( lms: landmarks, jc: pos ‘n, & : var. ) : landmarks OK-LMs + {} ForEach e E lms KeepLM + T ForEach f, E Filters( Sel, > If [ f*(4 k (i) - Ignore ] Then KeepLM c F End (inner) ForEach If [ KeepLM 3 T ] Then OK-LMs +- OK-LMs + l End (outer) ForEach Return( OK-LMs > End Select Figure 1: Pseudocode for Selj Selection Function where Type(e) f re ers to the type of the landmark !, which can be “Door”, “BlackStrip”, etc.5 The pa- rameter Ka specifies the subset of landmark-types that should be used. Using “Posn(!)” to refer to e’s real- world coordinates and “AngleWidth(!, 2)” to refer to the angle subtended by the landmark e, when viewed from 2, TooSmallk,,k,(e, ?, 6) rejects the landmark 4? if e is both too far away (greater than ICI meters) and also too small (subtends an angle less than k2 degrees), from R’s estimated position X. Using these filters, S = {Selkl,k2,K3} is the set of all selection functions, over a combinatorial class of settings of these three parameters. As stated above, we want to find the best settings of these variables, which minimize the expected error AveErr[ Selk, ,k2,~J 1. Hill-Climbing in Uncertain Space: There are two obvious complications with our task of finding this op- timal setting: First, as noted above, the error function depends on the distribution of situations, which is not known initially. Secondly, even if we knew that in- formation, it is still difficult to compute the optimal parameter setting, as the space of options is large and ill-structured (e.g., Ka is discrete, and there are subtle non-linear effects as we alter kl and kz). We use a standard hill-climbing approach to ad- dress the second problem, based on a set of opera- tors 7 = {ok} that each map one selection function to another; i.e., for each s E S, Q(S) E S is another se- lection function. We use the obvious set of operators: r: increments the value of ICI and 71 decrements ICI’s value; hence T:( Se1 5, 8, {tl,t3,t7} > = Se16, 8, {tl,t3,t7} and 7-;( Sel5, 8, {t1,t3,t7) > = Sel4, 8, {t1,t3,t7je Sim- ilarly, T.$ and 72 respectively increment and decre- ment the ka value. There are 9 different 7$ op- erator, each of which “flips” the ith bit of Ii’s; hence $t Sel5, 8, {t1,t3,t7) > = Sel5, 8, {t3,t7) and Ti”( Sel5, 8, {tl,t3,t7} > = Sel5, 8, {tl,t3,t7,t8}v To address the first problem - viz., that the distri- bution is unknown -- we use a set of observed examples 5The current system contains nine different types: Mis- cellaneous, Black-Strip, Concave-Corner, Convex-Corner, Dark-Door, Light-Door, Picture, FireExtinguisher and Support-between-Windows. Learning Agents 1253 LEARNSF( Sell : selectfn, 6: !l?+, 6: ?I?+ ) : select&i For j c l..oo do T7[se13 ] - { Tk((Sel,) }k Take 6 6 n + m( 5, 17-i Select, 11 32 79 ) samples, u - (Ul, . ..) un) [Each uzLI = (xI, &:,, &%, img;) ] If 3 Sel’ E I[ Sel, ] such that &(U1[Sel,] - ecU)[Sel’] 2 2 then Let Sel,+l t Sel’ else [ Here, VSel’, BU)[Sel,] - @(U)[Sel’] < $1 Return Sel, End For End LEARNSF Figure 2: (Simplified) Pseudocode for LEARNSF to estimate the relevant information: Let p) kl,k2,K3 = ficu)[ Err( Seh, ,k2,K3 > ] = j& xu,EU Err( Se1k,,k2,&, ui ) be the empirical average error of the selection func- tion Selk1,k2,K3 over the set of training samples U = { (xi, C, 6 imgJ }i, which we assume to be indepen- dent and identically distributed. We then use some statistical measure to relate the number of samples seen, to our confidence that .l?i”’ will be close to the real mean pi = Eu j [ Err( Seli, uj ) ] = AveErr( Se& ) value. In particular, we need a function m(. . a) such that, after m(e, S) samples, we can be at least 1-S con- fident that the empirical average a(u) will be within E of the population mean p; i.e., ]U] > m(~, S) + PY[ Ifi@) - ~1 > E] 5 S. If we can assume that the underlying distribution of error values is close to a nor- mal distribution, then we can use rnNorm(~9 6) = ( x y-l 5 2 Cl- -1) 2 where the z(p) = -& J[, e-Gdz function computes the pth quantile of the standard normal distribution n/(0,1) (Bickel & Doksum 1977). The LEARNSF algorithm, sketched in Figure 2,6 combines the ideas of hill-climbing with statistical sampling: Given an initial selection function Sell = Selkl,k2,K3 E S, and the parameters E and 6, LEARNSF will use a sequence of example situations {ui} to climb from the initial Sell through successive neighboring selection functions (Sell, Sel2, Sels, . . .) until reaching, and returning, a final Sel,. With high probabil- ity, this Sel, is essentially a local optimum, More- over, LEARNSF requires relatively few samples for each climb. To state this more precisely: 6We actually use much more efficient, but more com- plex, algorithm that, for example, decides whether to climb to a new Sel,+l c Sel’ after observing each image, (rather than a batch of n images); see (Greiner & Isukapalli 1994; Greiner 1994). Figure 3: RATBOT’S view (looking up at tree orna- ment), and “strip”, corresponding to annulus in image Theorem 1 (from (Greiner & Isukapalli 1994)) The LEARNSF( Se&, E, 6 ) process incrementally produces a series of selection functions Sell, Sel2, . . . , Se&, such that each Sel,+l = r3(SeZ,) for some r3 E I and, with probabil- ity at least 1 - 5, I. the expected error of each selection function is strictly better than its predecessors i.e., ‘4’2 5 j 5 m: AveErr(Sel,-1) < AveErr(Sel,); and 2. the final selection function (returned by LEARNSF), SeL, is an ‘k-local optimum” - i.e., 13 T E 7: AveErr( r(Se&) ) < AveErr( Sel, ) - e . given the statistical assumption that the underlying distri- bution is essentially normal. Moreover, LEARNSF will ter- minate with probability 1, and will stay at any Sel, (be- fore either terminating or climbing to a new Sel,+l) for a number of samples that is polynomial in k, i, 171 and X = max 7~7, SeZEs,u IErr(Se17 u, - Err(r(Sel), u)l, which is the largest diflerence in error between a pair of neighbor- ing selection functions for any sample. cl 3. Empirical To test the theoretical claims that a good selection function can help an autonomous agent to register its position efficiently and accurately, and also that LEARNSF can help find such good selection functions, we implemented various selection functions and the LEARNSF learning algorithm, and incorporated them within the implemented autonomous agent, RATBOT, described in (Hancock & Judd 1993). This section de- scribes our empirical results. We first took a set of 270 “pictures” at known loca- tions within three halls of our building. Each of these pictures is simply an array of 360 intensity values, each corresponding to the intensity at a particular angle, in a plane parallel to the floor; these are shown on right- hand side of Figure 3. 7 We have also identified 157 dif- ferent landmarks in these regions, each represented as 7These were obtained using a “NOMAD 200” robot with a CCD camera mounted on top, pointing up at a spherical mirror (which is actually a Christmas tree ornament); see left-hand side of Figure 3. We then extract from this image a l-pixel annulus, which corresponds to the light intensity at a certain height; see right-hand side of Figure 3. 1254 Robotics a normally-distributed random value with mean zero and variance 0’. Here, we used cr = 0.3m. Recall also that the Locate function needs a value for ti to con- 2--- ---p-2 strain its landmark-location process; we also set & to _ --- s be CT. l!J 560 1 obo 15bo 2obo Image Number Experiment # 1 Results: Figure 4: LEARNSF’S Hill-Climbs, for different initial Given these settings, Selection Functions LEARNSF observed 62 labeled samples before climbing to the new selection function Sell.1 = simply an object of a specified type (one of the nine cat- ((5, 0); [llOlllIlO]), which differs from Sell only by egories), located between a pair of coordinates (~1 9 ~1) not rejecting all Convex-Corners.g It continued us- and (~2, ~2); where, once again, this (x, y) plane is par- ing this selection function for 40 additional samples, allel to the floor and goes through the center of the before climbing to the Sell:2 = ((5, 2); [110111110]) bulb. selection function, which rejects landmarks that are Each experiment used a particular initial selection function, error function, values for E and S, way of es- timating R’s position, and statistical assumption. We first describe one experiment in detail, then discuss a battery of other experiments that systematically vary the experimental parameters. Experiment#l Specification: LEARNSF began with the Sell selection function shown in Figure 4. This function rejects a landmark if either it is more than 5 meters away from our estimated position and both more than 5m from R’s estimated position and also less than 2’. It continued using this Sell:2 function for another 700 samples before LEARNSF terminated, declaring this selection function to be a “0.1-local op- timum” - i.e., none of Sell:z’s neighbors has a utility score that is more than E = 0.1 better than Sell,a. (We found, in fact, that Sell,;! is actually a bona fide local optimum, in that none of its neighbors is even as good as it is.) The solid line (labeled “1”) in Figure 4 shows LEARNSF’S performance here. Each horizontal line- also subtends an angle less than 0 degrees,’ or if segment corresponds to a particular selection func- the landmark’s type is one of Concave-Corner, Con- tion, where the line’s y-value indicates the “average vex-Corner, or Support-between-Windows (these are test error9, of its selection function, which was com- the second, third and ninth types, correspbnding to the bits that are 0 in the Sell row of Figure 4). We used S = 0.05, meaning that we would be wiliing to accept roughly 1 mistake in 20 runs. The E = 0.1 set- ting means that we do not care if the average error of two selection functions differs by less than O.lm; as we allowed errors as large as 4m, this corresponds to an allowable tolerance of only 2.5%. puted by running this selection function through all 270 images.l’ These horizontal lines are connected by vertical lines whose x-value specify the sample numb& when LEARNSF climbed. Table 1 presents a more detailed break-down of this data. Other Variants: Our choice of Sell = ( (5, 0) ; [lnolllllo]) was fairly arbitrary; we also consid- ered the four other reasonable starting selection func- tions shown in Figure 4. Notice that Se12 = ((5, 10); [000000000]) rejects every landmark; and Se13 = ((5, 0); [111111111]) accepts every landmark. Figure 4 also graphs the performance of these func- tions. Notice that LEARNSF finds improvements in all five cases. As our goal is to minimize both positional error and computational time, we use an error function that is the weighted sum of the positional error (which is the difference between the obtained estimated position and the real position) and “#landmarks-to-pos’n-error ra- tio” times the number of landmarks that were selected. Here, we set the ratio to 0.01, to mean, in effect, that each additional landmark “costs” O.Olm. Finally, while we know that image imgi is taken at location xi, it unrealistic to assume that RATBOT will We also systematically varied the other parameters: trying values of E = 1.0, 0.2, 0.1, 0.05, 0.02,0.01, 0.005; 6 = 0.005, 0.01, 0.05, 0.1; 0 = know that information; in general, we assume that RATBOT will instead see an approximate ?jt,. We 8As nothing can subtend an angle strictly less than O”, this first clause is a no-op - i.e., it will not reject any landmark. gse1i:, refers to the selection function reached after j climbs, when starting from Sel,. Hence, Sel,,o E Sel,. “To avoid testing on the training data, we computed this value using a new set of randomly-generated positional estimates, { jti = xz + ul C0”}, where again I(~)’ is a random variable drawn from a O-mean a-variance distribution. Learning Agents 1255 0, 0.3, 0.5, 1.0; and the “#landmark-to-pos’n-error ratio” of 0, 0.02, 0.05, 0.1, 0.2. (The 0 setting tells LEARNSF to consider only the accuracy of a landmark set, and not the cost of finding those landmarks.) We also used LEARNSF HI, a variant of LEARNSF that re- places the ?nNo,-m (e) function with the weaker function, which is based on Hoeffding’s inequality (Ho- effding 1963; Chernoff 1952), and so does not require the assumption that the error values are normally dis- tributed. All of these results are reported, in detail, in (Greiner & Isukapalli 1994). Summary of Empirical Results: The first obvious conclusion is that selection functions are useful; notice in particular that the landmarks they returned enabled R to obtain fairly good positional estimates - within a few tenths of a meter. Notice also that the obvious degenerate selection function Sels which accepted all landmarks, was not optimal; i.e., there were functions that worked more effectively. Secondly, this LEARNSF function works effectively, as it was able to climb to successively better selection functions, in a wide vari- ety of situations. Not surprisingly, we found that the most critical parameter was the initial selection func- tion; the values of E, S, (T and even the “#landmark-to- pos’n-error ratio” had relatively little effect. We also found that this LEARNSF Norm system seemed to work more effectively than the version that did not require the normality assumption, LEARNSFHI: in almost all instances, both systems climbed through essentially the same selection functions, but LEARNSFN,,, re- quired many fewer samples - by a factor of between 10 and 100! (In the numerous different runs that used S = 0.05, LEARNSF Norm climbed a total of 84 times and terminated 24 times, and so had 84 + 24 = 108 opportunities to make a mistake; it made a total of only 3 mistakes all very minor.) Finally, LEARNSF'S behavior was also (surprisingly) insensitive to the ac- curacy of R’s estimated position, over a wide range of errors; e.g. 9 even for non-trivial values of Iz - ?I. 4. Conclusion While there are many techniques that use observed landmarks to identify an agent’s position they all de- pend on being able to effectively find an appropriate set of landmarks, and will produce degraded or unac- ceptable information if the landmarks are not found, or mis-identified. We can avoid this problem by using only the subset of “good” landmarks. As it can be very difficult to determine this subset a priori, we present an algorithm, LEARNSF, that uses a set of training samples to learn a function that selects the appropri- ate subset of the landmarks, which can then be used robustly to determine our agent9s position. We then prove that this algorithm works effectively - both the- oretically and empirically, based on real data obtained using an implemented robot. Acknowledgments We gratefully acknowledge the help we received from Thomas Hancock, Stephen Judd, Long-Ji Lin, Leonid Gurvits and the other members of the RatBOT team. References Bickel, P. J., and Doksum, K. A. 1977. Mathemati- cal Statistics: Basic Ideas and Selected Topics. Oakland: Holden-Day, Inc. Case, M. 1986. Single landmark navigation by mobile robots. In SPIE, volume 727, 231-38. Chernoff, H. 1952. A measure of asymptotic efficiency for tests of a hypothesis based on the sums of observations. Annals of Mathematical Statistics 23:493-507. Cox, I., and Wilfong, G., eds. 1990. Autonomous Robot Vehicles. Springer-Verlag. Engelson, S. P. 1992. Active place recognition using im- age signatures. In SPIE Symposium on Intelligent Robotic Systems, Sensor Fusion V, 393-404. Fennema, C.; Hanson, A.; Riseman, E.; Beveridge, J.; and Kumar, R. 1990. Model-directed mobile robot navi- gation. IEEE Transactions on Systems, Man and Cyber- netics 20(6):1352-69. Greiner, R., and Isukapalli, R. 1994. Learning to select useful landmarks. Technical Report SCR-LS94-473. Greiner, R. 1994. Probabilistic hill-climbing: Theory and applications. Technical report, SCR. Gurvits, L., and Betke, M. 1994. Robot navigation using landmarks. Technical Report SCR-94-TR-474, SCR/MIT. Hancock, T., and Judd, S. 1993. Ratbot: Robot navi- gation using simple visual algorithms. In 1993 IEEE Re- gional Conference on Control Systems. Hancock, T., and Judd, S. 1994. Hallway navigation using simple visual correspondence algorithms. Technical Report SCR-94-TR-479, SCR. Hoeffding, W. 1963. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58(301):13-30. Kosaka, A., and Kak, A. C. 1992. Fast vision-guided mobile robot navigation using model-based reasoning and prediction of uncertainties. Computer Vision, Graphics, and Image Processing 56(3):271-329. Kuipers, B. J., and Byun, Y.-T. 1988. A robust, qual- itative method for robot spatial learning. In AAAI-88, 774-79. Kuipers, B. J., and Levitt, T. S. 1988. Navigation and mapping in large-scale space. AI Magazine 9(2):25-43. Levitt, T. S., and Lawton, D. T. 1990. Qualitative navi- gation for mobile robots. Artificial Intelligence 44:305-60. Smith, R., and Cheeseman, P. 1987. On the representa- tion and estimation of spatial uncertainty. International Journal of Robotics Research 5(4):56-68. Sugihara, K. 1987. Location of a robot using sparse visual information. Robotics Research: The Fourth International Symposium, 319-26. MIT Press. Sugihara, K. 1988. Some location problems for robot nav- igation using a single camera. Computer Vision, Graphics and Image Processing 42(1):112-29. 1256 Robotics | 1994 | 261 |
1,610 | Agents that Learn to Explain Themselves W. Lewis Johnson USC / Information Sciences Institute 4676 Admiralty Way Marina de1 Rey, CA 90292-6695 johnson@isi.edu Abstract Intelligent artificial agents need to be able to explain and justify their actions. They must therefore understand the rationales for their own actions. This paper describes a technique for acquiring this understanding, implemented in a multimedia explanation system. The system de- termines the motivation for a decision by recall- ing the situation in which the decision was made, and replaying the decision under variants of the original situation. Through experimentation the agent is able to discover what factors led to the decisions, and what alternatives might have been chosen had the situation been slightly different. The agent learns to recognize similar situations where the same decision would be made for the same reasons. This approach is implemented in an artificial fighter pilot that can explain the mo- tivations for its actions, situation assessments, and beliefs. Introduction Intelligent artificial agents need to be able to provide explanations and justifications for the actions that they take. This is especially true for computer-generated forces, i.e., computer agents that operate within bat- tlefield simulations. Such simulations are expected to have an increasingly important role in the evaluation of missions, tactics, doctrines, and new weapons sys- tems, and in training (Jones 1993). Validation of such forces is critical-they should behave as humans would in similar circumstances. Yet it is difficult to val- idate behavior through external observation; behav- ior depends upon the agent’s assessment of the situa- tion and its changing goals from moment to moment. Trainees can greatly benefit from automated forces that can explain their actions, so that the trainees can learn how experts behave in various situations. Po- tential users of computer-generated forces therefore at- tach great importance to explanation, just as potential users of computer-based medical consultation systems do (Teach & Shortliffe 1984). Explanations based on traces of rule firings or para- phrases of rules tend not to be successful (Davis 1976; Swartout & Moore 1993; Clancey 198313). They con- tain too many implementation details, and lack in- formation about the domain and about rationales for the design of the system. More advanced explanation techniques encode domain knowledge and problem- solving strategies and employ them in problem solv- ing either as metarules (Clancey 1983a) or in com- piled form (Neches, Swartout, & Moore 1985). In the computer-generated forces domain, however, problem- solving strategies and domain knowledge representa- tions are matters of current research. An intelligent agent in such a domain must integrate capabilities of perception, reactive problem solving, planning, plan recognition, learning, geometric reasoning and visual- ization, among others, all under severe real-time con- straints. It is difficult to apply meta-level or compila- tion approaches in such a way that all of these require- ments can be met at once. This paper describes a system called Debrief that takes a different approach to explanation. Explana- tions are constructed after the fact by recalling the situation in which a decision was made, reconsidering the decision, and through experimentation determin- ing what factors were critical for the decision. These factors are critical in the sense that if they were not present, the outcome of the decision process would have been different. Details of the agent’s implementa- tion, such as which individual rules applied in making the decision, are automatically filtered out. It is not necessary to maintain a complete trace of rule firings in order to produce explanations. The relationships between situational factors and decisions are learned so that they can be applied to similar decisions. This approach of basing explanations on abstract as- sociations between decisions and situational factors has similarities to the REX system (Wick & Thompson 1989). But while REX requires one to create a sep- arate knowledge base to support explanation, Debrief automatically learns much of what it needs to know to generate explanations. The approach is related to techniques for acquiring domain models through ex- perimentation (Gil 1993), except that the agent learns to model not the external world, but itself. Learning Agents 1257 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Control Question Help1 My current lateral separation was too high The desired lateral separation was not achieved. t selected a missile. f started the maneuver to get into the missile’s LAR. 1 cut to increase lateral separation and target aspect. The desired target aspect was achieved. 1 performed a maintain-ta. 1 finished the maneuver to get into the missile’s LAR. The aim-54’s launch acceptability region was achieved. Control Question Figure 1: Part of a an event summary Debrief is implemented as part of the TacAir-Soar fighter pilot simulation (Jones et al. 1993). Debrief can describe and justify decisions using a combination of natural language and diagrams. It is written in a domain-independent fashion so that it can be read- ily incorporated into other intelligent systems, Cur- rent plans call for incorporating it into the REACT system, an intelligent assistant for operators of NASA Deep Space Network ground tracking stations (Hill & Johnson 1994). An Example Consider the following scenario. A fighter is assigned a Combat Air Patrol (CAP) mission, i.e., it should fly a loop pattern, scanning for enemy aircraft. During the mission a bogey (an unknown aircraft) is spotted on the radar. The E2C, an aircraft whose purpose is to scan the airspace and provide information to the fighters, confirms that the bogey is hostile. The fighter closes in on the bogey, fires a missile which destroys the bogey, and then resumes its patrol. After each mission it is customary to debrief the pi- lot. The pilot is asked to describe the engagement from his perspective, and explain key decisions along the way. The pilot must justify his assessments of the situation, e.g., why the bogey was considered a threat. TacAir-Soar is able to simulate pilots executing mis- sions such as this, and Debrief is able to answer ques- tions about them. TacAir-Soar controls a simulation environment called ModSAF (Calder et al. 1993) that simulates the behavior of military platforms. TacAir- Soar receives information from ModSAF about aircraft status and radar information, and issues commands to fly the simulated aircraft and employ weapons. After an engagement users can interact with Debrief to ask questions about the engagement. The following is a typical interaction with Debrief. Figure 2: Explanations of the agent’s decisions Questions are entered through a window interface, by selecting a type of question and pointing to the event or assertion that the question refers to. The first question selected is of type Describe-Event, i.e., describe some event that took place during the engagement; the event chosen is the entire mission. Debrief then generates a summary of what took place during the mission. The user is free to select statements in the summary and ask follow-on questions about them. Figure 1 shows part of a typical mission summary. One of the statements in the summary, “I started using my weapons ,” has been selected by the user, so that a follow-on question may be asked about it. Figure 2 shows the display at a later point in the dialog, after follow-on questions have been asked. First, a ques- tion of type Explain-Action was asked of the decision to employ weapons, i.e., explain why the agent chose to perform this action. The explanation appears in the figure, beginning with the sentence “I started using my weapons because the intercept geometry was selected and...” Debrief also lists an action that it did not take, but might have taken under slightly different circum- stances: flying toward the bogey to decrease distance. One can see that the agent’s actions are motivated largely by previous assessments and decisions. The bottom of Figure 2 shows the answer to a follow-on question relating to one of those assessments, namely “ROE was achieved ,” 1 Debrief lists the following fac- ‘ROE stands for Rules of Engagement, i.e., the condi- tions under which the fighter is authorized to engage the enemy. 1258 Robotics tors: the bogey was known to be hostile (i.e., a “bandit”), the bogey was identified through electronic means and confirmation of the identification was ob- tained from the E2C. In order to answer such questions, Debrief does the following. First, it recalls the events in question and the situations in which the events took place. When summarizing events, it selects information about the intermediate states and subevents that should be pre- sented, selects appropriate media for presentation of this information (the graphical display and/or natu- ral language), and then generates the presentations. To determine what factors in the situation led to the action or conclusion, Debrief invokes the TacAir-Soar problem solver in the recalled situation, and observes what actions the problem solver takes. The situation is then repeatedly and systematically modified, and the effects on the problem solver’s decisions are ob- served. Beliefs are explained by recalling the situation in which the beliefs arose, determining what decisions caused the beliefs to be asserted, and determining what factors were responsible for the decisions. Implementation Concerns Debrief is implemented in Soar, a problem-solving ar- chitecture that implements a theory of human cogni- tion(Newel1 1990). Problems in Soar are represented as goals, and are solved within problem spaces. Each problem space consists of a state, represented as a set of attribute-value pairs, and a set of operators. All pro- cessing in Soar, including applying operators, propos- ing problem spaces, and constructing states, is per- formed by productions. During problem solving Soar repeatedly selects and applies operators to the state. When Soar is unable to make progress, it creates a new subgoal and problem space to determine how to pro- ceed. Results from these subspaces are saved by Soar’s chunking mechanism as new productions, which can be applied to similar situations. The explanation techniques employed in Debrief are not Soar-specific; however, they do take advantage of certain features of Soar. e The explicit problem space representation enables Debrief to monitor problem solving when construct- ing explanations. o Since Soar applications are implemented in produc- tion rules, it is fairly straightforward to add new rules for explanation-related processing. o Learning enables Debrief to reuse the results of pre- vious explanation processing, and build up knowl- edge about the application domain. The current implementation of Debrief consists of thirteen Soar problem spaces. Two are responsible for inputing questions from the user, three recall events and states from memory, four determine the motiva- tions for actions and beliefs, three generate presenta- tions, and one provides top-level control. The follow- ing sections describe the system components involved in determining motivations for decisions and beliefs; other parts of the system are described in (Johnson 1994). Memory and Recall In order for Debrief to describe and explain decisions, it must be able to recall the decisions and the situa- tions in which they occurred. In order words, the agent requires an episodic memory. Debrief includes produc- tions and operators that execute during the problem solving process in order to record episodic information, and a problem space called Recall-State that recon- structs states using this episodic information. The choice of what episodic information to record is determined by a specification of the agent’s working memory state. This specification identifies the state attributes that are relevant for explanation, and iden- tifies their properties, e.g., their cardinality and signa- ture, and how the attribute values may change during problem solving. In order to apply Debrief to a new problem solver, it is necessary to supply such a specifi- cation for the contents of the problem solver’s working memory, and indicate which operators implement de- cisions what should be explainable. However, it is not necessary to specify how the problem solver uses its working memory in making decisions-that is deter- mined by Debrief automatically. When the problem solver applies an operator that as marked as explainable, Debrief records the operator application in a list of events that took place during the problem solving. It also records all attribute values that have changed since the last problem solving event that was recorded. Debrief then builds chunks that associate the state changes with the problem solving event. Once these chunks are built, the state changes can be deleted from working memory, because the chunks are sufficient to enable Debrief to recall the working memory state. During explanation, when Debrief needs to recall the state in which a problem solving event occurred, it invokes the Recall-State problem space. This space reconstructs the state by proposing possible attribute values; the chunks built previously fire, selecting the value that was associated with the event. Recall-State aggregates these values into a copy of the state at the time of the original event, and returns it. This result is chunked as well, enabling Debrief immediately to re- call the state associated with the event should it need to refer back to it in the future. This process is an instance of data chunking, a common mechanism for knowledge-level learning in Soar systems (Rosenbloom, Laird, & Newell 1987). Debrief thus makes extensive use of Soar’s long term memory, i.e., chunks, in constructing its episodic mem- ory. In a typical TacAir-Soar run several hundred such chunks are created. This is more economical than sim- ply recording a trace of production firings, since over Learning Agents 1259 Test-Qpc or-Applicability “i is useful because it causes chunks to be built that fa- cilitate subsequent analysis. After a state has been found in which the recalled operator is applicable, the next step is to determine applicability criteria, i.e., identify what attributes of the state are responsible for the operator being se- lected. This also involves applying the Test-Operator- Applicability operator to construct mental simulations. Mental simulation Figure 3: The process of evaluating decisions 6000 productions fire in a typical TacAir-Soar run. Since Soar has been shown be able to handle memories containing hundreds of thousands of chunks (Dooren- bos 1993), there should be little difficulty in scaling up to more complex problem solving applications. Explaining Actions and Conclusions Suppose that the user requests the motivation for the action “I started using my weapons.” Debrief recalls the type of event involved, operator that was applied, the problem space in which it was applied, and the problem solving state. In this case the event type is Start-Event, i.e., the beginning of an operator appli- cation, the operator is named Employ-Weapons, and the problem space is named Intercept. The situation was one where the agent had decided to intercept the bogey, and had just decided what path to follow in per- forming the intercept (called the intercept geometry). Analysis of recalled events such as this proceeds as shown if Figure 3. The first step, testing applicabil- ity, verifies that TacAir-Soar would select an Employ- Weapons operator in the recalled state. An operator called Test-Operator-Applicability performs the veri- fication, by setting up a “mental simulation” of the original decision, and monitoring it to see what opera- tors are selected. This initial test of operator applicability is impor- tant for the following reasons. State changes are not recorded in episodic memory until the operator has already been selected. The operator might therefore modify the state before Debrief has a chance to save it, making the operator inapplicable. This is not a problem in the case of Employ-Weapons, but if it were Debrief would attempt to establish applicability, which involves recalling the state immediately preceding the state of the event, and trying to find an interpolation of the two states in which the operator would be se- lected. But even when recalling the precise problem solving state is not a problem, verifying applicability Given the problem space Intercept, the recalled state, the operator Employ-Weapons, and the decision Start- event (Employ-Weapons), Test-Operator-Applicability operates as follows. It creates an instance of the In- tercept problem space as a subspace, and assigns as its state a copy of the recalled state. The working memory specification described above is helpful here: it deter- mines which attributes have to be copied. This state is marked as a simulation state, which activates a set of productions responsible for monitoring mental sim- ulations. Test-Operator-Applicability copies into the simulation state the event and the category of decision being evaluated. There are three such categories: per- ceptions, which recognize and register some external stimulus, conclusions, which reason about the situa- tion and draw inferences from it, and actions, which are operations that have some effect on the external world. Employ-Weapons is thus an action. The In- tercept problem space is disconnected from external sensors and effecters (the ModSAF simulator), so that mental simulation can be freely performed. Execution then begins in the problem space. The first operator that is selected is Employ-Weapons. The monitoring productions recognize this as the desired operator, re- turn a flag to the parent state indicating that the de- sired event was observed, and the mental simulation is terminated. If a different operator or event had been selected instead, Debrief would be checked to see if it is of the same category as the expected operator, i.e., another action. If not, simulation is permitted to continue; otherwise simulation is terminated and the a description of the operator that applied instead is returned. Whenever a result is returned from mental simula- tion, a chunk is created. Such chunks may then be applicable to other situations, making further men- tal simulation unnecessary. Figure 4 shows the chunk that is formed when Debrief simulates the selection of the Employ-Weapons operator. The conditions of the chunk appear before the symbol + and actions follow. Variables are symbols surrounded by angle brackets, and attributes are preceded by a carat (A). The condi- tions include the expected operator, Employ-Weapons, the problem space, Intercept, and properties of the state, all properties of the bogey. If the operator is found to be inapplicable, a different chunk is produced, that indicates which operator is selected instead of the expected one. 1260 (sp chunk-230 :chunk (goal <gl> -operator <ol> -state Csl>) (Cal> ?mtne test-operator-applicability -expected-operator employ-weapons -expected-step *none* -problem-space intercept) (<sl> *simulated-state <rl>) (<rl> *local-state <li>) (<li> -bogey <bi>) (Cbl> -intention known-hostile -roe-achieved *yes* *intercept-geometry-selected *yes* *contact *yes*> (<ll> -primary-threat <bl>) --> (<sl> -applicable-operator employ-weapons)) Figure 4: An example chunk These chunks built during mental simulation have an important feature-they omit the details of how the operator and problem space involved is implemented. This is an inherent feature of the chunking process, which traces the results of problem solving in a prob- lem space back to elements of the supergoal problem space state. In this case the state recalled from episodic memory is the part of the supergoal problem space state, so elements of the recalled state go into the left hand side of the chunk. Determining the cause for decisions At this point it would be useful to examine the chunks built during mental simulation in order to proceed to generate the explanation. Unfortunately, *productions in a Soar system are not inspectable within Soar. This limitation in the Soar architecture is deliberate, reflect- ing the difficulty that humans have in introspecting on their own memory processes. It does not a serious problem for Debrief, because the chunks built during mental simulation can be used to recognize which at- tributes of the state are significant. The identification of significant attributes is per- formed in the Determine-Applicability-Criteria prob- lem space, which removes attributes one by one and re- peatedly applies Test-Operator-Applicability. If a dif- ferent operator is selected, then the removed attribute must be significant. If the value of a significant at- tribute is a complex object, then each attribute of that object is analyzed in the same way; the same is true for any significant values of those attributes. Meanwhile, if the variants resulted in different operators being se- lected, the applicability criteria for these operators are identified in the same manner. This generate-and-test approach has been used in other Soar systems to enlist recognition chunks in service of problem solving (Vera, Lewis, & Lerch 1993), and is similar to Debrief’s mech- anism for reconstructing states from episodic memory. Since the state representations are hierarchically orga- nized, the significant attributes are found quickly. If chunking were not taking place, Debrief would be performing a long series of mental simulations, most of which would not yield much useful information. But the chunks that are created help to ensure that vir- tually every mental simulation uncovers a significant attribute, for the following reason. Subgoals are cre- ated in Soar only when impasses occur. Test-Operator- Applicability instantiates the mental simulation prob- lem space because it tries to determine whether the recalled operator is applicable, is unable to do so, and reaches an impasse. When chunks such as the one in Figure 4 fire, they assert that the operator is appli- cable, so no impasse occurs. Mental simulation thus occurs only in situations that fail to match the chunks that have been built so far. In the case of the Employ- Weapons operator, a total of seven mental simulations of variant states are required: two to determine that the bogey is relevant, and five to identify the bogey’s relevant attributes. Furthermore, even these mental simulations become unnecessary as Debrief gains experience explaining missions. Suppose that Debrief is asked to explain a different Employ-Weapons event. Since most of the significant features in the situation of this new event are likely to be similar to the significant features of the previous situation, the chunks built from the previous mental simulations will fire. Mental simulation is re- quired for the situational features that are different, or if the operator was selected for different reasons. Two kinds of chunks are built when Determine- Applicability-Criteria returns its results. One type identifies all of the significant features in the situa- tion in which the decision was made. The other type identifies an operator that might have applied instead of the expected operator, and the state in which the operator applies. These chunks are created when men- tal simulation determines that an operator other than the expected one is selected. Importantly, the chunks fire whenever a similar decision is made in a similar situation. By accumulating these chunks Debrief thus builds an abstract model of the application domain, associating decisions with their rationales and alter- natives. The problem solver’s performance-oriented knowledge is reorganized into a form suited to sup- porting explanation. Performing mental simulation in modified states complicates mental simulation in various respects. The result of deleting an attribute is often the selection of an operator in mental simulation to reassert the same attribute. Debrief must therefore monitor the simu- lation and detect when deleted attributes are being reasserted. The modified state may cause the problem solver to fail, resulting in an impasse. Mental sim- ulation must therefore distinguish impasses that are a normal result of problem solving from impasses that suggest that the problem solver is in an erroneous state. Learning Agents 1261 There is one shortcoming of the analysis technique described here. Chunking in Soar cannot always back- trace through negated conditions in the left hand sides of productions. Therefore if the problem solver opted for a decision because some condition was absent in the situation, Debrief may not be able to detect it. Developers of Soar systems get around this problem in chunking by using explicit values such as *unknown* to indicate that information is absent. This same tech- nique enables Debrief to identify the factors involved. Relationship to other exploratory learning approaches The closest correlate to Debrief’s decision evaluation capability is Gil’s work on learning by experimentation (Gil 1993). Gil’s EXPO system keeps track of operator applications, and the states in which those operators were applied. If an operator is found to have differ- ent effects in different situations, EXPO compares the states to determine the differences. Another system by Scott and Markovich (Scott & Markovich 1993) per- forms an operation on instances of a class of objects, to determine whether it has different effects on differ- ent members of the class. This enables it to discover discriminating characteristics within the class. Some exploratory learning systems, such as Raja- money’s systems (Raj amoney 1993)) invest significant effort to design experiments that provide the maximum amount of information. This is necessary because ex- periments can be costly and can have persistent effects on the environment. Debrief’s chunking-based tech- nique filters out irrelevant experiments automatically, without significant effort. Side events on the environ- ment are not a concern during mental simulation. Explaining Beliefs Explaining beliefs, e.g., that ROE was achieved, in- volves many of the same analysis steps used for ex- plaining decisions. Debrief starts by searching mem- ory for the nearest preceding state in which the belief came to be held. It determines what operator was being applied during that state, and uses Establish- Applicability if necessary to make sure that the opera- tor applies in the recalled state. If the belief had to be retracted in order to make Test-Operator-Applicability succeed, then the operator was responsible for assert- ing the belief. Such is the case for the belief that ROE is achieved, which is asserted by an operator named ROE-Achieved. Otherwise, Debrief would remove the belief and attempt mental simulation again; if the be- lief is asserted in the course of applying the operator, the operator is probably responsible for the belief. Summary of the Effects of Learning Learning via chunking takes place throughout the De- brief system. The following is a summary of the differ- ent types of chunks that are produced: 1262 Robotics Episodic memory recognition chunks: event + at- tribute value + recognition; State recall chunks: event ---) state; Mental simulation chunks: event + problem space + state - applicable or inapplicable + alternative operator; Applicability analysis chunks: event + problem space + state -+ significant state attributes; event -I- problem space + state + alternative operator + alternative state; Natural language generation chunks: case frame -+ list of words; content description -+ list of utter- ances; Presentation chunks: content description + user model -+ utterances + media control commands + user model updates. The presentation mechanisms that yield the latter two types of chunks are described in (Johnson 1994). Alto- gether, these chunks enable Debrief to acquire signif- icant facility in explaining problem solving behavior. These chunks result in speedups during the course of explaining a single mission. Future experiments will determine the transfer effects between missions. Evaluation and Status The implementation of Debrief comprises over 1700 productions; in a typical session these are augmented by between 500 and 1000 chunks. Debrief currently can describe and/or explain a total of 66 types of events in the tactical air domain. Its natural language gener- ation component has a vocabulary of 259 words and phrases. Debrief can explain a range of one-on-one and one-on-two air-to-air engagements. Formative evaluations of Debrief explanations have been performed with US Naval Reserve fighter pi- lots. These evaluations confirmed that explanations are extremely helpful for validating the agent’s per- formance, and building confidence in it. They also underscored the importance of having the agent jus- tify its beliefs-the evaluators frequently wanted to ask questions about assertions made by Debrief during the course of the explanation. This motivated the develop- ment of support for the Explain-Belief question type. There was immediate interest on the part of the sub- ject matter experts in using Debrief to understand and validate the behavior of TacAir-Soar agents. The weakest point of the current system is its natu- ral language generation capability. However, this was found not to be a major concern for the evaluators. Their primary interest was in understanding the think- ing processes of TacAir-Soar, and to the extent that Debrief made that reasoning apparent it was consid- ered effective. Conclusion This paper has described a domain-independent tech- nique for analyzing the reasoning processes of an in- telligent agent in order to support explanation. This technique reduces the need for extensive knowledge ac- quisition and special architectures in support of expla- nation. Instead, the agent can construct explanations on its own. Learning plays a crucial role in this process. Next steps include extending the range to questions that can be answered, improving the natural language generation, and making greater use of multi-media pre- sentations. There is interest in using the mental simu- lation framework described here to improve the agent’s problem solving performance, by discovering alterna- tive decision choices with improved outcomes. Acknowledgements The author wishes to thank Paul Rosenbloom, Milind Tambe, and Yolanda Gil for their helpful comments. Dr. Johnson was supported in part by the ARPA and the Naval Research Laboratory under contract number N00014-92-K-2015 ( via a subcontract from the Univer- sity of Michigan). Views and conclusions contained in this paper are the author’s and should not be inter- preted as representing the official opinion or policy of the U.S. Government or any agency thereof. References Calder, R.; Smith, J.; Courtemanche, A.; Mar, J .; and Ceranowicz, A. 1993. ModSAF behavior simulation and control. In Proceedings of the Third Conference on Computer Generated Forces and Behavioral Rep- resentation, 347-359. Orlando, FL: Institute for Sim- ulation and Training, University of Central Florida. Clancey, W. 1983a. The advantages of abstract con- trol knowledge in expert system design. In Proceed- ings of the National Conference on Artificial Intelli- gence, 74-78. Clancey, W. 1983b. The epistemology of a rule-based expert system: A framework for explanation. Artifi- cial Intelligence 20(3):215-251. Davis, R. 1976. Applications of Meta-Level Knowl- edge to the Construction, Maintenance, and Use of Lurge Knowledge Buses. Ph.D. Dissertation, Stanford University. Doorenbos, R. 1993. Matching 100,000 learned rules. In Proceedings of the National Conference on Artifi- cial Intelligence, 290-296. Menlo Park, CA: AAAI. Gil, Y. 1993. Efficient domain-independent experi- mentation. Technical Report ISI/RR-93-337, USC / Information Sciences Institute. Appears in the Pro- ceedings of the Tenth International Conference on Machine Learning. Hill, R., and Johnson, W. 1994. Situated plan attri- bution for intelligent tutoring. In Proceedings of the National Conference on Artificial Intelligence. Johnson, W. 1994. Agents that explain their own ac- tions. In Proc. of the Fourth Conference on Computer Generated Forces and Behavioral Representation. Or- lando, FL: Institute for Simulation and Training, Uni- versity of Central Florida. World Wide Web access: http://www.isi.edu/soar/debriefable.html. Jones, R.; Tambe, M.; Laird, J.; and Rosenbloom, P. 1993. Intelligent automated agents for flight training simulators. In Proceedings of the Third Conference on Computer Generated Forces and Behavioral Rep- resentation, 33-42. Orlando, FL: Institute for Simu- lation and Training, University of Central Florida. Jones, R. 1993. Using CGF for analysis and combat development. In Proceedings of the Third Conference on Computer Generated Forces and Behavioral Rep- resentation, 209-219. Orlando, FL: Institute for Sim- ulation and Training, University of Central Florida. Neches, R.; Swartout, W.; and Moore, J. 1985. Enhanced maintenance and explanation of expert systems through explicit models of their develop- ment. IEEE Transactions on Software Engineering SE-11(11):1337-1351. Newell, A. 1990. Unified Theories of Cognition. Cam- bridge, MA: Harvard University Press. Raj amoney, S. 1993. The design of discrimination experiments. Machine Learning 185-203. Rosenbloom, P.; Laird, J.; and Newell, A. 1987. Knowledge level learning in Soar. In Proceedings of the Seventh National Conference on Artificial Intelli- gence, 618-623. Menlo Park, CA: American Associa- tion for Artificial Intelligence. Scott, P., and Markovich, S. 1993. Experience se- lection and problem choice in an exploratory learning system. Machine Learning 49-68. Swartout, W., and Moore, J. 1993. Explanation in second generation expert systems. In David, J.-M.; Krivine, J.-P.; and Simmons., R., eds., Second Gen- eration Expert Systems. Springer-Verlag. 543-585. Teach, R., and Shortliffe, E. 1984. An analysis of physicians’ attitudes. In Buchanan, B., and Shortliffe, E., eds., Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project. Reading, MA: Addison-Wesley. 635-652. Vera, A.; Lewis, R.; and Lerch, F. 1993. Situ- ated decision-making and recognition-based learning: Applying symbolic theories to interactive tasks. In Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society, 84-95. 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1,611 | Learning to Explore and Build Maps* David Pierce and Benjamin Kuipers Department of Computer Sciences University of Texas at Austin Austin, TX 78712 dmpierce@cs.utexas.edu, kuipers@cs.utexas.edu Abstract Using the methods demonstrated in this paper, a robot with an unknown sensorimotor system can learn sets of features and behaviors adequate to explore a continuous environment and abstract it to a finite- state automaton. The structure of this automaton can then be learned from experience, and constitutes a cognitive map of the environment. A generate-and- test method is used to define a hierarchy of features defined on the raw sense vector culminating in a set of continuously differentiable local state variu bles. Con- trol laws based on these local state variables are de- fined for robustly following paths that implement re- peatable state transitions. These state transitions are the basis for a finite-state automaton, a discrete ab- straction of the robot’s continuous world. A variety of existing methods can learn the structure of the au- tomaton defined by the resulting states and transi- tions. A simple example of the performance of our implemented system is presented. Introduction Imagine that you find yourself in front of the control console for a teleoperated robot (Figure 1). The dis- play at the left of the console is your only sensory input from the robot. The joystick on the right can be used to move the robot through its environment. You do not know how the joystick affects the robot’s motion, but you do know that the robot does not move when the joystick is in its zero position. The robot could be a mobile robot in an office building or laboratory or it could be a submarine in the ocean. Your mission is to develop a model of the robot’s environment as well as its sensorimotor interface to that environment. We present a solution to this learning problem by showing how an autonomous agent can learn a discrete model of its continuous world with no a priori knowl- edge of the structure of its world or of its sensorimo- *This work has taken place in the Qualitative Reason- ing Group at the Artificial Intelligence Laboratory, The University of Texas at Austin. Research of the Qualita- tive Reasoning Group is supported in part by NSF grants IRI-8904454, IRI-9017047, and IRI-9216584, and by NASA contracts NCC 2-760 and NAG 9-665. I Sensory input I I Control Figure 1: The tubdu MSU learning problem is illustrated by this interface to a teleoperated robot with an unin- terpreted sensorimotor apparatus in an unknown environ- ment. The problem is to develop a practical understanding of the robot and its environment with no initial knowledge of the meanings of the sensors or the effects of the control signals. tor apparatus. The solution is composed of two steps: 1) learning an abstraction of the continuous world to a finite-state automaton and 2) inferring the struc- ture of the finite-state automaton. The second step has been studied extensively (e.g., Angluin 1978, Gold 1978, Kuipers 1978, Angluin 1987, Rivest & Schapire 1993). In this paper, we focus on the first step. The rest of the paper gives the details of the abstraction- learning method illustrated with an example from the world of mobile robotics. Overview: From continuous world to finite-state automaton The details of the method for learning a discrete ab- straction of a continuous world are given below and are illustrated in Figure 2. Given: a robot with an uninterpreted, well- behaved sensorimotor apparatus, in a continuous, static world. The definition of “well-behaved” is given in a later section. Learn : a discrete abstraction of the continuous world, specifically, a finite-state automaton. The solution method involves three stages. 1264 Robotics From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. 3. Interface Figure 2: The continuous world is abstracted to a finite- state automaton thereby reducing the task of modeling a continuous world to the well-understood task of modeling a finite-state world. The abstraction is created by 1) learning a set of smooth features y defined as functions of the raw sense vector s, 2) learning reliable path-following behav- iors based on those features, and 3) defining an interface that provides the discrete sense values and actions of the finite-state automaton. The discrete learning agent is any learning mechanism that can infer the structure of a finite- state automaton. 1. Feature learning Learn a set of almost-everywhere smooth (continu- ously differentiable) features, defined as functions on the raw sensory input. A generate-and-test method is used. 2. Behavior learning Learn a model of the motor apparatus, specifically, a set of primitive actions, one per degree of freedom. A typical mobile robot has two degrees of freedom: translation and rotation. Learn a model (called the static action model) for predicting the context-dependent effects of primitive actions on features. Use the static action model to define a set of be- haviors for finding paths using hill-climbing, and an initial set of open-loop behaviors for following paths. Learn a model (called the dynamic action model) for predicting the effects of actions while path-following. Use the dynamic action model to define closed-loop behaviors for following paths more reliably. 3. Defining the abstraction Define an interface to the robot’s sensorimotor appa- ratus that abstracts the continuous environment to a finite-state automaton. The learned path-following behaviors produce state transitions; their termina- tions define states. The abstraction-learning method has been applied to a simulated mobile robot. Its sensory system con- sists of a ring of 16 distance sensors giving distances to nearby objects up to a maximum distance of two meters away. It has a tank-style motor apparatus with two real-valued control signals in the range [-1 , l] spec- ifying the speeds of the left and right treads respec- tively. The robot can turn in place, move forward, move backward, or do a combination of both. The robot is placed in a simple environment consisting of a single room roughly ten meters square. Feature learning A feature, as defined in this paper, is any function over time whose current value is completely determined by the history of current and past values of the robot’s raw sense vector. Examples of features are: the raw sense vector itself (an example of a vector feature), the components of that vector (each an example of a scalar feature), the average value of those components, and the derivatives with respect to time of those com- ponents. Local state variables The state of a robot in a continuous world is repre- sented by a state vector x whose components are called state variables. For example, a mobile robot’s state can be described by the state vector x = (~1,22,13) where ~1 and ~2 give the robot’s position and 0 its orienta- tion. The tabda rasa robot does not have direct access to its state variables, but it can use learned scalar fea- tures as local state variables. A local state variable is a scalar feature whose gradient (its vector of deriva- tives with respect to the robot’s set of state variables) is approximately constant and nonzero over an open region in state space. When the robot is in that re- gion, a local state variable provides one coordinate of information about the state of the robot: constrain- ing that feature to have a specific value reduces the dimensionality of the world by one. With enough in- dependent features (i.e., features whose gradients are not collinear), the state of the robot can be completely determined, and hence the values of all of its features can be determined. The catch is that the robot cannot directly measure feature gradients since it does not have direct access to its state. However, if the world is static and the effects of the actions can be approximated as linear for a local open region R, then the robot can recognize features suitable as local state variables by analyzing the effects of the actions on the features as is shown below. In the following, x is the unknown state vector for the robot, y is a scalar feature, $ is the derivative of y with respect to time, and u is the robot’s vector of motor control signals. The first equation is the general Learning Agents 1265 formulation for a dynamical system. (1) - = f(x,u) (2) f(C 0) = 0 {static world} (3) f(x,u) = FRU { 2, linearity assumption) (4) j) = J%i {chain rule} (5) G M zFRu (1, 3) Here FR is a matrix used to approximate function 9 as a linear function of u for states in open region R con- taining x. The conclusion from equation (5) is that $ is a nonzero, linear function of the action vector u if and only if the gradient g is nonzero and approximately constant. Therefore m order to recognize a local state variable (a feature with a nonzero, approximately con- stant gradient), the robot need only demonstrate that the feature’s derivative can be estimated as a linear function of the action vector. This is the basis of the test portion of the generate-and-test feature-learning algorithm. A feature y is a candidate local state vari- able if its derivative is small for small actions. It is a bona fide local state variable, for a region R, if its derivative can be estimated by jl = WR u where WR is a matrix. Learning and representing this matrix is the job of the static action model. A sensorimotor appara- tus is well-behaved if the following is almost-everywhere true: Given state x there exists an open region R con- taining x such that the dynamics of the sensorimotor apparatus can be approximated by S = WRU where s is the raw sense vector and WR is a matrix that depends on the region. This is not as restrictive as it first ap- pears, since nonlinear and discontinuous functions can often be approximated by piecewise linear functions. A generate-and-test approach A robot’s raw sensory features may not be very suitable as local state variables. For example, sonar sensors have discontinuities due to specular reflection. Their values are smooth for small regions in state space, but it is preferable to have features usable over larger re- gions. Fortunately, by applying the min operator to a set of sonar values, a new feature is obtained that is smooth over a much larger region and thus more suitable as a local state variable. This example illus- trates the principle that, if a sensory system does not directly provide useful features, it may be possible to define features that are useful. This principle is the foundation for a generate-and-test approach to feature learning, implemented with a set of generators for pro- ducing new features and testers for recognizing useful features. The following set of generators, when applied to a sensory system with a ring of distance sensors, are instrumental in discovering features corresponding to minimum distances to nearby objects. The first two, the group and image generators, are useful for ana- lyzing the structure of a sensory system and defining features that are the basis for higher-level features such as motion detectors. 1266 Robotics o The group generator splits a vector feature into sub- vectors, called group features, of highly correlated components. When applied to a sensory system with dist ante sensors and compass, the distance sensors - I are collected into a single group. l The image generator takes a group feature and as- sociates a position with each component thus pro- ducing an image feature whose structure reflects the structure of the group of sensors. A relaxation algo- rithm (Figure 3) is used to assign positions to com- ponents so that the distance between two compo- nents sa and sj in the image is proportional to the measured dissimilarity d(i, j) = Et Isi - sj (t) I. The image generator is based on the principle that sensors that are physically close together will, on av- erage, produce similar values (Pierce 1991). (4 0') Figure 3: A relaxation algorithm is used to define an im- age feature for the group feature containing the 16 distance sensors. a) The components are randomly assigned to po- sitions in a two-dimensional plane. b) The components self-organize into a ring in which components with similar values appear close together in the image. The local-minimum generator takes an image feature and produces a “blob” image feature. A blob image feature provides a mechanism for focus of attention by associating a binary strength with each compo- nent. Each component in the image whose value is less than that of its neighbors is given strength 1. Figure 4a illustrates the application of this genera- tor to the image feature of distance values. The truclcer generator takes a blob image feature and monitors the blobs (components with strength equal to 1) within it. The output is a list of blob features giving the value and image-relative position of each input blob. Figure 4b illustrates the application of this generator. The generators are typed objects: the type of a gener- ator is given by the type of feature to which it applies and the type of feature that it creates. For example, the image generator applies to group features and cre- ates image features. The only tester needed for finding potential local state variables is the smoothness tester. A feature is considered smooth if the standard deviation of its derivative with respect to time is less than a certain value. The generate-and-test approach was applied to the robot with 16 distance sensors. None of the distance sensors were identified as smooth, but the 1 local-m&generator (a) J \ tracker-generator . Figure 4: The local-min and tmclcer generators are applied Figure 4: The local-min and tmclcer generators are applied to the learned image feature to produce new scalar features to the learned image feature to produce new scalar features that wiII serve as local state variables. (In this diagram, that wiII serve as local state variables. (In this diagram, sense values are represented by the sizes of the disks.) From sense values are represented by the sizes of the disks.) From the robot’s perspective, these features are local minima of a the robot’s perspective, these features are local minima of a sensory image formed by organizing an unstructured, unin- sensory image formed by organizing an unstructured, unin- terpreted sense vector into a structured ring whose orgam- terpreted sense vector into a structured ring whose orgam- zation reflects intersensor correlations. From our perspec- zation reflects intersensor correlations. From our perspec- tive, the features are minimum distances to nearby objects. tive, the features are minimum distances to nearby objects. learned blob value features were. The size of the search learned blob value features were. The size of the search space is kept reasonable by the typing of the feature space is kept reasonable by the typing of the feature generators which makes the search space deep but not generators which makes the search space deep but not wide. wide. Behavior learning Behavior learning With a good set of features that can serve as local state With a good set of features that can serve as local state variables, the problem of abstracting from a continuous variables, the problem of abstracting from a continuous world to a finite-state automaton is half solved. The world to a finite-state automaton is half solved. The features can be used to express constraints of the form features can be used to express constraints of the form Y Y = y* that define paths. = y* that define paths. By following such a path By following such a path until it ends, the robot executes a behavior that can until it ends, the robot executes a behavior that can be viewed as an atomic state transition by the discrete be viewed as an atomic state transition by the discrete learning agent. What remains is to learn behaviors for learning agent. What remains is to learn behaviors for following paths reliably. following paths reliably. A behavior has four components. The out compo- A behavior has four components. The out compo- nent is an action vector used to directly control the nent is an action vector used to directly control the motor apparatus. The app signal tells whether the be- motor apparatus. The app signal tells whether the be- havior is applicable in the current context. The done havior is applicable in the current context. The done signal tells when the behavior has finished. The init signal tells when the behavior has finished. The init input signal is used to begin execution of a behavior. input signal is used to begin execution of a behavior. The out and upp components will be defined using the The out and upp components will be defined using the static and dynamic action models that predict the ef- static and dynamic action models that predict the ef- fects of the robot’s actions on the local state variables fects of the robot’s actions on the local state variables used to define the path’s constraints. A path-following used to define the path’s constraints. A path-following behavior is done when its constraint is no longer sat- behavior is done when its constraint is no longer sat- isfied or when a new path-following behavior becomes isfied or when a new path-following behavior becomes applicable indicating that the discrete learning agent applicable indicating that the discrete learning agent has a new action to consider. has a new action to consider. Primitive actions The first step toward learning the action models is to analyze the robot’s motor apparatus to discover how many degrees of freedom it has and to learn a set of action vectors for producing motion for each degree of freedom. Since the effects of actions are grounded in the sensory features (the only source of information the robot has), we can analyze the motor apparatus by defining a space of action effects and then apply- ing principal component analysis (PCA) to that space in order to define the dimensions of that space and a basis set of effects. See Mardia et al. (1979) for an introduction to PCA. For example (see Figure 5), characterizing action ef- fects as motion vectors and applying PCA can be used to diagnose the set of primitive actions for a mobile robot with a ring of distance sensors and a motor ap- paratus that affords rotation and translation actions. For the robot of our running example, this method discovers the primitive action vectors u1 = (-1,1) for one degree of freedom (rotating) and u2 = (1,l) for the second degree of freedom (advancing). The action vector used to control the motor apparatus is a linear combination of the primitive actions, written u = ~$Lillf This method has been successfully ap- plied to both a ring of distance sensors and a small retina (Pierce 1991). The static action model The purpose of the static action model is to tell how the primitive actions affect the features that serve as local state variables. Knowing how to take a feature to a target value is necessary for satisfying a constraint, i.e., moving to a path. Knowing how to keep a feature at its target value while moving is necessary for following a path. In the simplest case, the effect of an action is con- stant. In general, however, the effect of an action on a feature is context-dependent, meaning that the static action model will have to take context information into account when making its predictions. For example, the advance action will decrease a minimum-distance fea- ture’s value when the robot is facing toward a wall; it will increase the value if the robot is facing away from the wall; and it will leave the value invariant if the robot is facing parallel to the wall. The orientation of the robot with respect to the wall is the context that determines the action’s effect on the feature. A brute-force way to define contexts is to break sen- sory space up into a large set of boxes (cf. Michie & Chambers 1968). In the current example, a more el- egant solution is possible. The learned blob features have associated context information, namely the posi- tions of the features in the image from which they are produced (see Figure 4). This information, which en- codes the angle of the object whose distance is given by the feature’s value, turns out to be sufficient to dis- criminate the different regions. Learning Agents 1267 a basis set of action effects feature feature (4 (W -Ul +u2 primitive actions (a Figure 5: The diagnosis of primitive actions. A motion generator is applied to the learned image feature (a). The resulting motion feature (b) is used to characterize actions in terms of average motion vectors (c). Principal component analysis is used to characterize this space of motion vectors to determine a set of actions for motion in each degree of freedom (d). 11 and the associated correlation, r. Figure 6: Learning the static action model, i.e., the ele- ments of the context-dependent matrix WC in j, z WC u. Linear regression is used to find the values of w3i and r. The correlation between 21; and gJ determines the good- ness of fit, i.e., the validity of the hypothesis that, for a given context, the relationship is approximately linear. The learning of the static action model is summa- rized in Figure 6. While the robot explores by ran- domly executing one primitive action at a time, linear regression is used to find the best values for ~lja in the equation J& = wji ui as well as a correlation that tells how good the fit is. With this information, it is possible to tell when an action has an effect on a fea- ture (namely, when the correlation associated with the feature’s current context is large) and how large that affect is. This is necessary for defining hill-climbing behaviors. It is also possible to tell when (i.e., in what context) an action leaves a feature’s value invariant. This is necessary for defining path-following behaviors. Hill-climbing behaviors. The purpose of hill- climbing behaviors is to move the robot to a state where a path-following behavior is applicable. For each primitive action ui and feature yj, a behavior for hill- climbing to the goal yi = yj* is defined as shown in Figure 7. It is applicable when the static action model predicts that the action is capable of moving the fea- ture toward its target value. It is done when it has succeeded in doing so. Its output is given by a simple control law. Open-loop path-following behaviors. The static action model does not have enough information to define closed-loop path-following behaviors with error correction to keep the robot on the path, but by using the static model, it is possible to define open-loop path- Given: fjj X Wji Ui with correlation r for context c. upp(c) - 17-j >> 0 Out(C) = UiU” done(c) E ej M 0 where ‘11; = ee +w2 Wji j -/ej dt wji ej = Yi - ?Jj. Figure 7: A hill-climbing behavior is defined for each prim- itive action u’ and feature yJ to achieve the goal yJ = y;. A simple proportional-integral (PI) control law is used with parameters c = 1.0, w = 0.05 (see Kuo 1982). following behaviors. For each primitive action and fea- ture, an open-loop behavior is defined (Figure 8) that is applicable in contexts where, according to the static action model, the action leaves the value of the feature invariant. A signal is superimposed on top of this ac- tion that will be used in learning the dynamic action model (next section). After the dynamic action model is learned, a small error-correcting component will be added to keep the robot on the path (i.e., to keep the feature y at the desired value y*). Figure 8: An open-loop path-following behavior is defined for each primitive action up and feature yJ. The output has two components: a base action and a small orthogo- nal component used in learning the dynamic action model. Only one of the ~6’s is nonzero at a time. The behavior is ap licable when the constraint is satisfied and the action u B does not change the feature’s value. It is done when the constraint is no longer satisfied or a new behavior becomes applicable. 1268 Robotics The dynamic action model The dynamic action model is used to define closed-loop ( i.e., error-correcting) versions of the path-following behaviors. Specifically, this model will tell, for each path-following behavior, the effect of each orthogo- nal action (each primitive action other than the path- following behavior’s base action), on every feature that is used in the definition of the path-following behav- ior’s constraint. To learn the dynamic action model, an exploration behavior is used that randomly chooses applicable hill- climbing and open-loop path-following behaviors. An open-loop path-following behavior works by produc- ing the action u = up us + x6 ub u6 where up is con- stant, us is much smaller than up, and only one u6 is nonzero at a time. The behavior runs until it is no longer applicable, it no longer satisfies its constraint, or a new path-following behavior becomes applicable. While it is running, linear regression is used to learn the relationships between the orthogonal actions and the features in the context of running the open-loop path-following behavior. The learning of the dynamic action model is described in Figure 9l. for each primitive action up for each feature y3 for each orthogonal action ug for each context c find the best values of n E { 1,2}, Ii in (n) y3 M kU6 when u = up + ~16 u6. Figure 9: Learning the dynamic action model. Here, ytn) is the nth derivative of y. Linear regression is used to find the best value of lc. The correlation between UJ and yin’ is used to discover which derivative of the feature is influenced by the action. It is assumed that for a given context, the relationship will be approximately linear. Closed-loop path-following behaviors. For each primitive action up and each feature vector y (i.e., each possible combination of features), a closed-loop path- following behavior is defined. It is applicable when up leaves y invariant according to the static action model. It is analogous to an open-loop path-following behav- ior except that it uses the orthogonal actions for error correction. Since each orthogonal action may affect each feature, there will be one term in the control law for each feature-action pair. The details are given in Figure 10. these up 1s give 6 = kpu~ = Ica216~~ = Icud, using constant for a path-following behavior. the fact that up&) - (y = y’) A (j+P,c) 2i 0) out(c) = up +x u& where xw 2 2163 = -e+W k k s e dt if yJ M kua, W2 WJ = 2cw -e+-i k k if sij szkw, e3 = Y; -513. Figure 10: Definition of a closed-loop path-following be- havior for constraint y = y*. Here, up is the base action for the behavior and j is the index ranging over the features that comprise vector y. Simple PI and PD (proportional- derivative) controllers are used. Again, C=l.O, w=O.OS. Defining the discrete abstraction Once the features are learned and the corresponding behaviors are defined, all that remains is to define an interface that presents the continuous world to the dis- crete learning agent as if the world were a finite-state automaton. A finite-state automaton (FSA) is defined as a tuple (Q, B,6, QO,~) where Q is a finite set of states, B is a set of actions, S is the next-state func- tion mapping state-action pairs to next states, QO is the start state, and y is the output function determining the sense value associated with each state. The abstraction we propose involves using a set of learned path-following behaviors that constrain the motion of the robot to a connected network of one- dimensional loci in state space. State transitions cor- respond to motions resulting from the execution of the pat h-following behaviors. A state, q E Q, is identified with the point where a path-following behavior ends. At a state, the set of actions B, c B is the set of applicable path-following behaviors. The output y(q) is a symbol that identifies the robot’s sensory input at state q. If two states have the same sense vectors, they will have the same output symbol. The next-state function S is defined by the set of all possible (q, b, q’) triples where action b takes the robot from state q to q’. The start state qo is taken to be the first state that the robot encounters. For a path-following behavior to implement a state transition, it must be sufficiently constrained so that the start state determines the termination state - in other words, the path’s constraints must limit the robot’s motion to one degree of freedom. A constraint y = y* and a c t ion up define a l-dof path-following be- havior if up maintains the constraint (according to the static action model) but does not maintain the con- Learning Agents 1269 straint when combined with any other action (accord- ing to the dynamic action model). Moreover, since the other actions all have an effect on the feature vec- tor y while action & is being taken, they can all be used as error-correcting actions in the closed-loop path-following behavior. For example, suppose the robot is facing parallel to a wall at a distance y = y* . The constraint y = y* and action u1 (advance) define a 1-dof path-following behavior: Advancing maintains the constraint, but turning and advancing together do not. Turning can be used to provide error correction. The interface between the continuous world and the discrete learning agent works as follows. The discrete learning agent is given the list B, of currently applica- ble l-dof path-following behaviors. It selects one which then executes until it ends. At this point, the process repeats. If, at a given state, no 1-dof path-following be- haviors are applicable, then the discrete learning agent is given a set of underconstrained path-following be- haviors. If no path-following behaviors are applicable, it is given a set of hill-climbing behaviors. If no hill- climbing behaviors are applicable, then it is given a single behavior that randomly wanders until another behavior becomes applicable. With this definition of the interface, the discrete learning agent’s actions are kept as deterministic as possible, simplifying the task of inferring the structure of the finite-state automaton that the interface defines. We are currently working to implement a discrete learning agent based on the map-learning approach used by the NX robot (Kuipers & Byun 1988, 1991; Kuipers et al. 1993) which provided the original moti- vation for this work. For now, a stochastic exploration behavior is used to demonstrate the interface. It oper- ates by randomly choosing an applicable hill-climbing or path-following behavior and executing it until it is done or no longer applicable, or a behavior becomes applicable that previously was not. An example inter- action with the interface is demonstrated in Figure 11 for a simple environment. Related Work Inferring the structure of finite-state worlds The task of inferring the structure of a finite-state envi- ronment is the task of finding a finite-state automaton that accurately captures the input-output behavior of the environment. In the case that the learning agent is passively given examples of the environment’s in- put/output behavior, it has been shown that finding the smallest automaton consistent with the behavior is NP-complete (Angluin 1978, Gold, 1978). With active learning, in which the agent actively chooses its ac- tions, the problem becomes tractable. Kuipers (1978) describes the TOUR model, a method for understand- ing discrete spatial worlds based on a theory of cog- nitive maps. Angluin (1987) g ives a polynomial-time algorithm using active experimentation and passively received counterexamples. Rivest 8z Schapire (1993) improve on Angluin’s algorithm and give a version that does not require the reset operation (returning to the start state after each experiment). Dean et al. (1992) h ave extended Rivest and Schapire’s theory to handle stochastic FSA’s. They assume that actions are deterministic but that the out- put function mapping states to senses is probabilistic. Their trick is “going in circles” until the uncertainty washes out. Dean, Basye, and Kaelbling (1993) give a good review of learning techniques for a variety of stochastic automata. Drescher’s schema mechanism (1991) employs a statistical learning method called marginal attribution. The set of learned schemas fills the role that S and y play in the FSA model. Schemas emphasize sensory effects of actions rather than state transitions and are ideal for representing partial knowl- edge in stochastic worlds. Inferring worlds the structure of continuous Applying the previous learning methods to the real world or a continuous simulation of it requires an abstraction from a continuous environment to a dis- crete representation. Kuipers and Byun (1988, 1991) demonstrate an engineered solution to the continuous- to-discrete abstraction problem for the NX robot. NX’s distinctive places correspond to discrete states and its local control strategies correspond to state tran- sitions. These constructs have to be manually re- designed in order to apply to a robot with a different sensorimotor apparatus. Kortenkamp & Weymouth (1994) have engineered a similar solution on a physical robot that exploits visual as well as sonar information. Lin and Hanson (1993) are using reinforcement learn- ing to teach a robot a predefined set of local control strategies such as hall following. A difference between their approach and ours is that our robot must discover and then learn path-following behaviors on its own. It has no concept of “hall” or “hall-following.” To summarize our position, we are developing meth- ods for learning from tabula rasa the interface that is engineered by Kuipers & Byun (1988) and Kortenkamp & Weymouth (1993), and is being taught by Lin and Hanson (1993). Results and Conclusions The method for diagnosing primitive actions has been successfully applied to a variety of sensory systems: distance sensors, a 5x5 grid of photoreceptors; and to a variety of motor apparatuses: turn-and-advance, tank, translate, turn-advance-slide (having 3 degrees of free- dom: rotation, forward-backward, and left-right). The method for discovering local state variables has been successfully applied to the ring of 16 distance sensors. The learning of action models and path-following be- haviors has been demonstrated on the simulated robot 1270 Robotics Figure 11: Exploring a simple world at three levels of competence. (a) The robot wanders randomly. (b) The robot explores by randomly choosing applicable hill-climbing and open-loop path-following behaviors based on the static action model. (c) The robot explores by randomly choosing applicable hill-climbing and closed-loop path-following behaviors based on the dynamic action model. with distance sensors and turn-and-advance motor ap- paratus. We have presented a method for learning a cogni- tive map of a continuous world in the absence of a priori knowledge of the learning agent’s sensorimotor apparatus or of the structure of its world. By choosing the finite-state automaton as the target abstraction, we inherit a powerful set of methods for inferring the structure of a world. In the process of developing this abstraction, we have contributed methods for model- ing a motor apparatus, for learning useful features, and for characterizing the effects of actions on features in two ways: The static action model captures first-order effects useful for defining hill-climbing behaviors and for deciding when an action leaves a feature invariant. The dynamic action model captures second-order ef- fects useful for error correction in robust path-following control laws. References Angluin, D. 1987. Learning regular sets from queries and counterexamples. Information and Computation 75:87-106. Dean, T.; Basye, K.; and Kaelbling, L. 1993. Uncer- tainty in graph-based map learning. In Connell, J. H., and Mahadevan, S., eds., Robot Learning. Boston: Kluwer Academic Publishers. 171-192. Dean, T.; Angluin, D.; Basye, K.; Engelson, S.; Kael- bling, L.; Kokkevis, E.; and Maron, 0. 1992. Infer- ring finite automata with stochastic output functions and an application to map learning. In Proceedings, Tenth National Conference on Artificial Intelligence, 208-214. San Jose, CA: AAAI Press/MIT Press. Drescher, G. L. 1991. Made-Up Minds: A Construc- tivist Approach to Artificial Intelligence. Cambridge, MA: MIT Press. Kortenkamp, D., and Weymouth, T. 1994. Topo- logical mapping for mobile robots using a combina- tion of sonar and vision sensing. In Proceedings of the Twelfth National Conference on ArtiJiciaZ Intelligence (AAAI-94). Kuipers, B. J., and Byun, Y.-T. 1988. A robust, qualitative method for robot spatial learning. In Pro- ceedings of the National Conference on Artificial In- telligence (AAAI-88), 774-779. Kuipers, B. J., and Byun, Y.-T. 1991. A robot explo- ration and mapping strategy based on a semantic hi- erarchy of spatial representations. Journal of Robotics and Autonomous Systems 8:47-63. Kuipers, B.; Froom, R.; Lee, W.-Y.; and Pierce, D. 1993. The semantic hierarchy in robot learning. In Connell, J. H., and Mahadevan, S., eds., Robot Learn- ing. Boston: Kluwer Academic Publishers. 141-170. Kuipers, B. J. 1978, Modeling spatial knowledge. Cognitive Science 2~129-153. Kuo, B. C. 1982. Automatic Control Systems. Engle- wood Cliffs, N.J.: Prentice-Hall, Inc., 4 edition. Lin, L.-J., and Hanson, S. J. 1993. On-line learn- ing for indoor navigation: Preliminary results with RatBot. In NIPS93 Robot Learning Workshop. Mardia, K. V.; Kent, J. T.; and Bibby, J. M. 1979. Multivariate Analysis. New York: Academic Press. Michie, D., and Chambers, R. A. 1968. BOXES: An experiment in adaptive control. In Dale, E., and Michie, D., eds., Machine InteZZigence 2. Edinburgh: Oliver and Boyd. 137-152. Pierce, D. M. 1991. Learning a set of primitive ac- tions with an uninterpreted sensorimotor apparatus. In Birnbaum, L. A., and Collins, G. C., eds., Ma- chine Learning: Proceedings of the Eighth Interna- tional Workshop (ML91), 338-342. San Mateo, CA: Morgan Kaufmann Publishers, Inc. Rivest, R. L., and Schapire, R. E. 1993. Inference of finite automata using homing sequences. Information and Computation 103(2):299-347. Learning Agents 1271 | 1994 | 263 |
1,612 | High Dimension Action Spaces in Robot Skill Learning Jeff G. Schneider * Department of Computer Science University of Rochester Rochester, NY 14627 schneider@cs.rochester.edu Abstract Table lookup with interpolation is used for many learning and adaptation tasks. Redundant map- pings capture the important concept of “motor skill,” which is important in real, behaving sys- tems. Few robot skill implementations have dealt with redundant mappings, in which the space to be searched to create the table has much higher dimensionality than the table. A practi- cal method for inverting redundant mappings is important in physical systems with limited time for trials. We present the “Guided table Fill In” algorithm, which uses data already stored in the table to guide search through the space of potential table entries. The algorithm is illus- trated and tested on a robot skill learning task both in simulation and on a robot with a flexible link. Our experiments show that the ability to search high dimensional action spaces efficiently allows skill learners to find new behaviors that are qualitatively different from what they were presented or what the system designer may have expected. Thus the use of this technique can al- low researchers to seek higher dimensional action spaces for their systems rather than constrain- ing their search space at the risk of excluding the best actions. Introduction Memory-based models such as table lookup with in- terpolation have been used for many robotic learning tasks [Raibert 77, Atkeson 88, Atkeson 91, Mukerjee & Ballard 85, Moore 90, Moore 911. The block diagram for a general learning task, and a specific task exam- ple (throwing a ball) are shown in Fig. 1. A table residing in the box marked “Skill” holds values for a mapping from a task parameter space to a plant com- mand space. The plant command space is all possible vectors that could be stored in the table. The task parameters are used to index into the table. In the l-d throwing task, the plant command space is the set *This material is based on work supported by DARPA contract MDA972-92-J-1012. The government has certain rights in this material. 1272 Robotics Diagram of One-Dimensional Throwing l&k Figure 1: Skill learning system and Id throwing task of possible joint velocity sequences that can be sent to the robot controller and the single task parameter is the distance the ball travels. We assume that our learning system operates in two modes: training and operational. It may train first and then remain in operational mode, or it may switch between the two frequently. In either case our goal is one of optimization: to minimize the amount of time required in training to attain a certain performance level in operation, or to maximize the performance level given a certain amount of training time. Per- formance may be measured with respect to accuracy, range of operation achieved, or a control effort metric. Often, memory-based learning systems have relied on random search to fill in the table with the neces- sary information. This works when: the action space is inherently the same size as the task result space, the system designer has explicitly constrained the action space to be of moderate size using partial task mod- els, or despite the size of the action space the system is interested in learning the results of all possible ac- tions. Robot kinematic and dynamic learning systems often fall into the first and/or last categories. Skill learning systems often fall into the second category. In these kinds of system configurations random search is acceptable. Moore [Moore 901 considered tasks whose action space is of moderate size, but whose desirable actions make up a small portion of the space. He pro- posed an efficient search strategy for these tasks. We consider tasks whose space of task parameters has low dimensionality (a small table), but whose space of plant commands has high dimensionality (large vec- tors stored in the table slots). Tasks of this type arise with open-loop control or planning, when an entire se- From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. quence of actions is derived from a single current state or goal. Each action in the sequence makes up a dimen- sion of the space of possible action sequences, and dif- ferent sequences can achieve the goal at different costs: there is redundancy in the mapping. Discrete closed- loop control avoids high-dimensional action spaces by choosing a single action at each time step. Three rea- sons for open-loop control are: 1) the action is fast with respect to sensor or control time constants. This problem could also be addressed by increasing sensing, computation, and control bandwidth. 2) there is a lack of sensors or controls for state during the task (e.g. during the flight of a thrown ball). 3) delay, which can destabilize a feedback system [Brown & Coombs 911. The “Guided Fill In” algorithm given here addresses the problem of high-dimensional search to fill a small table. We test the algorithm with an open-loop robot throwing task both in simulation and on a real system. In addition to standard table lookup methods, local function approximation methods like Kohonen maps [Ritter et al. 921, CMACs [Albus 75, Miller et al. 891, radial basis functions [Poggio & Girosi 891, and back propagation neural networks [Rumelhart et al. 861 store, retrieve, and interpolate between given data points. [Mel 901 combines a neural network approach with a depth first search of possible reaching strategies. Each method develops an efficient representation once a suitable set of input-output pairs has been found. However, none of these addresses the problem of ef- ficiently obtaining the data to be learned. Often, the method is to let the system execute random plant com- mands and observe the results, which works well when the space of possible plant commands is not unreason- ably large. There is other work that attempts to perform the types of robot skills used to test the “Guided Fill In” algorithm. The use of global function approxima- tion methods for robot skill learning was reported in [Schneider & Brown 931. Work on throwing and jug- gling is reported in [Schaal & Atkeson 93, Rizzi 921. In contrast to our work the task is usually constrained to remove redundancy or accurate models are used to approximate the desired mapping. Guided Table Fill In The Guided table Fill In algorithm is a modification of the SAB controller in Moore’s thesis [Moore 901. He was concerned with the efficient search of action spaces, but did not specifically address the issue of inverting a redundant action to task result mapping. Because of time constraints in real systems, it is often impractical to search the entire plant command space. Therefore, skills with redundant mappings have an increased need for search efficiency during training. The unique inversion of a redundant mapping from some m-space of plant commands to an n-space of task parameters (m > n) requires a penalty function to op- timize. For example, our l-d ball throwing robot has Fields of a Table Entry P act P ?-es peff P good action task results control effort goodness value Table 1: Table entry for skill learning 1. Initialize table using approximate task model, teacher, or random choice. 2. Evaluate each point in memory according to its control effort. Assign a “goodness” value based on a comparison of a point’s control effort value to its neighbors’ 3. Randomly choose goal from desired portion of task parameter space. 4. Generate candidates from plant command space using these methods: b Find the table entry whose penalty function is lowest for the desired goal (considering accuracy of task result and control effort). Make random modifications to the action sequence of that en- try. o For a n-d task space choose n+l “good” samples from the table and interpolate or extrapolate to produce an action for the new goal. 5. Evaluate the probability of success for each of the candidate points. 6. Execute the action with the highest probability of success and store the results in the table (Option- ally, readjust the desired range of performance). Goto 2. Figure 2: See text for a detailed eon two joints controlled via a sequence of six joint velocity settings (m = 12, n = 1). The penalty function mea- sures the accuracy of the throw and the control effort (sum of squared joint accelerations). The goal of the system is to find the n-subspace of the plant command space that optimally maps onto the n-dimensional task parameter space. The result of each system execution is stored in a ta- ble. The fields of each entry are listed in Table 1. Pact is the action sequence tried and pr”” the result in task space. Pef f is a measure of the control effort required by the action sequence. Pgood is a goodness value for the entry (its computation is described below). Guided table Fill In is summarized in Fig. 2. In the first step existing models or teachers can deter- mine points from the plant command space to become the first entries into the table. Random choice is a worst case, but possible. There are two parts to a ta- ble entry’s evaluation. First (done only once): given a point in plant command space, the system executes the corresponding action (p”““) and observes the output (p’““) and its control effort value (p”f f). The task out- Learning Agents 1273 put parameters determine where the point is recorded in the table. Second (executed once each iteration): compare each point against its neighbors in the table (nearest points in the output space). A point’s good- ness (pgood) is th e p ercentage of neighbors whose effort value is worse than its own. Step 3 randomly chooses a goal from part of the task space. There are several ways ,the desired portion of the task space may be specified (discussed later). Step 4 generates candidate actions to accomplish the goal task result. Some of the actions are generated by local random modifications to existing “good” points. The table is searched for the entry that best accomplishes the desired goal considering both accuracy and con- trol effort. The action for that entry is altered with small random changes. Several alterations are done to produce a set of candidate actions. Moore advocates generating some actions from a uniform distribution over the entire space of actions. The purpose of these candidates is to keep the learner from converging to local minima. Experiments with re- dundant mappings showed that these candidates were not useful. The probability of a random action in a high dimensional space being useful proved to be too small. However, it is still necessary to generate candi- date actions far from the existing set of actions in the table. This is done by using linear combinations of ex- isting “good” points in the table. Several sets of points are chosen randomly with the “best” points having a higher probability of being chosen. Interpolation or ex- trapolation is done from the chosen points to generate new actions. These actions may be in completely unex- plored regions of the action space, but are likely to be more useful than completely random actions because of the way they are generated. Step 5 evaluates the probability of success as Moore suggests. For each candidate action, pact, the table en- try whose action, p$,, is nearest the candidate action is determined and used to estimate this probability. When several task result dimensions are considered, a probability is computed for each dimension and the product of them is the probability for the whole task result. When considering redundant mappings, reduc- ing control effort is also a goal. Therefore, a goal effort is selected (usually a constant, unattainable, low value) and control effort is considered to be another dimen- sion in the above computation. Finally, the candidate with the highest probability of success is executed at step 6. The results of the execution are recorded and a new table entry is made. Steps 2-6 are iterated during the training process. Simulation Experiments The table filling and lookup algorithms were tested on robot skill learning and performance on the task of throwing a ball. The results of these experiments are summarized in Table . The skill goal is a vector de- scribing the position of a target and its output is se- quences of joint velocities for a throwing robot. Here, the robot is the controlled plant and the forces affect- ing the ball’s flight after it leaves the robot make up the uncontrolled plant. Skills are called n-dimensional where n is the number of parameters in the output space of the task: thus a 2-d throwing task has a tar- get lying in a plane, such as the floor. Experiments were simulated for l-d and 2-d throw- ing tasks. For the l-d task the robot consists of two joints in a vertical plane (Fig. 1). The control signal is a sequence of joint velocities to be executed over 6 time steps (also called a trajectory), thus making a total of 12 input command parameters. The single output di- mension is the distance the ball lands from the base of the robot. In the terms of table lookup, a 12-d space must be searched to fill in a l-d table. The 2-d throw- ing task is done with a three joint robot configured like the first 3 joints of a PUMA 760; a rotating base is added to the l-d thrower. The additional joint yields an 18-d search space. The two task parameter dimen- sions are the x and y coordinates of the ball’s landing position on the floor. The penalty function includes the approximate amount of energy required to execute the throwing trajectories and the average task output error. The approximate energy measure has a second purpose. Robots have limits on their joint velocities and the metric tends to prefer trajectories that stay away from those limits. Later, the average value of the penalty function over the task parameter space will be referred to as the performance and the two terms will be re- ferred to separately as error and eflort. Standard Table Lookup with Interpolation Standard table lookup with interpolation using a Ran- dom Fill In (RFI) 1 earning strategy was implemented to provide a baseline from which to compare the new algorithms. The fill in procedure is random. At each step a new random trajectory is formed by choosing ending joint velocities and positions from a random, uniform distribution over the range of valid values. The new command sequence is executed and recorded in the table. Retrieval from the table is done by find- ing two (three) points for linear interpolation in the l-d (2-d) case. Extrapolation is never used for data retrieval. If no points can be found for interpolation, the nearest point in the task parameter space is cho- sen. When interpolation is possible, a scalar value is given to each possible pair (triple) of points to deter- mine which should be used. It includes terms for the distance of the points from the goal in task parameter space, the average effort associated with each point’s command sequence, and the distribution of the points about the goal point. Fig. 3 shows some sample results of using RF1 for l-d throwing tasks. The desired range of operation is 1274 Robotics 1300-5000 mm (the robot’s arm has a length of 1000 mm). The graphs represent averages over 20 runs. The x axis is the number of robot executions, or the number of trajectories that can be placed in the table. The y axis is an evaluation of the robot’s progress learning the skill. To evaluate the robot’s ability, ten targets evenly spaced in the desired range are attempted and the average effort and accuracy are recorded. One characteristic of the graph is that effort appears to grow as the learning progresses. That happens be- cause the robot is capable only of short throws initially (it is given the same sample short-throw trajectories that are given to the GFI algorithm in the next sec- tion). It uses those trajectories when long throws are requested and pays the penalty in accuracy (because it refuses to extrapolate). As it finds trajectories to throw greater distances, it uses them and accuracy is improved. These trajectories require greater effort thus causing the average effort to look worse. This initial decreasing error and increasing effort is a characteristic of many of the graphs presented here. Results with Guided Table Fill In The l-d throwing experiments of the previous section were repeated with Guided table Fill In (GFI). The evaluation and trajectory retrieval methods are the same as for RFI. Five initial trajectories capable of throwing distances from 1370 to 1450 were given in Step 1 (for fair comparison, the same five were given to the learners using RFI). Fig. 4 shows some sample results. The GFI execution attains a value of 254 after 200 iterations compared to 818 in the RF1 run. Improvements can be made when using GFI for longer distances. Automatic range expansion is a mod- ification that allows the algorithm to choose its range of attempts according to its current abilities. Step 6 updates the current range of operation achieved by the system. Step 3 calls for choosing goal task parameters within some desired range. That range is set to be the current range of achieved results plus some distance farther. A parameter controlling how much farther trades off how quickly the range of operation will be increased with how many trials will be spent searching for low-effort actions within the current range. Fig. 5 shows standard GFI for a range of 10000 and Fig. 6 shows the results of using automatic range expansion to a distance of 10000. The additional set of points represent the maximum distance attained (divided by 10 to fit in the graph). Shorter distance throws are eas- ier (there are more trajectories in the command space for them). The algorithmic modification allows the robot to learn the easy part first and then move on to more difficult throws. As the graph shows, it reaches a distance of 10000 after 200 iterations and attains a final performance value of 1072 (compared to 1448 with standard GFI). Traditional engineering practice calls for the range of operation to be pre-specified for 1800 p 1600 e 1400 ; 1200 0 1000 r 800 !$ 600 n 400 c 200 e 0 error - 0 50 100 150 200 Iteration Number Figure 3: l-d RFI: range 5000 0 50 100 150 200 Iteration Number Figure 4: l-d GFI: range 5000 Task 1 Opt. 1 GFI 1 RF1 1 RF1 tries 1 Table 2: Summary of experimental results: Optimal is numerically estimated. GFI is the performance of the new algorithm after 200 iterations using automatic range expansion when it produces improved results. RF1 is from traditional table lookup with random trials. The last col- umn indicates how many trials RF1 needs to equal GFI’s performance. system design. However, when dealing with complex plants this may be difficult. Therefore, this modifica- tion is also important when a system designer does not know the range of performance that can-be achieved, but wishes to maximize it. A 2-d throwing experiment was also done comparing SF1 with GFI. The x distance was 2500 mm and the y distance was 1200 mm. GFI is significantly better than RF1 for the 2-d task. It gets a final value of 155 compared to 1247 for RFI. This result is important because it shows that performance gains can also be seen in tasks of higher dimensionality. A revealing statistic is the number of runs RF1 re- quires to reach the performance attained by GFI. For a l-d range of 2500 RF1 requires an average of over 100000 iterations to reach the level GFI attains after only 200. For a l-d range of 10000, RF1 requires 10000 iterations to match 200 of GFI with automatic range Learning Agents 1275 r 3500 f 3000 ; 2500 m2000 a 1500 n 1000 ; 500 0 I I error - . I I I -30 -20 -10 0 10 20 30 0 50 100 150 200 Joint 1 Vel Figure 7: Inputs attempted: RF1 range 30 c’ Iteration Number Figure 5: l-d GFI: range 10000 ml2oo 1 I I I I F 1000 i 800 r 600 m a 400 n c 200 0 1 error - 0 50 100 150 200 Iteration Number Figure 6: l-d GFI: automatic range expansion expansion. The larger discrepancy between RF1 and GFI on the shorter task shows the benefits of using a fill in algorithm that is guided by desired range of performance vs one that randomly tries valid trajecto- ries. GFI is able to concentrate its trials on the por- tion of the space that throws in the range 1300-2500. Similarly, RFI for the 2-d case required over 100000 iterations to equal the GFI performance with 200 iter- ations. When skill learning is attempted on real robots, the number of executions required becomes important. The actions attempted during l-d GFI and RF1 learning show how the algorithm works. Since the search space contains the velocities of two joints, the skill learner is looking for a curve through a 12-d space. Figs. 7 through 10 are projections of the space onto the plane defined by the ending joint velocities. Fig. 7 shows that the distribution of attempted points is fairly uniform throughout the search space when us- ing RFI. The lower density at the left is caused by a higher number of invalid trajectories there. Fig. 8 shows a projection of the optimal curve for a range of 300-5000. A description of how the optimal curve was numerically estimated is in [Schneider & Brown 921. Figs. 9 and 10 show the points attempted by GFI at different ranges. The figures show that the GFI con- centrates its trials in a small part of the search space. The optimal curve verifies that GFI trials are concen- trated in a good portion of the space. The dark spot near the center of the two GFI graphs is where the five initial points are located. A comparison of the two GFI graphs shows the algorithm starting from the initial points and working toward the optimal for the Joint Vel 20 10 0 2-lo -20 -30 -30 -20 -10 0 10 20 30 Joint 1 Vel Figure 8: Input space points: Optimal desired range. 1.3-5k 0.3-5k Experiments on a PUMA The algorithms presented here were tested on a PUMA 760 with a flexible link attached (a metal meter stick). At the end of the meter stick a plastic cup is attached to hold a tennis ball for throwing experiments. The release point of the ball is not directly controlled. It comes out whenever it is moving faster than the cup. A CCD camera watches the landing area and deter- mines where the ball landed with respect to the base of the robot. Most of the parameters of the experi- ment were set the same as the l-d throwing done in simulation. Two joints of the robot are controlled by specifying joint velocities over six 200 ms time steps. The low-level controller, RCCL, interpolates to pro- duce a smooth velocity profile. As in the simulation, the effort function prefers trajectories that are far from the robot’s physical limits. The GFI algorithm was given three sample actions that resulted in throws ranging from 143 cm to 164 cm. Automatic range expansion was used because that option performed the best for l-d throwing in simula- tion and because it was not possible to determine the robot’s range of capability beforehand. After 100 iter- ations the robot had learned to throw accurately out to a range of 272 cm (a comparison execution of Moore’s algorithm attained a maximum distance of 211 cm). Its accuracy is good enough that it consistently hits a 2 cm screw placed upright anywhere within its learned range of performance. The same cameras that watch the landing position of the ball during learning locate the target during performance mode. The most interesting result of the learning was the 1276 Robotics -30 1, 1 -j , , , , , -30 -20 -10 0 10 20 30 Joint 1 Vel Figure 9: Inputs attempted: GFI range O-1.5k -30 -20 -10 0 10 20 30 Joint 1 Vel Figure 10: Inputs attempted: GFI range 1.3-5k type of action found to produce long throws. The three sample actions smoothly accelerate both joints forward. It seems reasonable that longer throws can be obtained by accelerating more quickly. The learn- ing algorithm tried this and it worked up to a distance of approximately 210 cm (this is also what Moore’s al- gorithm did). It was unable to produce longer throws with that type of velocity profile, though, because of the joint velocity limits on the PUMA. It finally learned to do the following “whipping” motion (shown in fig. 11): The joints are moved forward until the meter stick begins to flex forward. Then the robot reverses the direction of its joints so that the stick is pushed forward past its flat state. Just as the stick begins to fall back again, the joints accelerate forward. This causes a large bend in the stick. Finally, the un- coiling of the stick combines with the large forward acceleration of the robot to produce a much higher ball release velocity than could be achieved by simple accelerating the joints forward. The significant aspect of the long throws that are learned is that they are qualitatively different from any given to the system at the start. The sequence of events that led to the robot trying the action in Fig. 11 il- lustrates the GFI algorithm at its best. At iteration 15 the system was shooting for a goal of less than 200 cm (within its current range of operation). It chose an action created as a local random modification in step 3. That action had a significantly lower veloc- ity at time step 2 for joint 3. The result was a throw for a distance of 164 cm with considerably lower con- trol effort than any previous action for that distance. Later, at iteration 30, a similar thing happened with time step 3 of joint 5. The result was a low effort throw of 176 cm. Following that, the algorithm chose several actions that were generated by linear combi- nations of these unique actions. Large extrapolations from the new points created velocity profiles with the “whipping” motion shown in fig. 11. The penalty func- tion, small random modifications, and extrapolation all worked together to find new, useful actions in un- explored portions of a high dimensional space without having to resort to brute force search. Discussion and Conclusions There are many important tasks with highly redundant plant command to task parameter mappings. When inverting redundant mappings it is necessary to opti- mize according to additional cost functions. This poses a problem for standard table lookup methods, which require a random or brute force search of the plant command space to optimize performance. The Guided table Fill In algorithm extends lookup table learning methods to redundant mappings. It uses data already stored in the table to select plant com- mand space candidates that are more likely to produce good data to add to the table. Linear interpolation and extrapolation between existing good points in the table will yield more good points if the mapping is reason- ably smooth. The algorithm also allows natural mod- ifications to learn the easy parts of a task first since it explicitly includes a desired range of task parameters in its decision process. Experiments with robot skill learning show that Guided table Fill In can yield significant improvements in the number of training trials required to attain given levels of performance. They also demonstrate how GFI may be used to learn the easy part of a task first and the performance benefits of doing so. Many sequential task learners [Watkins 891 must operate closed-loop be- cause of the exponential explosion of action possibili- ties that occurs when a sequence of actions is consid- ered. The results presented here demonstrate one way to deal with the large number of potential actions and thus offer an open loop alternative for these problems. The gains can be significant when the cost of percep- tion is considered or feedback delay in a real-time sys- tem becomes a problem. Experiments using a flexible manipulator for throw- ing demonstrate the power of the new learning algo- rithm. Previously, researchers applying learning to robotics attempted to constrain the action space to make the problem tractable. With efficient techniques for searching high dimensional spaces that step may not be necessary. More importantly, the ability to handle high dimensional spaces enables the learner to generate qualitatively different behaviors. Often these are the behaviors that the researcher would have elimi- nated by applying constraints based on poor intuition. One of the disappointing aspects of work in learning is that it is often applied to tasks where the system de- signer “already knows the answer.” In these situations Learning Agents 1277 1 2 3 4 ‘ learning functions more as a fine-tuner to improve ac- curacy or to fit model parameters. In the throwing experiments presented here, we had speculated that improvements could be made by storing energy in the manipulator. However, it was assumed that this would be done by making an initial backward motion, fol- lowed by a forward motion. Only through the use of the GFI algorithm was it revealed that a forward- backward-forward motion was the way to attain a high release velocity, given the constraints on joint velocity, the length of time allocated for the throwing motion, and the natural frequency of the meter stick. References [l] J. Albus. A new approach to manipulator control: The cerebellar model articulation controller (cmac). Journal of Dynamic Systems, Measures, and Controls, 1975. [z] C. Atkeson. Using associative content addressable memories to control robots. In Proceedings of the 27th Conference on Decision and Control, December 1988. [3] C. Atkeson. Using locally weighted regression for robot learning. In Proceedings of the 91 IEEE Int. Confer- ence on Robotics and Automation, April 1991. [4] C. Brown and D. Coombs. Notes on control with delay. Technical Report 387, University of Rochester, 1991. [5] B. Mel. Connectionist Robot Motion Planning: A Neu- rally Inspired Approach to Visually Guided Reaching. Academic Press, 1990. [6] W. Miller. Real-time application of neural networks for sensor-based controlof robots with vision. IEEE Trans on Systems, Man, and Cybernetics, July 1989. [7] A. Moore. Eficient Memory-Based Learning for Robot Control. PhD thesis, University of Cambridge, Novem- ber 1990. [8] A. Moore. Variable resolution dynamic programming: Efficiently learning action maps in multivariate real- valued state-spaces. In Proceedings of the 8th Interna- tional Workshop on Machine Learning, 1991. [9] A. Mukerjee and D. Ballard. Self-calibration in robot manipulators. In Proceedings of the 85 IEEE Int. Con- ference on Robotics and Automation, 1985. [lo] T. Poggio and F. Girosi. A theory of networks for approximation and learning. Technical Report 1140, MIT AI Lab, 1989. [ll] M. Raibert. Analytical equations vs table look-up for manipulation: a unifying concept. In Proceedings of the IEEE Conference on Decision and Control, 1977. [12] H. Ritter, T. Martinetz, and K. Schulten. Neural Com- putation and Self-Organizing Maps. A-W, 1992. [13] A. Rizzi and D. Koditschek. Progress in spatial robot juggling. In Proceedings of the 92 IEEE Int. Confer- ence on Robotics and Automation, 1992. [14] D. Rumelhart, G. Hinton, and R. Williams. Learning Internal Representations by Error Propagation. MIT Press, 1986. 151 S. Schaal and C. Atkeson. Open loop stable control strategies for robot juggling. In Proceedings of the 93 IEEE Int. Conf. on Robotics and Automation, 1993. 161 J. Schneider and C. Brown. Robot skill learning and the effects of basis function choice. Technical Report 437, University of Rochester, September 1992. 171 J. Schneider and C. Brown. Robot skill learning, basis functions, and control regimes. In Proceedings of the 93 IEEE Int. Conf. on Robotics and Automation, 1993. [18] C. Watkins. Learning from Delayed Rewards. PhD thesis, Cambridge University, 1989. 1278 Robotics | 1994 | 264 |
1,613 | Robot Behaviour Conflicts: an Intelligence Amol Dattatraya Mali and Amitabha Mukerjee Center for Robotics, IIT Kanpur Kanpur 208016, INDIA e-mail:amitBiitk.ernet .in Abstract In this paper, we examine the modularity assump- tion of behaviour-based models: that complex func- tionalities can be achieved by decomposition into simpler behaviours. In particular we look at the issue of conflicts among robot behaviour modules. The chief contribution of this work is a formal characterization of temporal cycles in behaviour systems and the development of an algorithm for detecting and avoiding such conflicts. We develop the mechanisms of stimulus specialization and re- sponse generalization for eliminating conflicts. The probable conflicts can be detected and eliminated before implementation. However the process of cycle elimination weakens the behaviour structure. We show how (a) removing conflicts results in less flexible and less useful behaviour modules and (b) the probability of conflict is greater for more pow- erful behaviour systems. We conclude that purely reactive systems are limited by cyclic behaviours in the complexity of tasks they can perform. 1 Introduction Complex robot interactions are conveniently modeled in terms of stimulus-response sequences often called behaviours. It is easier to model and debug the be- ha&our modules as opposed to the larger and more integrated centralized controllers. Impressive results have been achieved using this strategy in a can collec- tion robot (Connell 1990), navigation of mobile robot (Arkin 1992), a prototype airplane controller (Hartley & Pipitone 1991), ffi o ce rearrangement robot in AAAI- 93 robot competition etc. This behaviour-based intel- ligence paradigm propounded by Brooks and others has challenged the role of representation in AI. In a sense, these approaches treat the world as an external memory from which knowledge can be retrieved just by percept ion. Brooks argues that when intelligence is approached in such an incremental manner, reliance on representation disappears (Brooks 1991). In response, traditional AI researchers such as Kirsh have argued that control cannot serve as a complete substitute for representation (Kirsh 1991). At the same time, behaviour systems have also been moving away from the purely reactive paradigm. A well-known ex- tension of the Brooks’ approach includes the SONAR MAP (Brooks 1986) which is a module that learns what looks suspiciously like a central representation. Some researchers (Gat 1993) are beginning to propose that the internal state be used, but only for modeling highly abstract information. All modular designs (databases, architectures, fac- tories) face the problem of intermodular conflict. In robot behaviour implementations, conflicts which do not result in cycles can be removed by prioritization schemes (e.g. suppressive links), but this is usually ad hoc, with the primary objective of demonstrating suc- cess in the current task objectives. Brooks stresses that additional layers can be added without chang- ing the initial system - our results show that such a claim is most probably not tenable. Then how does one put the behaviour modules together and get useful performance ? This depends on identifying the possi- ble sources of inter-modular conflicts that are likely to arise in behaviour chains. This paper is one of the first formal investigations on the issue of combining behaviours and inter-behavio ur conflicts. Despite the attention such models have been receiving, the issue of inter-behaviour conflict, which challenges the fundamental assumption of mod- ularity, has not been investigated. For example, if the consequence of a behaviour a triggers the stimulus for behaviour b and b precedes a, then we have an unend- ing cycle. Such conflicts are also beginning to show up in the more complex behaviour implementations. For example, Connell records an instance where a can col- lecting robot attempts to re-pick the can it has just deposited in the destination area as shown (Figure 1); this conflict was detected only after a full implemen- t ation (Connell 1990). Cyclical wandering and cyclic conflict of going back and forth between two obstacles have been reported (Anderson & Donath 1990) (Miller 1993). Can behaviour systems be constructed so that Control 1279 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. such conflicts can be detected beforehand? How can one modify the structure so as to avoid such conflicts? These are some of the questions we set out to answer. Our analysis in this paper is dependent on a crucial observation regarding the temporal structure of purely reactive systems. The conflicts we are addressing are not control conflicts but temporal sequence conflicts for which it is necessary to define the temporal struc- ture of behaviours, which is usually sequential since one behaviour usually provides the stimulus for an- other, so that there is often a clear temporal sequence in which behaviours are executed. In this paper we show that cycles occuring in this temporal sequence can be avoided only by modifying the behaviours them- selves, and we introduce two such modifications, based on specializing the stimulus or restricting the action of a behaviour. One of the key results of the paper is that any such modification reduces the usefulness of the behaviour structure and makes it less flexible. r-71 I I Figure 1. Conftict in picking and placing the can. 2 What Is a Behaviour? AI researchers, psychologists, cognitive scientists, ethol- ogists and roboticists, all use the term behaviour in senses that are related but are fundamentally differ- ent. At one end of the spectrum is Brooks who looks upon behaviours as a type of intelligent module, an input-output relation to solve small problems (Brooks 1986). Hopefully these modules can be combined to solve larger problems. There is no shared global mem- ory. The stimulus to a behaviour is boolean and is tested by an applicability predicate. This is the model of behaviour investigated in this paper. Minsky suggests thinking about goal directed be- haviour as an output of a difference engine that mea- sures the differences between the world state and the goal state and takes actions to reduce these differences (Minsky 1986). On th e other hand, Simon feels that complex behaviour need not necessarily be a product of an extremely complex system, rather, complex be- haviour may simply be the reflection of a complex en- vironment (Simon 1969). Arkin proposes the motor schema as a model of behaviour specification for the navigation of a mobile robot (Arkin 1992). Notation Maes models a behaviour as a 4-tuple <c, a, d, a> which represent pre-conditions, add list, delete list and level of activation respectively (Maes 1990). In this work we have followed the behaviourists and adopted a 3-tuple model of behaviour: stimulus, action, conse- quence . An elemental behaviour module p takes the form <s, a, c>, although the action a is not directly referred to by us, and we sometimes abbreviate the notation to <s, c>. Both the stimulus s and the con- sequence c are commonly defined in terms of a predi- cate. We define the dominant period of a behaviour as that period when the behaviour is active. In most behaviour implementations, behaviours become domi- nant in a temporal sequence. We use the symbol “:” (precedes) to denote this. /3r : ,& implies that be- haviour p2 becomes dominant following behaviour PI. Behaviour Chain We define a behawiour chain as a sequence of be- haviour modules { ,& : pZ : ,& : . . . : &} . Here the ac- tion of the earlier module changes the situation in such a way that the newly changed part of the situation is in turn a stimulus for the next module in the sequence. If the consequence and stimulus include a finite uni- versal state as well, then we can say that the stimulus si+l of the behaviour module &+r is logically implied by the consequence of the module p, i.e. (q + si+r). What we mean by the finite universal state can be clarified by an example. Let Universe = X A Y A 2 and cl = A and s2 = X A A. Then 01 leads to p2 but (cl + ~2). Thus when we say that (cl + sp) we mean that a part of s2 was true in the Universe and some literals in cl cause the rest of s2 to come true. Thus in order for (~1 + ~2) to be true, both stimulus and consequence should always contain the “state of the universe predicate.” This allows us to develop the argument effectively, skirting the philosophical debate on the frame problem (Georgeff 1987). We define a behaviour space B as a set of be- haviour modules. A temporal chain of behaviours C is said to be composable from B (written as C+B), if and only if (C = ordered set {pz} A (t/i) fli E B). A stimulus space C of a behaviour space B is the union of the stimuli of all behaviour modules in B. Power, Usefulness and Flexibility of Behaviours To compare different behaviour systems, we define a few relative measures. Definition 1 m Power : A behaviour (/3 := <s, a, c>) is more pow- erful than (,D’ := <s’, a’, c’>) iff (s’ + s) A (c + c’). In other words, it can be triggered at least as frequently as a less powerful behaviour and results in at least as strong a consequence. A behaviour space B is more powerful than the behaviour space B’ if B’ can be oh tained from B by replacing some module DEB by less 1280 Robotics powerful module 0’. 0 Usefulness : A behaviour space B spans the task space r if and only if ( V (t E r) (3 (C-+ B) fulfills (C, t)) }. The greatest fulfillable task space 7~ (B) is the largest task space that is spanned by the behaviour space B. The usefulness of a behaviour space is de- * Je(W[ fined as the ratio ,B, . e Flexibility : A behaviour space B is at least as flexible as behaviour space B’ if { ‘d t E (rG (B) fl 7-@‘))3(C + B){ fulfills(C,t) A V(C’-i B’) {fuZfiZZs (C’,t) * 1 c 1 < 1 C’ I}}}. 3 etection of Conflicts In the broad sense of the word conflict, any behaviour chain leading to non-fulfillment of the desired objec- tives can be said to have a conflict. Let a chain C = { p1 : p2 : ..* : pn} be the desirable behaviour sequence that achieves a desirable outcome. There are three types of conflicts that can cause the chain C from not being executed, by breaking the sequence pi : &+I. Definition 2 (a)Extraneous behaviour Conflict: /3i : ,B’, p’$C. (b)Cyclic Conflict : /?i : Pk, /?k E C, k < i. (discussed - later) (c) Skipping Conflict: pi : ,&, /3k E C, k > (i+l). This type of conflict can be treated in a manner anal- ogous to extraneous behaviour conflicts. The type of behaviour that we are investigating is the cyclic conflict, where, both ,&+I and & may be triggered and clearly the triggering of pk would lead to a cycle (Figure 2). Figure 2. Cycle in a temporal chain of behaviours. Terminated Cycles All cycles do not result in a conflict. Let us say that a large block of butter needs to be cut into a number of smaller pieces. A module cut achieves it. Let scZLt = butter(z) A cut-table(z) A breadth(z, b) A (b 2 2X). We specify the smallest acceptable size of the piece of butter by specifying the limit X, which introduces the termination condition. Prioritization There are three types of prioritization used in robot behaviour control. If CY : p is a possible but undesirable sequence of behaviours, the sequence can be modified. In suppression, a module y suppresses the output of ,B, and instead of CY : ,O, CY : y occurs. In inhibition the action of 0 may take place, but only after y is no longer dominant. Here the chain a : /3 has the module y inserted, so c~ : y : 0 may occur, if the stimulus for p is not affected by y. Delayed action is a special case of inhibition, where the inhibitive link remains effective for SOme time t&&y even after the inhibiting module is no longer dominant. Connell uses the term retrigger- able mono.stable to capture this sense (Connell 1990). These mechanisms are not guaranteed to kill the stim- ulus of &, hence & may be active after dominant pe- riod of the suppressing module is over. Thus within the scope of the three prioritization schemes discussed here, it is not possible to guarantee that cyclic conflicts will be avoided. Detecting Cycles in Behaviour Graphs Representing a behaviour chain as a graph, we present without proof the following lemmas: Lemma l(a). Whenever there is a cyclic conflict, there is a cycle in the temporal graph of behaviours. Lemma l(b). Wh enever there is a cycle in the tem- poral graph of behaviours that is not terminated by a recursive condition, there is a cyclic conflict. Thus detecting conflicts in a behaviour chain is equiv- alent to detecting cycles in the corresponding graph. 4 ehaviour efinement From definition 2, whenever there is a cycle in a be- haviour chain C = (01 : p2 . . .pk...pi : ,&+I . ..&}. there must be a triggering of the kind pZ : Pk, where k 5 i. Then both /3i : ,&+I and pZ : pk are possible at this point. Our objective is to break the pi : & link with- out disturbing the pZ : ,&+I or ,&r : /3k triggerings which are essential to the successful execution of the chain. We have seen that priority based methods are not guaranteed to achieve this, so we look for behaviour modification approaches which will maintain (~+.s,+r) whereas (Q+s~) would be negated. We develop two methods for achieving this: in stimulus specialization, sk is specialized, and in response generalization, q is generalized. Stimulus Specialization Let us consider the conflict in picking up the soda cans, where the freshly deposited can is picked up. If we were to add the condition “not-deposited-just- now (x)” to the stimulus predicate for pickup, then we would only need a small recency memory (recently dropped can). Thus the stimulus for & becomes more specialized. However, in doing this, one must be careful so as not to disturb the rest of the chain, i.e. (ck -r+sk) should still hold but (G +sr;) must be broken. Clearly this will not be possible where (q~ck-r), then any Control 1281 changes we make in Sk such that 1 (Q + Sk) will also result in 1 (c&r =f st). Thus stimulus specialization can be used only if (Q + c&r) is not true. One model for this is to say that there must be a literal y such that (c&l + Sk A 7) but 1 (q + Sk A 7). The conjunc- tion of all such literals I’ = (71 A 72 A . ..rm) is called the maximal difference between c&l and Q. Stimu- lus specialization works only when I? # 0, and involves modifying Sk to (Sk A+y), y E I’. It is advisable not to specialize it more than necessary (e.g. by adding more than one literal), since this adversely affects the power of the behaviour. A simpler understanding of the pro- cess is obtained if both Q and ck-1 are in conjunctive form. Then I? is nothing but the difference (CA -1 - G) and Sk is modified by conjunction with one of the lit- erals that is in c&-l but not in q. Note that since the stimulus is specialized, any stimuli that are required by the action are still available to it. Response Generalization Here the action is modified so that the consequence of the action is weaker i.e. if the old consequence was c and the new one is c’ then (c + c’) but 1 (c’ + c). For example, we can modify the action of the module drop so that while dropping the can on the ground, the robot puts it in an inverted position which pre- vents the robot from detecting that the object is a can. The original consequence was (visible(x) A can(x) A graspable(x)) and the modified consequence is (visi- ble(x) A graspable(x)), assuming the sensors cannot identify cans that have been inverted. Otherwise, we may modify the consequence by covering the can to make the predicate visible(x) false, then this leads to addition of a new behaviour module or modifying the action part of the original module, both of which re- quire considerable re-programming, and are expensive. In response generalization, (Q +- Sk) must be negated, while (q + si+r) must hold. Hence response general- ization can be used only when (sit-r +- Sk) does not hold. In fact, one could characterize the process of response generalization by saying that there must ex- ist 0 s.t. (q Va) + s~+~ but l(c.j V(T) + Sk. The disjunction of all such 0’s is C. Again, if Sk and si+r are in conjunctive form, then a simpler understanding is obtained, since c =N (Sk - si+r) i.e. the negation of all the conjunctions that appear in Sk and not in &+1* This negation is a disjunction of many negative literals (- 7). In this instance, modifying ci is better understood as dropping the literal y already appearing in G, written as (Q - 7). Since stimuli/consequences are often conjunctive, this difference notion is a useful concept in practice. Thus ci is modified to (G - 7)) where y E (Sk - &+I). Stimulus specialization is easier to do than response generalization, as response generalization requires that the action should be modified. However, stimulus spe- cialization may not always be possible; e.g. with “not- deposited-just-now(x)” the robot may still pick up an older deposited can. Better solutions to this, such as “never-deposited-before(x)” or “not-at-depository(x)” would require considerable global memory. Therefore, stimulus specialization, while cheaper to implement, may not be available in many instances, since the ac- tions require a minimum stimulus, and specializing it without memory may be counter-productive. Effects Of Behaviour Refinement Let us now investigate the effects of stimulus spe- cialization and response generalization. Lemma 2. Removing a cycle from chain C by stim- ulus specialization or response generalization cannot introduce a cycle in any other chain C’, that did not have a cycle before. Proof :- Let flk be the behaviour that was special- ized. Now to introduce cycles when no cycles existed before, some link p’ : ok must have become possible, i.e. (c’ + Sk) has become true. This is not possible since c’ is the same and Sk is more specific. Similarly, since ck has not been modified, no new links /& : ,@ could have been created. Hence no new cycle will be initiated. Similarly it can be shown that response gen- eralization does not introduce new cycles. •I Lemma 3. Whenever a behaviour space is modified to eliminate cyclic conflicts by response generalization and/or stimulus specialization, either the flexibility or usefulness of the behaviour space decreases. Proof :- Let C be the stimulus space and s c C and s is a conjunction of its members. Now let s be spe- cialized to s’ so that s’ C s. Now tasks or subsequent behaviours requiring the predicates in (s - s’) will no longer be at tended to by B. Thus we need a new be- haviour p” such that (s” U s’) = s, so that p and p” together serve the stimulus set s which implies that IBI increases and the usefulness of B decreases. Similarly, if the response of /? is generalized so that c has more literals than c’. Thus (c - c’) is not being performed by /?. Hence other new behaviours are needed to com- plete tasks requiring (c - c’) which increases IBI, and also increases the chain lengths for performing tasks, reducing flexibility. Otherwise, some tasks requiring (c - c’) cannot be performed which implies that lr’l < 171 which again means that the usefulness of the behaviour space decreases. 0 Let us say that we have a behaviour p whose conse- quence c = p A Q leads to a cycle. If we use response generalization, we may have to design two behaviours p’ and ,@’ such that c’ = q and c” = p. If ‘8 has a stimulus s = p V q which is triggered leading to a cy- 1282 Robotics cle and if we use stimulus specialization, we may have to design two more behaviours p’ and p” such that s’ = p and Q” = q. In some cases, it may not be pos- sible to ‘design an action such that it will fulfill these conditions. This discussion brings us to our most im- portant results, which have to do with the power and usefulness of behaviour spaces. Behaviour Modification Theorem. Given two be- haviour spaces B and B’ such that B is more powerful than B’ (i.e. B’ can be obtained from B by replacing some behaviours 0 of B by the less powerful ones 0’) then: (a) The greatest fulfillable task space for behaviour space B’ is less than that for B, i.e. h(B’>t<trG(B>t (b) Usefulness of B is greater than that of B’ i.e. . , ]TG(B)[ jTG(B’>[ IBI 2 IB’I * (c)Probability of a cycle is also greater in B. Proof (u) :- First, let us consider the case where a sin- gle behaviour p has been replaced by the less powerful ,0’. The set of chains of behaviours composable from a behaviour space represents a tree with initial point cor- responding to the availability of the right initial stimu- lus and each node in this tree represents a world state which may correspond to the desired task. The great- est fulfillable task space is proportional to the total size of this tree of behaviour chains. Now, either the be- haviour ,0 will have more applicability due to smaller stimulus length as compared to the behaviour /3’, or the behaviour p will have stronger consequences resulting in more behaviours being triggerable. In terms of the task tree, either p will have more parent nodes, or it will have more children. In either case, the branching factor is higher in B than in B’ and the size of the task tree will be as large or larger. Since IBI has not changed, the usefulness of the behaviour space, ]WG(B)( PI has decreased which proves part (b). This treatment can be extended to multiple instances of replacing a strong behaviour by a weak one. 0 Proof (c) :- Let ,& E B and ,& E B’ be two behaviours s.t. fli is more powerful than ,@, i.e. (8: + ai) or si is weaker than si. Now consider any chain composable in B and B’ of n modules, which differ only in that the module pi is replaced by pi’. Now consider all be- haviours @j E C, j > i, with consequence cj. The prob- ability of a cycle prob- cycle (B) is & prob(ci + s,) and prob-cycle (B’) is xT>iprob(cj + 3:). Clearly, since (‘si + si), {VjIprob(q + si) > prob(cj j s:)]}. Similarly (Q + ci) for which similar analysis can be carried out. Thus prob-cycle (B) 2 prob-cycle (B’). Eorollar y :-If B and B’ have the same greatest fulfill- able task space ?-G, but 3(pE B) A 3(p’~B’){p is more powerful than p’}, but N [3(p E B) A 3 (p’ EB’){P’ is more powerful than /3], then 1 B I< 1 B’ I. Residual In this sect ion we consider the parsimony of the logical chain underlying the behaviour chain. If pZ : &+I, then (Q + si+i). There may be some literals in q which are not necessary in this implication, or there may be some disjunctive literals in si+i not referred to by Q. We call this difference between c, and si+l, the residual. If q and si+i are identical, then their residual is null. If 8 is the most general matching string between ci and .si+l , i.e. 0 is the most general construct for which ci + 8 and 0 + s~+~, then we can write ci = 8 A y , sit-l = 0 V CT, then the residual consequence = y, the remedial stimulus = CT and the total residual between (Pi, ,&+I>, &, is defined as y A 10. Residuals are a measure of the degree of coupling in a behaviour chain. The intuition behind this is that as the residual increases, the flexibility as well as probability of cycles increase. Stimulus specialization as well as response generalization decrease the residual. Lemma 4. If two chains C and C’ have identical resid- uals except for some residuals R in Cwhich are stronger than corresponding R’ in C’, then the probability of a cycle is greater in C. Proof :- Consider two behaviour chains Cand C’ where C’ is formed from C by replacing the single behaviour pZ by ‘0:. Then all residuals in the two chains are also identical except fi- 1 and R, . If the residuals in C are stronger, then (ri + 7,‘) and (al-i =+ o,,i), i.e. be- haviour 0 is more powerful than ,0’. Hence by part (c) of the behaviour modification theorem, probability of a cycle is greater in C than in C’. The same argu- ments can be extended for multiple behaviour changes between C and C’. 0 Conclusion In this paper we have focussed on the temporal re- lations between behaviours as opposed to the control relations. This has highlighted an important similar- ity between behaviour-based modeling and the classical models of planning in AI. The effect of actions, which become new stimuli is similar to the postcondition - precondition structure in means ends planners such as STRIPS (Georgeff 1987). One of the approaches used to avoid cyclic conflicts in planning is the meta-level reasoner, idea which has also been used in behaviour systems such as in (Arkin 1992). But purists would not consider these to be true reactive behaviour sys- tems. However, behaviour models differ from plan- ning in some* crucial aspects. Locality of behaviour programming makes opportunistic plan-generation au- tomatic, since the relevant behaviour is triggered au- Control 1283 tomatically when stimulus becomes very strong. Also, cycles are much more of a problem in behaviour models since unlike planners, a behaviour does not “switch-off- and-die” after execution; if the stimulus reappears, it may re-execute, causing a cycle. One of the benefits of this work is that by testing for cycles, the designers will not have nasty surprises awaiting them after implementation. We also show that approaches such as prioritization will not avoid cycles. Thus the only guaranteed met hod for avoid cy- cles is to modify the behaviour itself, and this can be done either by specializing the stimulus or generalizing the response of some behaviour module. Unlike learn- ing, which makes the behaviours more powerful, this reduces the usefulness of the behaviour module. If a robot can pick up a soda can, it should be able to pick up a coffee cup or other similar object. Using stimulus specialization, such a general behaviour would be split into many separate behaviour for picking up separate objects. The principal insight to be gained from this discussion is that in behaviour design, there is a trade- off between the power of a behaviour and the likelihood of cycles. The crucial task of the behaviour designer is to achieve just the right amount of refinement, with- out involving conflicts and without sacrificing too much flexibility. Can conflicts be avoided by using alternate archi- tectures such as fuzzy logic (which allows behaviour designers to model strength of stimulus), meta-level reasoning (Yamauchi & Nelson 1991), or connectionist architectures (Payton, Rosenblatt & Keirsey 1990)? If we ported the can-pickup example into any of these representations, the conflict does not go away, since the conflict arises at the knowledge level and not at the representation level. Using internal state would not, in itself, be able to remove this type of conflict, although it would make it easier to modify the behaviours so that the conflict can be avoided. Another issue related to in- ternal state is the intention of the robot (psychologists read z&l). Knowing the intention at some meta-level, it may be possible to construct tests for detecting con- flicts, and even possibly of avoiding them. At the same time, models involving will or intention (as in Searle) are one of the most debated and difficult quagmires in AI today. Is there then some limit on the complexity of a system of behaviours before self-referential cycles de- velop? A deeper question raised by the presence of such cycles in behaviour based robotics, as well as in other branches of AI, is that of its significance to the entire search for artificial intelligence. Is there some bound on the complexity of any system claiming intelligence, before it begins to develop cyclic conflicts? This paper is a beginning of the search for these answers which are sure to affect the future of the behaviour-based robot 1284 Robotics modeling paradigm in particular for intelligence in general. and that of models References PI PI PI PI PI PI PI PI PI DOI WI I91 WI WI WI Anderson, T. L.; Donath, M. 1990. Animal Be- haviour As A Paradigm For Developing Robot Autonomy, Robotics and Autonomous Systems, 6(1 & 2): 145-168. Arkin, R. C. 1992. Behaviour-Based Robot Nav- igation for Extended Domains, Adaptive Be- haviour l(2): 201-225. Brooks, R. A. 1986. A robust layered control sys- tem for a mobile robot, IEEE transactions on robotics and automation, 2(l): 14-23. Brooks, R. A. 1991. Intelligence without represen- tation, Artificial Intelligence, 47(1-3): 139-159. Connell, J. 1990. Minimalist mobile robotics, A colony style architecture for an artificial creature, Academic press Inc. Gat, E. 1993. On the Role of Stored Internal State in the Control of Autonomous Mobile Robots, AI Magazine, 14(l): 64-73. Georgeff, M. P. 1987. Planning, Annual Review of Computer Science, 2: 359-400. Hartley, R.; Pipitone, F. 1991. Experiments with the subsumption architecture, In Proceedings of the IEEE Conference on Robotics and Automa- tion, 1652-1658. Kirsh, D. 1991. Today the earwig, tomorrow man?, Artificial Intelligence, 47(1-3): 161-184. Maes, P. 1990. Situated Agents Can Have Goals, Robotics and Autonomous Systems, 6(1-2): 49- 70. Miller, D. P. 1993, A Twelve-Step Program to More Efficient Robotics, AI Magazine, 14(l): 60- 63. Minsky M. L. 1986. The Society of Mind, Simon and Schuster. Payton, D.W.; Rosenblatt J. K.; and Keirsey, D. M. 1990. Plan guided reaction, IEEE Transactions on Systems, Man and Cybernetics, 20(6): 1370- 1382 Simon, H. A. 1969. The Sciences of the Artificial, The MIT Press. Yamauchi, B.; Nelson, R. 1991. A behaviour- based architecture for robots using real-time vi- sion, Proceedings of the IEEE Conference on Robotics and Automation, 1822-1827. | 1994 | 265 |
1,614 | Merging Path Planners and Controllers through Local Context Sundar Narasimhan MIT Artificial Intelligence Laboratory, Room 826 Cambridge, MA 02139 sundar@ai.mit .edu Abstract This paper presents an implemented approach to robotic tasks involving intermittent contact and changing dynamics in uncertain environments. The approach is to use global planning to find paths in a tesselated representation of the envi- ronment, and a set of local controllers to take into account possibly time varying dynamics. The important difference from conventional path- planning in robotic tasks is how this approach uses local sensory information, and the impor- tant difference from reactive or behavior-based approaches is that the local controllers are learnt from simulation models or actual trials and are not programmed in a-priori. Introduction Consider a scene as shown in Figure 1. This scene shows a number of polygonal objects resting on the plane. Also shown is a rod (which is a simplified form of a robot) which can move in the plane. While so doing, this rod contacts and pushes the objects in the environment. To simplify what follows, we will assume that the objects in the environment are fixed and only one of them beside the robot can move in the envi- ronment . The task is, stated very simply, to move a specified shape from a starting configuration si to a specified ending configuration sg . This task looks simple. Yet it shares a number of important features with other tasks: It requires interacting with the environment, espe- cially with the object the robot intends to move. In this particular task, because of the lack of a gripper, contact is intermittent. The environment is filled with uncertainty. The po- sitions of the objects are known only to within a certain accuracy, and the effect of actions cannot be predicted with arbitrary precision. More im- portantly, the pressure distribution at the object ’ surface in contact with the table underneath is un- known. While moving the object in its environment, the robot and the moving object can come into contact Figure 1: The Robot and its Environment with obstacles in the environment. The dynamics of predicting the evolution of the object ’ state through such contact situations is difficult if not impossible (see Mason & Wang 1988, Erdmann 1984 and more recently Baraff 1993 about inconsistencies that can arise when one tries to apply models of Newtonian mechanics along with the Coulomb model of fric- tion). Previous Work Given the nature of this problem, how can one program a robot to carry out this task? There have been many approaches to this fundamental problem of a robot interaction with its uncertain environment. However, one can classify almost all of these into two broad cat- egories. In what follows, we will instantiate the two approaches in our pushing domain, in order to illus- trate their main characteristics. The first approach relies on a rather clean separation Control 1285 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. of a planning component from the execution unit. In this approach, a geometric model of the environment is acquired and a path for the object to be pushed is planned. A highly abstract description of an example program for such a task might look like: environment = sense path = findpath (object, s-i, s-g, env) push-object (object, path) The last line in the above program suggests where the execution component is utilized. This execution unit is saddled with the task of actually pushing the object along the path in an uncertain and possibly changing environment. This basic idea has been explored for a wide variety of robot tasks. By separating the planning problem from execution, one could optimize and study them independently. The output of the planner is a sequence of actions. Its input comes from the sensors. However, the raw sensor values are usually pre-processed and related to the retention of state in our reactive compo- nent, this paper does not present those results. In our pushing domain, the state of an object can be parametrized by three variables s = (x:, y, 0)) and con- sequently the configuration space (see Lozano-Perez 1983) of the moving object in its environment is three dimensional. Our model for the dynamics will be quasi-static because it allows the state space to be iden- tified with the configuration space of the moving ob- ject. It should be noted that our model for S is infinite (i.e. s E S = R2 x Sol). Our model for an action will be a tuple Ai = (x, y, dx, dy) where the first two numbers quantify a point on the pushed object where the robot starts to push the moving object, and the last two specify the length and direction of the push in a co-ordinate sys- tern fixed on the moving object. This model of ac- tions is object-centered and comprises the set of linear one-step pushing actions. It should be noted that our model for A is also infinite. merged into a world model. In contrast to this approach stands the reactive and behavior-bused approach for programming robot tasks’. The behavior-based technique was originally suggested to address problems in robot navigation (Brooks 1986) and h as een extended by a number of b researchers (Connell 1990, Brooks 1991). To program a robot to push an object using this approach, one would construct a series of behaviors that map sensory values to actions. Each of these behaviors can be thought of as finite-state machines in the behavior-based approaches or as simple table-lookups in purely reactive systems. Many such behaviors are hooked up in a topology pre- determined by the programmer. Examples have been presented for the navigation task (Mataric 1990), the grasping task (Brock 1993) and numerous others. Conventional planners are brittle in the sense that they cannot handle uncertain or changing environ- ments. They also have to face the problem of sensor fusion in order to merge different sensing inputs into a common world model. Reactive and behavior-based systems on the other hand require careful construction and anticipation, at design time, of the consequences of entire sequences of actions. Approach As has been recognized by many researchers, a frame- work that provides for both global geometric planning and local sensory interaction in order to take uncertain dynamics into account would be extremely useful. In what follows, we describe our approach to this prob- lem and illustrate how it works in the pushing domain. Our approach is a hybrid one that has planning and reactive components. While we have explored issues 1 We ackno w d e the distinction between purely reac- le g the and behavior-based systems. The latter retain state, can use internal representations and are often implemented on distributed systems. Our approach will be to use a geometric planner to plan feasible paths for the pushed object without tak- ing into account any model of uncertainty. This as- sumption makes the planning problem tractable. An execution unit that attempts to push the object along this path will be presented. Both these components are assumed to be running in parallel. The informa- tion that is communicated from the planner to the ex- ecution unit is the set of geometric parameters that specifies the next segment along a path to the goal configuration. We rely on feedback loops to ensure disturbance re- jection and robustness. We will present a controller that can deal with the varying pressure distributions at the support surface quite effectively, when the envi- ronment contains no obstacles. To deal with the fact that the dynamics of pushed objects can change quite drastically upon contacting these obstacles, we present an approach that relies on switching controllers based on sensed local configurations. Global Path Planning We assume that a model of the environment exists and that a global path planner operates on this environ- ment to produce a path. In our experiments, such a model is sensed and built from a vision system that uses a camera mounted beneath the plane in which the objects move. All our objects are assumed to be polyg- onal. In this paper, we do not address the algorithms used in the perceptual component. Furthermore, in the following sections, we will consider the task of moving only one object from a specified starting configuration to a specified goal configuration. The configuration space of the environment charac- terizes all legal positions for the moving object where no collisions exist between the moving object and the stationary obstacles. Obstacles in the configuration space consist of configurations where the moving ob- 1286 Robotics ject would collide with one or more of the stationary obstacles. Our planner constructs these configuration space obstacles using the truce algorithm (Guibas, et al. 1983) extended to handle rotations. We then search a discretized representation of this configuration space to find paths connecting start and goal configurations. Two views of the constructed configuration space for the example in Figure 1 are shown in Figure 2. Figure 3: Paths found by FindPath Figure 2: Two views of 2+1D C-space Paths found in the tesselated configuration space can be displayed graphically. In Figure 3 we show two such paths found by the planner, the second of which con- tains many more segments involving rotations than the first. The path-planner output is encoded by a series of configurations P = xi, yi, 8;. Local Control Even though we now have a desired path for the pushed object, we have not yet specified how the robot is to effect the motion of a pushed object along this specified path. We have explored three alternatives for specifying local controllers. 1. The first approach hand-codes specific behaviors in- tended to effect particular object-relative motion. For example, we wrote behaviors tuned to trans- late the object along the path, and other behaviors that sought to rotate the object clock-wise or counter clock-wise. 2. The second approach was to apply the principles of traditional feedback control to the problem. The idea can best be illustrated graphically. In Figure 4 we illustrate the L-shaped object ’ s initial and final configuration at some stage along the path. A line Od is drawn opposite the line segment connecting the positions occupied by the center of mass of the object as it moves along the path. This line intersects the line segments comprising the polygon in a number of places. The segment that contains the furthest point from 0 is chosen as the segment on which the pushing action will be applied. Since the direction of rotation desired is counter-clockwise, we use Mason Control 1287 along an edge of the object, d the length of the push and d the number of directions along which the pushing action is exerted. Values for these parameters are cho- sen by measuring the performance of the controller on a set of sample tasks. First a set of Ic equally spaced points are chosen along each edge of the pushed ob- ject. This specifies the first two values x, y of the ac- tion tuple. To derive values for the next two values, directions of pushes are sampled into I values in the range [fi + 8,,, , h - e,,,] about this point. ti denotes the normal to the edge and 0,,, was set to 60 degrees. The length of pushes d, is at present held constant to 2 cm. By considering the number of pushes, length travelled between pushes, and the ratio of successful pushes to failures in a specified time period on a set of previously chosen pushing tasks, the algorithm chose Ic = 4, and I = 5 in the examples shown below. This results in the size of A being 120 in this case for the L-shaped object. Figure 4: Geometrical Control Rule rude (Mason 1986) to find a point along the segment RQ and use a small incremental push da:, dy along the translation direction indicated. If no such point can be found, then we choose another edge adjacent to PQ and retry. 3. The third approach uses a local controller that re- lies on a simulated model of the physics of the do- main. The model is based on a randomly varying S-point pressure distribution. We implemented a 2- d minimization procedure (similar to Mason 1982) that takes as input an executed robot motion Ai and produces as output ds = (Sx, Sy, 60) which is the predicted object motion if that action were to be executed. Using this, we produce a forward map from actions to changes in state by repeatedly exe- cuting this simulation procedure for various values of the action tuple. To implement the local controller, we invert this ta- ble using particular choices for distance functions. The last approach uses a table which could be built from actual trials (Christiansen et al. 1991). Other work that is also relevant includes work on bounding loci of possible centers of rotation (Peshkin & Sander- son 1988) and estimating friction parameters of pushed objects (Lynch 1993). The last approach has proven to be robust in car- rying out the required motions in simulations and in actual experiments. In Figure 5 we illustrate the per- formance of this controller in two different trials where the L-shaped object is moved from (40,40,0.8) and (40) 40) 1.57) to (0,O) 0). We choose a particular sampling of the action space based on performance metrics. The parameters we at- tempt to choose are k, the number of pushing points 1288 RobQtics Figure 5: Two execution trails produced by local con- troller Adding Context If the environment had been sensed accurately, and if our model of control is perfect, and if indeed our path-planner produces collision-free paths, we would be done. Unfortunately, reality is rarely this forgiving. Control, sensing and model error all conspire against perfect executions of our nominal paths. The most obvious failures occur because of interac- tions between the pushed object and other obstacles in the environment. Failures include limit cycling on segments of the path, chattering about certain points, and getting into trap states. In such states, the set of applicable actions that produce a noticeable effect reduces to zero. One approach to handling this difficulty would be to attempt to model the dynamics of such interactions and include in the planner the ability to plan paths that take into account these explicit models of dynam- ics. However, we will describe an approach that we have implemented that seems to work quite well. It presently cannot handle trap states. The approach is motivated by the observation that when collisions hap- pen and contact occurs to change the dynamic behav- ior of the pushed object from what the controller ex- pects it to do, what really matters is the locally sensed geometry of the environment. The basic idea is to gen- erate a number of simple controllers to handle each of these local configurations much like the first level con- troller handles object motion in free-space. Figure 6: Illustration of Local Similarity To illustrate the idea, consider Figure 6. Here we show a 2-D representation of a configuration space ob- stacle. The double lines indicate locations where the local contact geometry is similar. The expanded view indicates how if the robot is in a configuration cell marked Z, its local view of the configuration space is identical if 4 or 8 neighbouring cells are considered. The reason for defining locality in configuration space should now be obvious. Since one can essentially view the pushed object as having been reduced to a point in this space, tests for locality can be much simpler even for objects of complicated shapes. If we use only or- thogonal neighbor& in a tesselated representation of the configuration space to define locality, then in an n-dimensional space we have 22n possible local config- urations. For each one of these, our approach attempts to learn a local control rule that applies, much like the first level controller was learnt in free-space. It is this local configuration that we label context. The planning, control and learning algorithm for the pushing task now looks like: push-object (object, segment) context = sense-local-context controller = find-control (context) if ( controller = NIL > learn-rule (context 1 find-action (controller, object, segment) Figure 7: Peg-In-Hole Assembly by Pushing Such a decomposition of the task-level strategy us- ing local context has been the key to deriving robust strategies (see Figure 7 for four intermediate frames from the vision system during an assembly task). This approach has been the first one to solve all our exam- ples we have thus far tested it on2. In our simulated examples, with a , library of 30 part shapes on 20 tasks this approach is the only one that solves some of the complicated examples, and the only one not to exhibit significant limit cycling or chatter. It should be noted that: 1. The locally sensed configuration space allows us to implement robot relative control loops extremely easily. Reactive behaviors that attempt to follow a moving object can be expressed quite easily in this framework. 2Control and angular error in our similations have been [-lo, lo] d e g rees in the direction of the push, and position sensing error has been a ball of 1 cm. Control 1289 2. 3. 4. 5. We do not seek to compute a single controller to handle the entire task, but settle for a set of con- trollers instead. We thus tread a path that is mid- way between approaches that seek a single sequence of actions, and approaches that attempt to derive a single map from sensed states to actions. In practice, we do not actually need 22n controllers. Our examples seem to require about 2n controllers on average. This is still exponential and a more pre- cise bound would be desirable. There is no inherent restriction that we only plan the path once. In fact, in domains where fast path planning can be implemented easily, we can envision the path to be the output of an any-time planner that is in continous operation. At present, we do not change the different con- trollers once they are built. However, the frame- work does not prevent controllers whose parameters are changeable over time, or choosing actions using different algorithms than the ones we have presently implemented. Conclusion We have presented an approach that solves the prob- lem of pushing objects around in the plane from con- figuration to configuration in a robust fashion. The approach’s strength lies in the combination of a global path planner along with a set of local control laws or feedback rules that are activated depending upon the local context the pushed object is in. The global path planner can be viewed to be con- tinually in operation, while the local controllers can be derived automatically from simulation models or actual trials. In certain domains, geometry crucially affects dynamics especially when objects interact. The success of manipulator operations hinges on taking into account such geometrical effects. Our approach relies on a decomposition which allows the planner to oper- ate in configuration space while ignoring the dynamics and the evolution of a set of controllers to deal with lo- cal dynamics. We expect such an approach to be more successful than others that attempt to take all of the dynamics into account at planning time, and others that rely entirely on local controllers. References 1. Baraff, D., 1993. Issues in Computing Contact Forces for Non-Penetrating Rigid Bodies, Algorith- mica, 10 : 292-352. 2. Brock, D. L., 1993. A Sensor Based Strategy for Automatic Robotic Grasping, Ph. D. Thesis, De- partment of Mechanical Engineering, Massachusetts Institute of Technology. 3. Brooks, R. A., 1986. A Robust Layered Con- trol System for a Mobile Robot, IEEE JournaE of Robotics and Automation, RA-2 (1) : 14-23. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13 14 15 Brooks, R. A., 1991. Intelligence Without Reason, Proceedings of the International Joint Conference on Aritifical Intelligence, 569-595. Connell, J., 1990. A Colony Architecture for an Artificial Creature, MIT AI-TR-1151, Artificial In- telligence Laboratory, Massachusetts Institute of Technology. Christiansen, A. D., Mason, M. T. and Mitchell, T. M., 1991. Learning Reliable Manipulation Strate- gies Without Initial Physical Models, Robotics and Autonomous Systems, 8 : 7-18. Erdmann, M. E., 1984. On Motion Planning with Uncertainty, S. M. Thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology. Guibas, L., Ramshaw, L., and Stolfi, J., 1983. A Kinetic Framework for Computational Geometry, Proc. of the 2d’th Annual IEEE Conference on the Foundations of Computer Science, 100-111. Lozano-Perez, T., 1983. Spatial Planning: A Con- figuration Space Approach, IEEE Transactions on Computers, C-32 (2) : 108-120. Lynch, K., 1993. Estimating the Friction Param- eters of Pushed Objects, IEEE/RSJ International Conference on Intelligent Robots and Systems, 186- 193. Mason, M. T., 1982. Manipulator Grasping and Pushing Operations, Ph. D. Thesis, Dept. of Elec- trical Engg. and Computer Science, Massachusetts Institute of Technology. Mason, M. T., 1986. Mechanics and Planning of Manipulator Pushing Operations, International Journal of Robotics Research, 5 (3) : 53-71. Mason, M. T. and Wang, Y., 1988. On the incon- sistency of rigid-body frictional planar mechanics, Proc. IEEE Conference on Robotics and Automa- tion, 524-528. Mataric, M., 1990. A Distributed Model for Mobile Robot Environment Learning and Navigation, AI- TR-1228, Artificial Intelligence Laboratory, Mas- sachusetts Institute Of Technology. Peshkin, M. A. and Sanderson, A. C., 1988. The Motion of a Pushed, Sliding Workpiece, IEEE Jour- nal of Robotics and Automation, 4 (6) : 569-598. 1290 Robotics | 1994 | 266 |
1,615 | Teleassistance: Contextual Guidance for Autonomous Manipulation* Polly K. Pook and Dana IX Ballard Computer Science Department University of Rochester Rochester, NY 14627-0226 USA pookldana@cs.rochester.edu Abstract We present teleassistance, a two-tiered control struc- ture for robotic manipulation that combines the ad- vantages of autonomy and teleoperation. At the top level, a teleoperator provides global, deictic refer- ences via a natural sign language. Each sign indi- cates the next action to perform and a relative and hand-centered coordinate frame in which to perform it. For example, the teleoperator may point to an object for reaching, or preshape the hand for grasp- ing. At the lower level autonomous servo routines run within the reference frames provided. Teleassistance offers two benefits. First, the servo routines can po- sition the robot in relative coordinates and interpret feedback within a constrained context. This signif- icantly simplifies the computational load of the au- tonomous routines and requires only a sparse model of the task. Second, the operator’s actions are sym- bolic, conveying intent without requiring the person to literally control the robot. This helps to alleviate many of the problems inherent to teleoperation, in- cluding poor mappings between operator and robot physiology, reliance on a broad communication band- width, and the potential for robot damage when solely under remote control. To demonstrate the concept, a Utah/MIT hand mounted on a Puma 760 arm opens a door. Introduction Autonomous servo control and teleoperation have com- plementary advantages and disadvantages as robotic control schemes. Servo control of robotic manipula- tion has benefited from the development of compliant manipulators with rich position and force sensing ca- pabilities. When situated in a local context, fast dis- tributed servo feedback enables a robot to react quickly and appropriately [Brooks 19861 [Connell 19891. Servo control currently suffers, however, from a poor ability to perceive and plan according to global state. Tele- operation addresses this weakness by putting a person *This work was supported by NSF research grant no. IRI-8903582 and by a research grant from the Human Sci- ence Frontiers Program. in the loop, one who can provide more global guid- ance. But teleoperation eliminates local servo control, resulting in slow jerky movement that is quite tedious for the teleoperator. Local reactivity is lost. What is needed is a two-layer control strategy: a high level to select a context in which low-level behaviors situate Consider the advantages of each control mechanism for the hypothetical task of planing a board. A tele- operator can more easily set up the task by locating and positioning the planer on the board, than an au- tonomous robot can. Once context is established the servo controller more readily maintains a smooth, slid- ing contact with the board. It moves along the central axis of the planer, independent of world coordinates, while tightly monitoring force feedback on an orthog- onal axis, independent of the orientation of the board. Feedback is interpreted within the context of planing to adjust force and position. The teleoperator provides a high-level reference context that low-level servo be- haviors could exploit. Setting up a reference frame for subsequent relative actions is an example of a deictic, or pointing, strat- egy [Agre & Chapman 19871. We propose a teleas- sisted controller for robotic manipulation that inter- faces high-level deictic strategies with context-sensitive servo behaviors. A person wearing a master teleopera- tion device provides the deictic references. Rather than literally teleoperate the robot and bear the concomi- tant problems of delayed and limited feedback, the op- erator uses a gestural sign language to select successive contexts for low-level autonomous force and position control. Deictic strategies Studies suggest that animals use high-level deictic strategies to bind low-level perceptual and motor behaviors to the current context [Kowler & Anton 19871 [Ballard et al. 19921. Visual fixation is an ex- ample of a deictic strategy that binds motor behavior to a relative coordinate frame. For example, an object can be grasped by first looking at it and then direct- ing the hand to the center of the image coordinate frame. In depth, the hand can be servoed relative to Control 1291 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. the horopter using binocular cues. This strategy is in- variant to agent movement and task locale. Like visual fixation, the act of grasping an object provides a framework for interpreting the associated kinesthetic feedback. For example, bi-manual animals often use one hand as a vise and the other for dexter- ous manipulation. We hypothesize that the vise hand marks a reference frame and that the dexterous mo- tions are made relative to that frame. Similarly, body position creates a reference for motor actions. Stud- ies of human hand-eye coordination have found head movements to often be closely associated with hand movements. [Pelz et al. 19941 found that most subjects square their head with respect to the site of a complex manipulation action and then hold it very still during the manipulation, even when the eyes are looking else- where. This fits our hypothesis if we consider head position as a reference frame for relative hand motion. To make this more concrete as a control strategy, we assign a deictic strategy two roles: to make a temporal and a spatial binding to the world. Temporal binding The intended action, such as reaching or grasping, binds the servo controller to the temporal context. Without a detailed model of the world, many interpre- tations of feedback are possible; temporal context can allow the controller to select the correct one. Earlier studies demonstrate the importance of temporal con- text in reducing the complexity of robot motor tasks. In [Pook & Ballard 19921, a Utah/MIT dexterous ma- nipulator autonomously grasps a spatula, positions it in a pan and flips a plastic egg without relying on pre- cise positioning or force information. Each successive action is controlled by interpreting qualitative changes in force feedback within the current context. For ex- ample, identifying force contact can be done by sim- ply noting a significant change in tension on any hand joint, regardless of the particular hand or task config- uration. To determine what event is associated with a qualitative change in force, whether it be from grasping the spatula, placing it in the pan or sliding it under the egg, the controller can refer to the current context. In deterministic sequential tasks, this context is implicit in the control program. This approach has parallels with the behavioral approach of [Salganicoff & Bajcsy 19911 but relies on local feedback. Spatial binding A spatial binding defines a relative coordinate frame for successive perceptual and motor behaviors. Deic- tic bindings avoid world-centered geometry that varies with robot movement. For fixation the reference is gaze-centered. To open a door, for instance, looking at the doorknob defines a relative servo target. [Crisman & Cleary 19941 demonstrate the computational advan- tage of target-centered frames for mobile robot navi- gation. Pointing and preshaping the hand create hand- centered spatial frames. Pointing defines a relative axis for subsequent motion. In the case of preshaping, the relative frame attaches within the opposition space [Arbib, Iberall, & Lyons 19851 of the fingers. With adequate dexterity and compliance, simply flexing the fingers toward the origin of that frame coupled with a force control loop suffices to form a stable grasp. Since the motor action is bound to the local context, the same grasping action can be applied to different ob- jects, a spatula, a mug, a doorknob, by changing the preshape. A teleassisted control strategy In teleassistance, the operator, wearing a master de- vice, guides the robot with natural gestures that cor- respond to the task at hand. These gestures form a sign language. The signs are deictic in that they define a spatial and temporal context for subsequent robot behaviors. A sign is recognized by monitoring the operator’s finger positions and matching them to stored models. On recognition of a hand sign, the controller calls the servo behaviors, with the current spatial context as a parameter. In this way, a per- son motions the robot through a complex and possibly non-deterministic task. Each sign can be mapped to a high-level state in a non-deterministic finite state machine (FSM), as shown in Figure 1. At top are the deictic states, marked with dashed lines. From each high-level state, control is passed to the appropriate low-level servo rou- tines, shown at bottom, that perform the intended ac- tion. The two state classes are separated in the figure for clarity. In practice, all states belong to a single FSM for the task. The topology encodes the task con- text. We will illustrate teleassistance through the task of opening a door. A simple scheme for door-opening is to reach for the handle, then grasp and turn it. Under teleassistance, the task might be performed as follows. The operator steers the robot to the door handle by poigting and shapes the hand and wrist for the handle type. The robot in turn moves along the given direc- tion until it bumps into the door, copies the operator’s hand shape, moves to contact the handle, then grasps and turns it. These behaviors are described in detail in the next section. The non-determinism of the FSM affords the opera- tor some flexibility. The operator may choose to com- pose task actions arbitrarily when order is not crucial. Or the operator may wish to take emergency action when an error is detected. The FSM topology can be designed to support such deviations. In our simple ex- amples, the operator can rest or stop at intermediate points in the task. It is worth noting that the topology must be pre-specified for each task and so this flexibil- ity is restricted. 1292 HMM for “Openinu a Door” contexts REACH GRASP TURN ____________________________.______________________.._____..__.._........................................ /---. I ‘\ ,---. ,---. , -\ , *\ deictic I’ point behavior?< torfixate) ‘\, I/’ grasp ‘\, II’ grasp ‘\, -[ preshape ,I -\ preshape ’ \ ,I \ I’ Underlying servo behaviors servo behaviors _____________________.___________________..______.__.________________..............~..-.......-.......... subtasks REACH GRASP TURN Figure 1: A FSM for opening a door. The flow of control among high-level states is shown at top. Each deictic ges- ture, marked with a dashed line, defines a relative coordi- nate frame and a task context (REACH, GRASP, TURN). From a deictic state, control is passed to appropriate low- level robot behaviors that perform the sub-task (shown at bottom). Each low-level action moves within its relative frame, servoing on guard conditions such as force contact. Example: Opening a door To illustrate the two-tiered control strategy, a robot manipulator opens a small door equipped with a lever handle. The door is placed arbitrarily within the work- ing space of the hand. Each high-level deictic routine, ties a temporal context (REACH, GRASP, TURN) and a relative coordinate frame to subsequent low- level actions. In this example, all coordinate frames are hand-centered. The low-level servo routines are a sequence of guarded moves. The direction of each move (of the fin- gers and/or the arm) is implicit in the context of the task and is made relative to the current frame. Feed- back consists of finger position error, i.e., the difference between the actual and commanded finger joint angles. A change in the position error is interpreted within the current context of REACHING, GRASPING, etc., to control the action appropriately. Each routine is de- scribed in greater detail below. Lab Setup Hardware The manipulator is a sixteen degree-of- freedom Utah/MIT hand mounted on a six degree-of- freedom PUMA 760 arm. The hand has four fingers with four joints apiece. A pair of pneumatically driven agonist-antagonist tendons actuates each joint. Hall effect sensors monitor each joint angle. The hand is both dexterous and compliant so its control strategy can ignore many inessential variations in the task con- figuration, such as the precise shape and orientation of a door handle [Pook & Ballard 19921. The teleoperator wears an EXOS Dexterous Hand Master (TM) that measures four joint angles on each of four fingers. Additionally, an Ascension Bird (TM) polhemus sensor mounted on the back of the teleoper- ator’s hand measures the position and orientation of the operator’s arm and wrist in lab coordinates. Coordinate frame mapping The teleoperator and the robot each have their own relative coordinate sys- tems with a mapping between them. For arm motion, only the orientation of the teleoperator’s polhemus sen- sor is mapped to the corresponding robot frame. For finger motion, only the joint angles are mapped. In either case, translation is ignored. The sign language The sign language for this task consists of six signs: point, preshape, rest, emergency stop, speedup, and slow down. Previously, we empiri- cally derived a range of permissible joint angles for the operator’s hand and arm for each sign. To recognize a sign on-line, the program monitors the joint angles on the EXOS and polhemus devices and identifies a match when it occurs. We are currently working on learning new signs automatically, rather than through empirical determination. See the last section, Future Work, for details. The program REACHING for the door. The teleoperator com- mences action by pointing the robot arm toward the door, as shown in the upper left of Figure 2. This provides a temporal launching point for the program and defines a spatial coordinate frame centered on the back of the robot hand. While the operator points, the PUMA moves in the direction of the pointing axis, independently of world coordinates. Thus the robot reach is made relative to a deictic axis which the tele- operator can easily adjust. The autonomous move monitors the guard condition of a change in position error on any of the Utah/MIT finger joints. In the context of REACHING, the change in robot finger position is interpreted as contact with a non-compliant surface and the reach halts and backs off a small distance from the point of contact. So, when the hand bumps into the door, the arm stops. Control 1293 Figure 2: At top are the teleoperator reference poses to REACH, GRASP and TURN the door handle. For illustrative purposes both a lever and a knob are shown, although only the lever is used. Snapshots of subsequent robot behavior are shown at bottom. In REACHING, the context of a pointing index finger signifies that only the x-direction of the polhemus sensor is important. In GRASPING the overall shape of the three fingers and the thumb define a preshape for the particular handle. In TURNING, the grasp shape reveals the handle type and, by extension, its pivot point. Notably, the robot hand itself could provide the deictic reference for TURNING, by noting its current pose. The FSM has self-loops in each deictic behavior so that the operator can successively point in new direc- tions to accurately place the robot hand. In a typi- cal trial, the operator points the robot arm toward the door. When the robot reaches the door by sensing con- tact, the operator repeatedly points anew to position the hand over the door handle. Each movement halts when the operator changes the pointing axis, stops pointing, or the hand detects contact. A new point- ing axis initiates a new movement. When satisfied, the teleoperator adopts a grasp preshape. The FSM recognizes the new sign and shifts context to that of GRASPING. GRASPING the door handle. A grasp preshape defines a new spatial frame centered on the palm of the hand. The robot mimics the preshape using a lin- ear, joint to joint mapping between the EXOS and the robot hand [Speeter 19931. The middle column of Fig- ure 2 shows the preshape for turning the door lever. Subsequent servo routines find the handle and grasp it. In the new spatial context, the negative Z-axis points out of the palm. To find the handle, the robot hand moves along this axis until it senses contact. The ad- vantage of a deictic framework can be seen by compar- ing this action for different door handles. For the door lever, the hand-centered Z-axis points downward. For a knob, the Z-axis is horizontal. The move is indepen- dent of world coordinates, however, because it is made rn1qt;. re to the hand frame. iange in position error, resulting from contact with the doorhandle, stops the motion. In either case, the controller interprets the error as contact and so, within the current context, proceeds to grasp. To grasp the door handle, the robot flexes the finger joints until they are all either fully flexed or maintain- ing a position error. The preshape set the fingers in opposition to one another as needed to grasp the par- ticular door handle. Because the grasp is performed within the context of that preshape this strategy ap- plies to either door handle. TURNING the handle. The robot pose (or the human preshape) defines whether the context is one of grasping a knob or a lever. The rightmost column of Figure 2 shows the hand grasping the door knob. In this case the pivot point of the handle is set to the center of the palm (i.e., the origin of the current deictic frame). If the hand shape corresponds to a wrap grasp, then the pivot is about a point alongside the grip, i.e., offset along the current Y-axis which corresponds to the axis of the lever. A new spatial frame is attached to the pivot point and the arm rotates about the new Z- axis. Such a rotation is much simpler than computing an equivalent trajectory in lab space. ‘ hand must be positioned fairly accurately over the lever, such that one or more of the finger links makes con- tact with it. A better solution is to have a contact sensor on the palm or a force sensor in the wrist. 1294 Robotics The arm continues its rotation until a position error is sensed. In this context, the controller interprets the error to mean the handle’s mechanical stop has been reached. Results Four different operators each performed ten trials of the task under teleoperation control and ten trials un- der teleassistance. For each controller, the operators trained until they were comfortable: 10 to 15 minutes for teleoperation and 2 to 10 minutes for teleassistance. Twice during each lo-trial set, the door was moved to a new position selected arbitrarily within the workspace. The results are shown in Table 1, along with the results of a completely autonomous controller. Teleas- sistance required about the same amount of time as the autonomous controller, and both are, on average, 33% faster than teleoperation. The time is occupied dif- ferently by each controller, however. 60% of the time spent under teleassistance is in fact under autonomous control. Thus, the operator actually spent only 8 sec- onds, on average, controlling the robot via hand signs. The teleoperator, in contrast, spent more than treble the time (29 sec.) in literal master-slave control of the robot. The teleoperator, however, is able to avoid failures that other two controllers cannot. In the case of teleas- sistance, all failures were due to not turning the door handle far enough to free the catch. The servo con- troller did not detect the mechanical stop correctly. The autonomnous controller failed due to its reliance on hard-coded position information. Thus, changing the doors position twice during the trials resulted in the controller failing (not finding the door or the han- dle) two-thirds of the time. This figure is not general- izable as it depends entirely on the degree of certainty in the task. In a structured, static environment, the autonomous controller would work very well. In an un- structured world, however, teleassistance is preferable. Conclusion and related work The idea of combining traditional teleoperation and autonomous servo controllers has been suggested in various forms by several researchers. [Sayers, Paul, & Mintz 19921 at the University of Pennsylvania Grasp Lab allows the teleoperator to select among a menu of geometric targets. The teleoperation apparatus (the master) is then constrained to motions along the se- lected geometry. [Yokohoji et al. 19931 suggest build- ing a manual control box which the teleoperator can pre-set to a desired strategy as needed: full teleop- eration, full autonomy, or one of two combinations . [Kuniyoshi, Inaba, & Inoue 19921, [Ikeuchi & Suehiro 19921, and [Kang & Ikeuchi 19941 visually recognize teleoperator motions to guide the robot. Our approach is to make the transfer of control be- tween teleoperator and robot implicit in the context of the task. A task specific FSM encodes the context in its topology. The teleoperator, rather than being responsible for direct control of the robot, guides the robot with gestures and supplies the spatial and tem- poral frameworks in which to situate the autonomous servo behaviors2. The behavior can then operate in a relativistic constrained domain and perform with computational efficiency. This method of providing for local interpretation of feedback compares with the qualitative vision strategies made possible with gaze control vision systems [Ballard 1991][Ballard & Brown 19921 . Given the task context, these methods can rely on a very sparse model of the world. Such strategies are common to animal systems [Bower 1982][Twitchell 19701 but are a notable departure from traditional robot control schema that rely on precise force and position models. Future work: acquiring and recognizing new hand signs The transfer of control between high and low-level be- haviors, implicit in the task, requires explicit recogni- tion of the sign language used by the operator. Cur- rently, we provide an a priori empirical model of each hand sign. This method has at least two drawbacks. One is that the models must be robust to different operators and to the non-linearities of the EXOS de- vice. We have handled this by defining the models quite loosely. However, as more signs are added to the lexicon, overlap will occur and ambiguity will arise. A more accurate, but still robust, method is needed. Secondly, it would be useful to learn signs dynamically, allowing for operator preference. Earlier studies suggest a remedy to these drawbacks. These studies demonstrate the ability to learn and rec- ognize manipulation primitives from temporal features in the robot state [Pook & Ballard 19931. (see also [Hannaford & Lee 19911). In this experiment, sev- eral teleoperators performed samples of each primi- tive while we recorded the finger joint tensions and velocities. By applying Learning Vector Quantization (LVQ) [Kohonen 19901 to these recordings we could create canonical patterns for each primitive. Using these learned patterns we could segment a compound manipulation task, flipping an egg, into its recogniz- able primitives, although with numerous errors. How- ever these errors, in the form of ambiguities and spuri- ous misclassifications, could be eliminated by perform- ing the segmentation within the context of the task. The context was encoded in the topology of a hidden markov model (HMM), just as the context of opening a door is encoded in an FSM. An HMM is a probabilis- tic finite state machine that models a markov process; i.e., it accommodates natural variation and is sensitive only to the current state[see Rabiner & Juang 19861. ‘If other deictic inputs are puter vision system with gaze the teleoperator where desired. available, such as a com- control, they could replace Control 1295 Avg. Time Mean Time % Time under Failure Controller (sec.) (sec.) Operator control Auto control Rate Teleoperation 29 24.5 100% 0% 0% Teleassistance 20 19.0 40% 60% 13% Autonomy *see text Table 1: Results for the task of opening a door under the three controllers. The probabilistic contextual constraint provided by the HMM makes matching considerably easier. This method of pattern-matching within a known context was robust to the vagaries of different opera- tors and changes in the task configuration. We are now investigating the use of this method to dynamically and automatically learn the deictic sign language. Prelim- inary results are promising and address the drawbacks of our present empirical scheme. Acknowledgments The authors wish to thank Ray Frank, Tim Becker and Luid Bukys for their technical assistance and for- bearance and John Lloyd and Vincent Hayward for the RCCL Puma controller. PI PI PI Bl PI PI VI PI PI WI References P. E. Agre and D. Chapman. Pengi: An implementa- tion of a theory of activity. In Proceedings of the Sixth National Conference on Artificial Intelligence, pages 268-272. Morgan Kaufmann, Los Altos, CA, 1987. M. Arbib, T. Iberall, and D. Lyons. Coordinated con- trol programs for movements of the hand. Technical report, COINS Dept. of Comp. and Inf. Science, Uni- versity of Massachussetts, 1985. D. H. Ballard. Animate vision. Artificial Intelligence, pages 57-86, February 1991. D. H. Ballard and C. M. Brown. Principles of animate vision. CVGIP: Image Understading, July 1992. D.H. Ballard, M.M. Hayhoe, F. Li, and S.D. White- head. Hand-eye coordination during sequential tasks. Proc. of the Phil. Trans. Royal Sot. of London, 1992. T. G. R. Bower. Development in Infancy. New York: W.H. Freeman and Co., 1982. R. Brooks. A layered intelligent control system for a mobile robot. IEEE Journal of Robotics and Automa- tion, pages 14-23, April 1986. J. Connell. A colony architecture for an artificial crea- ture. Tech. Report 1151, MIT AI Lab, 1989. J. Crisman and M. Cleary. Deictic primitives for gen- eral purpose navigation. Proc. of the AIAA Conf. on Intelligent Robots in Factory, Field, Space, and Ser- vice (CIRFFSS), March 1994. B. Hannaford and P. Lee. Hidden markov model anal- ysis of force/torque information in telemanipulation. International Journal of Robotics Research, pages 528- 538, October 1991. WI P21 WI PI P51 PI PI PI PI PO1 WI PI PI WI K. Ikeuchi and T. Suehiro. Towards an assembly plan from observation. Proc. of the IEEE International Conference on Robotics and Automation, May 1992. S.B. Kang and K. Ikeuchi. Grasp recognition and ma- nipulative motion characterization from human hand motion sequences. Proc. of the IEEE International Conference on Robotics and Automation, May 1994. T. Kohonen. Improved versions of learning vector quantization. Proc. of the International Joint Con- ference on Neural Networks, June 1990. E. Kowler and S. Anton. Reading twisted text: Im- plications for the roIe of saccades. Vision Research, pages 27:45-60, 1987. Y. Kuniyoshi, M. Inaba, and H. Inoue. Seeing, under- standing and doing human task. Proc. of the IEEE Int’l Conf. on Robotics & Automation, May 1992. J. Pelz, M. M. Hayhoe, D. H. Ballard, and A. Forsberg. Separate motor commands for eye and head. Submit- ted, Investigative Ophthalmology and Visual Science, Supplement 1994, 1993. P. K. Pook and D. H. Ballard. Sensing qualitative events to control manipulation. Proceedings of the SPIE Sensor Fusion V Conference, November 1992. P. K. Pook and D. H. Ballard. Recognizing teleoper- ated manipulations. Proc. of the IEEE International Conference on Robotics and Automation, May 1993. L.R. Rabiner and B.H. Juang. An introduction to hidden markov models. IEEE ASSP Magazine, Jan. 1986. M. Salganicoff and R. Bajcsy. Sensorimotor learning using active perception in continuous domains. AAAI Fall Symposium Series: Sensory Aspects of Robotic Intelligence, November 1991. C. Sayers, R. Paul, and M. Mintz. Operator inter- action and teleprogramming for subsea manipulation. 4th IARP Workshop on Underwater Robotics, 1992. T. H. Speeter. Transforming human hnad motion for telemanipulation. Presence: Teleoperators and Virtual Environments, 1992. W. Twitchell. Mechanisms of motor development. In Reflex Mechanisms and the Development of Prehen- sion. New York: Academic Press, 1970. Y. Yokohoji, A. Ogawa, H. Hasanuma, and T. Yoshikawa. Operation modes for cooperating with autonomous functions in intelligent teleoperation sys- tems. 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1,616 | Automatically Tuning Control Systems for Simulated Legged Robots Robert Ringrose MIT Leg Lab MIT Artificial Intelligence Laboratory 545 Technology Square Cambridge, MA 02139 ringrose@ai.mit .edu Abstract Rather than create a control system from scratch each time we build a new robot creature, we would like to generate control systems automatically. I have imple- mented an algorithm which, given a control system that works well for one creature, automatically tunes it to work for a new, similar creature. Using this ap- proach, the control system for a horse might be ad- justed for use with elephants, giraffes, and dogs. The adjustment is accomplished by gradually altering the original creature to make it like the new one and re- peatedly tuning the control system as these changes are made. Because the creature’s alteration is grad- ual, the control system can be tuned using a local search such as gradient descent. In simulation tests, the tuning algorithm has successfully tuned the con- trol system of a planar quadruped simulation to ac- commodate a reduction in leg length by a factor of two, an increase in body mass by a factor of three, and changes in the commanded speed while trotting. Introduction Within the domain of actively balanced legged locomo- tion, it is necessary to tune control systems to reflect physical alterations of the robot. I have designed and implemented a tuning algorithm which will tune an ex- isting control system to control a different robot, or to exhibit different behavior. This algorithm has success- fully tuned the control system of a planar quadruped simulation to accommodate a reduction in leg length by a factor of two, an increase in body mass by a factor of three, and changes in the commanded speed while tr0tting.l Any control system has some set of control param- eters, numbers which determine how it performs. For example, a parameter might control how rapidly it tries to accelerate to a desired speed or how much energy it injects at each step. For a complicated system, the ‘This material is based upon work supported under a National Science Foundation Graduate Research Fellow- ship. Any opinions, findings, conclusions, or recommen- dations expressed in this publication are those of the au- thor and do not necessarily reflect the views of the National Science Foundation. appropriate values for these control parameters are not obvious. There are several advantages to having a com- puter search for a set of parameters which minimizes an evaluation function rather than having a human tune the control system directly. Automatically tuning the control system does not require that a human with ex- perience tuning invest a large amount of time. One can also specify the desired behavior without considering the interactions between any specific input parameters to the control system. Additionally, it is easier for a computer to optimize for something which is not obvi- ous to a human, such as minimal energy consumption. Properly specifying the desired behavior is not a triv- ial task, but it seems easier than manually tuning the control system. Other work on self-tuning controllers (Helferty, Collins, & Kam 1988), which frequently used search- ing techniques such as spacetime constraints (Witkin & Kass 1988) or genetic algorithms (Pearse, Arkin, & Ram 1992), h as addressed similar problems. Tuning controllers for dynamically balanced legged systems is particularly challenging because there is typically only a small “sweet spot” near the global minimum where one can effectively evaluate the robot’s behavior. A pa- rameter set outside this sweet spot will generally make the robot fall over or not take any steps, while a pa- rameter set inside the sweet spot will make the robot run well enough that its performance can be evaluated objectively. The vast majority of the possible parame- ter sets for dynamically balanced legged locomotion lie outside of the sweet spot. As a consequence, general search methods like genetic algorithms and simulated annealing will take a long time to find any working so- lution, and searches which follow a local slope will only find a useful minimum if they start in the sweet spot. A frequently used method for getting around this chal- lenging search space is to simplify the problem so as to drastically increase the sweet spot’s size (for exam- ple, one can add constraints to the model that prevent the robot from falling over). Instead of modifying the search space tosuit my algorithm, however, I have at- tempted to adjust my algorithm to fit the search space. In the event that there is a parameter set which is Control 1297 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Figure 1: Illustration of the simulated quadruped and the associated model. The actuators at the hips are imple- mented as torque sources. The leg actuator is implemented as a spring with controllable rest length and different constants in compression and extension. The simulation is a planar rigid-body model. in the sweet spot, a simple gradient descent search can find a local minimum. Additionally, most of the time a small change in the robot’s configuration will result in only a small change in the sweet spot. The tun- ing algorithm presented here uses this characteristic to break the search for a new set of parameters into a series of smaller searches for which minima are eas- ier to find. For example, assume the control system for a quadruped running simulation has been tuned to run with legs of a particular length. To find a set of control parameters for a quadruped running with legs half as long, the tuning algorithm gradually reduces the leg length and optimizes at several leg lengths be- tween full and half length. As the leg length changes, the location of the sweet spot will change. For small changes the sweet spot’s motion will usually be slight enough that the control parameters for the unchanged leg length will still be within the new sweet spot. The tuning process may fail if gradient descent cannot find a local minimum (the sweet spot might not be contin- uous), if the sweet spot changes dramatically with a small alteration in the robot, or if there is no way for the given control system to control the robot. To find appropriate values for the control param- eters, the tuning algorithm described in this paper starts with an existing control system, simulation, and parameter set. It finds out how far it can modify the simulation and still get acceptable behavior, makes that modification, and then uses a gradient descent search to improve the performance of the modified sim- ulation. This process of modifying the simulation and re-tuning the control system is repeated until you have the desired final simulation. The Simulation I have used a planar quadruped simulation to test the tuning algorithm. It retains enough complexity to il- lustrate most of the problems that come up, but is sim- ple to visualize and easy to explain. The simulation is 1298 Robotics based on a physical robot described by Raibert (Raib- ert, Chepponis, & Brown 1986)(Raibert 1990). The simulation is a rigid body simulation, the dy- namics of which are generated using a commercial dynamic modeling program (Rosenthal & Sherman 1986)(Ringrose 1992a). Simulation creation is auto- mated so that it is possible to change and re-create any simulation as part of the tuning process. The pla- nar quadruped which I used is illustrated in figure 1. The simulated robot is controlled by a planar varia- tion of the finite state controller for the Raibert trot- ting quadruped (Raibert et al. 1992). The control system uses measurements which could be sensed or calculated on a physical robot, such as position, veloc- ity, actuator lengths, and ground contact. The control system’s behavior can be modified through 20 param- eters, including maximum acceleration, desired speed, spring constants, and desired leg length during differ- ent running phases. Some previous investigations into robotic running are described in references (Hodgins & Raibert 1989)(Hodg ins & Raibert 199l)(Playter & Raibert 1992)(Raibert et al. 1992). Further details of the controller and model are available in (Ringrose 1992b). Searching for Solutions In order to search for an appropriate set of control parameters, you need a way to compare the behavior generated by different sets of control parameters. I use the results from an evaluation function which sim- ulates the creature and returns an objective measure of the creature’s performance. Most evaluation func- tions for dynamically stable running motions result in a search space whose structure makes global searching algorithms ineffective. However, once you have a rea- sonably good solution, a gradient descent search (Press et al. 1988) modified to take into account local min- ima (Ringrose 1992b) will frequently be able to find a better solution. Figure 2: Graph of evaluation results over changes in leg spring and damping constants for the planar quadruped, using the evaluation function described in the text. The noisy, high-valued regions are outside the sweet spot. The right graph is the same as the left, with a lower maximum value imposed to emphasize the structure of the sweet spot. Most evaluation functions for legged locomotion have a nearly pathological search space because if the parameters are out of a small sweet spot around the good solutions the simulated creature fails catastroph- ically, usually by falling over or not taking any steps. When such a failure occurs, a meaningful evaluation of performance is difficult since the causes of the sim- ulation’s failure to trot are difficult to determine. The creature could fall over if it stubs its toe, the leg springs are not strong enough, the swing legs do not come for- ward fast enough to catch the robot, or some other reason. It is not difficult to make an evaluation func- tion which recognizes when it is out of the sweet spot, but it is difficult to ensure that when outside the sweet spot the gradient of the evaluation function leads to- wards the sweet spot. Because of the inherent difficulty evaluating a catas- trophic failure, most evaluation functions only have a useful section near the global minimum and the rest is noise. Evaluation functions usually have more dimen- sions than can be readily visualized, but cross sections can give an idea of the search space’s general struc- ture. A two dimensional cross-section of the evaluation function is somewhat like a smooth canyon (the sweet spot) in noise, with the noise being uniformly higher- valued than the sweet spot. There are many parameter sets that do not generate information except to indi- cate that the creature failed (in the noisy section) and there is a smaller number of parameter sets where the creature may actually run well. Figure 2 illustrates the general shape of evaluation functions, using data from the simulated quadruped. Evaluating Performance In order to evaluate the performance of a set of control parameters, I created an evaluation function which re- flects the fact that a control algorithm for a trotting quadruped needs to do more than propel the quadru- ped forward. Raibert’s experimentation in quadruped control suggests that it should (Raibert 1990): control the forward velocity. regulate the body attitude. put reasonable constraints on the forces and torques applied. limit the vertical motion of the body. keep the running cycle stable. The evaluation function I used is the integration of the departures from these goals over the course of seven simulated seconds (Ringrose 199213). Seven seconds, the length of time over which the behavioral error is integrated, is several times the length of the step cycle, allowing transients to die out. This evaluation function does not guarantee that the running cycle is stable be- yond the seven seconds of running actually simulated. In practice, however, if the simulation successfully trots for that length of time it is stable enough that it is un- likely to fail later. Getting a Close Solution A goal of this work is to be able to automatically tune the control system when there are large changes in the physical characteristics of the creature. When the sim- ulation changes by a small amount, a good parameter set may no longer be locally optimal, but it may still be within the sweet spot. Figure 3 shows a cross section of a sample evaluation function and how it changes as the simulation is altered. If the simulation’s change is small enough that the new location of the sweet spot still overlaps the old set of control parameters, those original control parameters can be used with a local search such as gradient descent to find a new set of acceptable control parameters. Generally, if there is a large physical change, the control parameters which were originally acceptable give poor results because the sweet spot moves too far. However, by splitting the large change into a series of smaller changes one can follow the motion of the sweet spot as the simulation changes. Control 1299 Figure 3: Leg spring constant in compression as weight on the quadruped increases. Note how by staying in the minimum as weight is added to the quadruped’s trunk it is possible to find a spring constant for 50 kg which is within the sweet spot. Parameters other than the leg spring con- stant in compression are optimized for the appro- priate weight. In order to have the tuning process work efficiently, it is desirable to take large steps when possible. I use a divide-and-conquer algorithm which splits large changes in half if necessary and recursively solves each half. Set up the simulation with a fraction f which goes from 0 to 1, where 0 is the original configuration and 1 is the final configuration. Let F,(P) represent running the simulation with the fraction f = a and the parameter set P, applying the evaluation function to the run, and returning the result. Let a and b be num- bers between 0 and 1. Let Pa be a parameter set such that F, (P,) is “acceptable” (less than a user-defined constant). The algorithm used to find some &, a pa- rameter set such that Fb(pb) is acceptable, is: If Fb( pa) is “good enough” (less than a constant sup- plied by the user), pb = Pa. Otherwise, if Fb(p,) is “acceptable”, pb is the set of parameters arrived at by a gradient descent search with Pa as a starting point and using the model with fraction b until the result Fb(pb) is “optimized” (less than another user-defined constant). Let c = (a + b)/2. Recursively use this algorithm to find PC, a param- eter set such that FC(PC) is acceptable, from Pa, a, and c. Recursively use this algorithm to find pb from PC, c, and b. Setting the constants “optimized”, “good enough” and “acceptable” requires some care. If the level at which the simulation is considered “optimized” is too low, the gradient descent search will take a long time finding a good parameter set (recall that low evalua- tion results correspond to desired behavior). On the other hand, if “optimized” is too high, the gradient descent search could return a parameter set which is close to the edge of the sweet spot, reducing efficiency. The constant “good enough” corresponds to the point at which the control system performs well and does not need further optimization. This means that the condi- tions for beginning optimization are less rigorous than the conditions for ending optimization, so that each time the gradient descent search is used it is required to perform a non-trivial amount of work. Finally, “ac- ceptable” corresponds to the edge of the sweet spot. If the result of the evaluation is too high, it is consid- ered to be in the area where the evaluation function is essentially useless. Note that the fractions at which the gradient descent search is used increase monotonically from 0, and the only time the parameter set P is modified is when the gradient descent search is used. There are restrictions to this procedure. It must be possible to gradually change the parameter set and configuration from the initial parameter set and config- uration to the final one, without leaving the sweet spot. Also, the control system must be able to control the new configuration. For example, the person designing the control system might neglect one of the moments of inertia, and in a new configuration that moment could be extremely important for stability. Since this tuning method will not alter the control system, it will not be able to address this type of problem. Additionally, the behavior for the initial configuration must be similar to the behavior required in the final configuration. If there is a drastic change in strategy involved, such as a change in gait, it may not be able to find suitable pa- rameters. Finally, if the global minimum is on the edge of the sweet spot, this type of tuning will be inefficient, although still functional. Results In order to evaluate the algorithm described in the previous chapters, I applied it to adjusting the control of the simulated quadruped running machine shown in figure 1. I used a planar quadruped simulation because it allowed the solution of interesting problems with a reasonable amount of processing time. I tested the algorithm for variations in leg length, body weight, and desired speed; it performed well on all of these. Due to space considerations, only the data on variations in leg length is included here. The tuning algorithm was used to reduce the leg length to half its initial value, while maintaining the trotting gait. Interestingly, the problem of getting the quadruped to trot with half-length legs was more dif- ficult than expected because of the very short travel allowed for the leg actuators. The initial configuration was the quadruped simula- tion and control system mentioned earlier. The final 1300 Robotics 2 -1 0 1 2 3 4 5 6 7 OO 1 2 3 4 5 6 7 Time (s) Time (s) Figure 4: Height above ground and forward velocity over time, included to illustrate that the trotting achieved is stable before and after tuning. Solid lines indicate original leg length and original parameter set and dashed lines indicate half leg length and the corresponding tuned parameter set. Note that the initial conditions remain the same, so the quadruped with shorter legs actually falls to the ground, stops, and begins trotting. Parameter Initial Final Units Maximum acceleration 0.31284 0.36085 m Leg spring constant, compression 7803.57 8731.33 N/m Leg damping coefficient, compression 471.971 630.748 Ns/m Leg spring constant, extension 21183.7 19637.5 N/m Leg damping coefficient, extension 462.931 1071.51 Nslm Stance leg length 0.62217 0.35498 m Stance leg length increase 0.08635 0.07645 m Swing leg length 0.45252 0.28027 Increase in swing hip torque with speed -0.0042 -0.0058 NT Acceleration rate 0.65024 0.05992 Hip servo 282.093 182.354 Nit Hip damping 21.3930 17.0266 Nms Desired forward speed 1.50000 0.34164 ds Table 1: Parameters modified while decreasing the quadruped leg length. configuration was the same quadruped simulation and control system, with legs half as long and leg moments of inertia and masses scaled as cylinders. The tun- ing experiment took three and a half days on an IBM RS/SOOO model 550 to find the result listed in table 1. Figure 4 illustrates the stable running elicited by the original and final parameter sets when used with their respective simulations. Figure 5 shows the leg lengths at which the optimization occurred. Note that that the original control parameters for full length legs will not work on the final quadruped. Conclusions The tuning algorithm presented here has successfully solved several optimization problems relating to dy- namically stable legged locomotion. All of these prob- lems involve a planar trotting quadruped simulation and vary the amount of weight on the body, the leg length, or how closely it tracks a desired speed. I have also used this tuning algorithm to increase the amount of weight on the quadruped’s feet and to increase the running speed of a kangaroo-like robot. Many searching methods fail when dealing with dy- namically balanced legged locomotion because easily created evaluation functions tend to result in a search space which is only tractable near a solution. The 20 Attempt Figure 5: Leg lengths where the tuner tried to op- timize (dotted line) and leg lengths where it suc- ceeded (solid line). Control 1301 tuning algorithm presented here succeeds because it makes the simplifying assumption that the tractable area moves slowly as the simulation is altered. This simplification allows the use of a fairly simple search within the tractable area. Because of the assumptions behind it, there are lim- itations to the usefulness of this tuning algorithm. It must be possible to gradually change the parameter set and configuration from the initial parameter set and configuration to the final one, without leaving the sweet spot. If there is a drastic change in strategy involved, such as a change in gait, it may not be possi- ble to gradually change the control parameters. Also, the control system must be capable of controlling the new configuration, as the tuning algorithm will not al- ter the structure of the control system. Finally, if the global minimum is on the edge of the sweet spot, this tuning algorithm will be inefficient. Some of these lim- itations can be overcome by carefully constructing the evaluation function. Even with its limitations, this tuning method will prove useful for modifying simulations and eliciting de- sired behaviors. I believe that tuning methods such as the one presented here will turn the art of tuning a simulation into the art of constructing an evaluation function-still an art, but one which is a little easier. Acknowledgments The author would like to thank Marc Raibert for his guidance during the course of this research. References Helferty, J. J.; Collins, J. B.; and Kam, M. 1988. A learning strategy for the control of a mobile robot that hops and runs. In Proceedings of the 1988 Inter- national Association of Science and Technology for Development. IASTED. Hodgins, J. K., and Raibert, M. H. 1989. Biped gym- nastics. International Journal of Robotics Research. Hodgins, J. K., and Raibert, M. H. 1991. Adjust- ing step length for rough terrain locomotion. IEEE Transactions on Robotics and Automation 7(3). Pearse, M.; Arkin, R.; and Ram, A. 1992. The learn- ing of reactive control parameters through genetic al- gorithms. Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems 1~130-137. Playter, R. R., and Raibert, M. H. 1992. Control of a biped somersault in 3d. In IFToMM-jc International Symposium on Theory of Machines and Mechanisms. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. 1988. Numerical Recipes in C. Cambridge University Press. chapter 10, 290-352. Raibert, M. H.; Hodgins, J. K.; Playter, R. R.; and Ringrose, R. P. 1992. Animation of maneuvers: Jumps, somersaults, and gait transitions. In Imag- ina. Raibert, M. H.; Chepponis, M.; and Brown, Jr., B. 1986. Running on four legs as though they were one. IEEE Journal of Robotics and Automation RA-2(2). Raibert, M. H. 1990. Trotting, pacing and bounding by a quadruped robot. Journal of Biomechanics 23. Ringrose, R. 1992a. The creature library. Unpub- lished reference guide to a C library used to create physically realistic simulations. Ringrose, R. 199213. Simulated creatures: Adapting control for variations in model or desired behavior. Master’s thesis, Massachusetts Institute of Technol- ogy* Rosenthal, D. E., and Sherman, M. A. 1986. High per- formance multibody simulations via symbolic equa- tion manipulation and kane’s method. Journal of As- tronautical Sciences 34(3):223-239. Winston, P. H., and Shellard, S. A., eds. 1990. Ar- tificial Intelligence at MIT: Expanding Frontiers, vol- ume 2. Cambridge, MA: MIT Press. 149-179. Witkin, A., and Kass, M. 1988. Spacetime con- straints. In Computer Graphics, 159-168. 1302 Robotics | 1994 | 268 |
1,617 | Reactive Deliberation: An Architecture for Real-time Intelligent Control in Dynamic Environments Michael K. Sahota Laboratory for Computational Intelligence Department of Computer Science University of British Columbia Vancouver, B.C., Canada, V6T 124 sahota@cs.ubc.ca Abstract Reactive deliberation is a novel robot architecture that has been designed to overcome some of the problems posed by dynamic robot environments. It is argued that the prob- lem of action selection in nontrivial domains cannot be in- telligently resolved without attention to detailed planning. Experimental evidence is provided that the goals and ac- tions of a robot must be evaluated at a rate commensurate with changes in the environment. The goal-oriented be- haviours of reactive deliberation are a useful abstraction that allow sharing of scarce computational resources and effec- tive goal-arbitration through inter-behaviour bidding. The effectiveness of reactive deliberation has been demonstrated through a tournament of one-on-one soccer games between real-world robots. Soccer is a dynamic environment; the locations of the ball and the robots are constantly changing. The results suggest that the architectural elements in reactive deliberation are sufficient for real-time intelligent control in dynamic environments. Introduction A robot operating within the real-time constraints of the external environment must answer the question: “What to do now?’ It is not sufficient for a robot to react and interact with its environment; it must act in goal-oriented ways to produce externally observable intelligent behaviour (Brooks, 1991) and not just any behaviour. The importance of real-time control is identified by the following quote: “An oncoming truck waits for no theorem prover.” (Gat, 1992) The moral is that robots operating in dynamic domains must keep pace with changes in the environment. This point has been argued more formally by Maes (Maes, 1990). Robot architectures specify the organizing principles of a robot controller. Key issues are: the computational model used, locus of control, response time, and action selection mechanism. Depending on trade-offs made in design, architectures may only be appropriate for specific classes of problem domains. This paper argues that the challenges posed for robots in complex dynamic domains have not been adequately addressed by extant architectures and describes one possible solution. Related Work The Good Old Fashioned AI and Robotics (GOFAIR) (Haugeland, 1985; Mackworth, 1993) research paradigm has shaped the area of robotics since the time of the robot Shakey (Nilsson, 1984). Some of the fundamental assump- tions made of the world in the pure form of GOFAIR were that there is only one agent, that the environment is static, that actions are discrete and are carried out sequentially, and that the world can be accurately and exhaustively mod- eled by the robot. Under these assumptions, the problem of robot control is reduced to generating a plan (a sequence of actions that will, if executed, achieve a goal) and mon- itoring the execution of the plan. These assumptions are invalid in complex dynamic environments where it is no longer possible to accurately predict the outcome of a se- quence of actions. More recent planning-based architec- tures (Firby, 1992; Gat, 1992) allow for local adaptation to changes in the environment, but still commit the robot to the nearly blind pursuit of arbitrary length plans. AT- LANTIS (Gat, 1992) is a notable exception since it allows the consideration of alternate plans, but the commitment to the plans-as-communication view (Agre & Chapman, 1990) prevents specific plan details from being computed until they are needed, thus resulting in a greater latency in response time. The failure of GOFAIR has led to the development of architectures that provide a direct coupling of perception to action in order to provide highly reactive behaviour. The most notable of these is the Subsumption architec- ture (Brooks, 1986), where the control system of a robot is composed of a hierarchy of task-achieving behaviours in which higher levels of behaviour can subsume lower levels. The concrete-situated approach (Agre & Chapman, 1987; Chapman, 1991) formulates the control system for a robot as a collection of action proposing modules. Conflicts be- tween proposals for external actions are resolved through a fixed priority scheme. In the situated automata approach (Kaelbling & Rosenschein, 1990), a fixed ranking of goal priorities and a set of goal reduction rules are compiled into a set of condition-action pairs so that an appropriate action can be selected at each time step. All of these approaches allow the robot to react immediately to changes in the en- vironment, but are based on a fixed ranking of actions (or Control 1303 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. equivalently behaviours or goals). With a fixed ranking, the designer of a robot is limited in adapting the controller to the environment. A key feature of these approaches is the ability to compile the specification for a robot con- troller into circuits or augmented finite state machines for fast execution. A potential drawback is that controllers based on the concrete-situated and situated automata ap- proaches cannot perform the search-type algorithms needed for planning. Although the subsumption architecture sup- ports arbitrary computations, the subsumption mechanism and the commitment to avoid representations seems to be a significant hinderance in the development of more sophis- ticated robots. Some evidence for this point is given with the discussion of experimental results. Maes proposed action selection mechanism for dynamic domains is a network consisting of goals, input predicates, and competence modules that represent actions (Maes, 1990). Activation energy flows about the network accord- ing to the dependencies and conflicts among the elements. Global parameters allow the network to be tuned to an envi- ronment; these can be learned automatically (Maes, 1991). Possible drawbacks of this mechanism are that inputs are restricted to predicates and all goals are of equal weight. The use of predicates forces potentially useful information about the environment to be discarded, while the equal weighting of goals does not reflect the likely possibility that some goals are more important than others. Overview The bulk of this paper is divided into two sections. The first introduces the reactive deliberation architecture while the second describes the experiments used to test it. The architectural elements and the motivations for reactive de- liberation - a robot architecture targeted towards dynamic domains - are discussed. A tournament of one-on-one soccer games has been conducted using real-world robots to demonstrate the utility of the proposed architecture. The use of soccer is motivated, the experimental testbed is briefly described, and the results are discussed. This paper ends with conclusions and future work. The Reactive Deliberation Architecture Reactive deliberation is a robot architecture that integrates reactive and goal-directed activity. Even deliberation must be to some extent reactive to respond to changes in the en- vironment. Although the name is apparently an oxymoron, it is consistent with Artificial Intelligence nomenclature (cf Reactive Planning). Under reactive deliberation, the robot controller is parti- tioned into a deliberator and an executor; the distinction is primarily based on the different time scales of interaction. Informally, the deliberator decides what to do and how to do it, while the executor interacts with the environment in real-time. These components run asynchronously to allow the executor to interact continuously with the world and the deliberator to perform time consuming computations. This partition is inspired by recent architectures that attempt to integrate planners with more reactive components (Firby, 1304 Robotics Shoot Wait clh Dfend behaviours Go to Mi@eti own Igod cjo to Mi(flelif !De$nd CjOlZC From Sensors Sensor Data Action and and Status Executor , Parameters Follow Path stop b action schemas Idle - Servo Defend To Effecters Figure 1 The Reactive Deliberation Controller 1992; Gat, 1992) A structural model illustrating the parti- tion with examples of a soccer-playing robot can be seen in Figure 1. The Executor The executor is composed of a collection of action schemas. An action schema is a robot program that interacts with the environment in real-time to accomplish specijic actions. Action schemas exhibit the same level of complexity as controller modules in RAP (Firby, 1992) and primitive actions in ATLANTIS (Gat, 1992). They are designed in the spirit of behaviour-based approaches, where each schema is experimentally verified. All the schemas together define the capabilities of the robot and are independent of the robot’s goals. The deliberator enables a single action schema with a set of run-time parameters that fully defines the activity. Only one action schema is enabled at a time and it interacts with the environment through a tight feedback loop. In the world of real-time control there is no room for time consuming planning algorithms. Computations in action schemas are restricted to those that can keep pace with the environment, so lengthy computations are performed in the deliberator. Several examples of action schemas applicable to the soccer domain are shown in Figure 1. The follow path schema follows a path that consists of circular arcs and straight line segments to within a certain tolerance mea- sured in absolute position and heading errors. The servo schema tries to servo the robot into the ball by driving to the predicted future location of the ball that is computed using an internal model of the ball’s dynamics. The defend schema alternates between two modes. Normally, the robot stays between the ball and the center of the net. However, if the projected motion of the ball will carry it past the line the robot is defending, the robot moves to intercept it in an effort to keep the ball away from the net. The Deliberator The focus of the deliberator is on an effective mechanism for selecting actions or goals in a timely manner. A central feature of reactive deliberation is that the deliberator is composed of concurrently active modules called behaviours that represent the goals of the robot. The notion of a behaviour is used in the sense of Minsky’s mental proto- specialists (Minsky, 1986). The examples given in Figure 1 illustrate the goals of a simple soccer-playing robot. These include goals of achievement such as shoot or clear the ball and goals of prevention such as Defend Coal where goals are prevented from being scored by the other robot. A behaviour is a robot program that computes an action that may, if executed, bring about a specific goal. Be- haviours propose actions whereas action schemas perform actions. Each behaviour must perform the following: 1) se- lect an action schema, 2) compute run-time parameters for the schema (plan the action), and 3) generate a bid describ- ing how appropriate the action is. The most appropriate behaviour, and hence action, is determined in a distributed manner through inter-behaviour bidding. Each bid is an estimate of the expected utility and is based on the current state of the world as well as the results of planning. Currently, the criteria for generating the bids are hand coded and tuned so that the most appropriate be- haviour is active in each situation. This approach requires the designer of a system to explicitly state the conditions under which certain behaviours are suitable or favourable. A simplified version of this appears in architectures with fixed ranking schemes. For example, the concrete-situated approach uses binary preference relations to establish an ordering of proposers or actions. Modularity The principal advantage of behaviour-based bidding is modularity. Since bids are calibrated to an exter- nal measure of utility, behaviours can be added, modified or deleted without changing the bidding criteria of the es- tablished system. A new behaviour must, of course, be tuned to be compatible with existing ones. Behaviours are independent, so they can have different representations and approaches to generating actions. For instance, a behaviour could incorporate a traditional planner and generate a bid that reflects the utility of the current step of the plan. There is no central decision maker that evaluates the world and decides the best course of action, so behaviours can be run concurrently on different processors (instead of timeshar- ing a single processor), thus improving the speed of the system. In our approach, there is no negotiation between behaviours, unlike in systems such as contract nets (Smith, 1980). As a result, it is not possible to combine the pref- erences of multiple behaviours, and this remains an open problem. Real-time computations In a real robot there is more to the problem of action selection than just deciding what to do. In dynamic environments, a robot needs to quickly decide what to do and how to do it. The deliberator must keep pace with changes in the environment to produce in- telligent behaviour. Each behaviour is responsible for com- puting a bid and planning the action. Fixed computational resources (processor cycles) need to be distributed among the behaviours, since it is typically the case that there is too much computation to be done. The exact mechanism for distributing computational re- sources is left unspecified as it is strongly dependent on the real-time requirements of the system, the number of behaviours, and the resources needed by each behaviour. However, the basic principle is to divide the available computational resources among the behaviours such that the ruling behaviour receives more resources. This allows behaviours that perform minimal computations to respond quickly, while those that perform lengthy computations will respond slowly. It might be appropriate to allocate re- sources according to the importance and needs of each be- haviour, but there are no provisions for this in the current implementation. There is no perfect architectural solution to the problem of limited computational resources: if the computations are slow, then the robot will be slow too. The only possible solutions are to get more computers, faster computers, better algorithms, or switch to simpler tasks. Why this partition? Reactive deliberation, like GOFAIR approaches, partitions the controller for a robot into a deliberator and executor. One difference is the level of abstraction at which the split between reasoning and execution monitoring occurs; our claim is that the reactive deliberation split is more suitable for dynamic environments. The deliberator is responsible for answering the ques- tions: “What to do now?’ and “How should it be done?’ Believers in the theory of plans-as-communication (Agre & Chapman, 1990) argue that these questions can and should be resolved independently (Gat, 1992). In this case a plan- ner decides what to do based on an abstract world model, while the problem of resolving how each action should be performed is postponed until it is to be executed. In a dy- namic environment, however, these questions are usually interrelated. Before committing to an action, it is impor- tant to verify that the action is both feasible and more ap- propriate than other actions. Architectures that follow the planning paradigm check to see if an action is feasible, but not if there is a better action. Answering the question “How should it be done?’ pro- vides information about the utility of an action. For ex- ample, detailed planning may show that one action is im- possible, while another can be accomplished quickly. This suggests that generating plans at a high level of abstraction may not provide an effective solution for the problem of action selection. Unless all actions of the robot are feasible and the outcomes can be predicted at design time, the ques- tion “What to do now?’ cannot be intelligently answered without also answering “How should it be done?’ Another advantage of reactive deliberation is that the deliberator is responsible for generating a single action (schema), whereas other planning-based architectures gen- erate a complete plan (i.e. sequences of actions). This dis- tinction allows behaviours to focus on either the immediate situation or some interval of time depending on what is ap- Control 1305 propriate. The boundary between appropriate and inappropriate computations in the executor is a function of the comput- ing power of a particular system and specific environmen- tal constraints. Any computations that can be performed within the time constraints of the environment are suitable for use in the executor. All other computations are rel- egated to the deliberator to avoid degrading the ability of the robot to interact in real-time. Regardless of advances in computing power, there will likely be interesting algorithms that do not run in real-time. This suggests that the partition between the executor and the deliberator is indicative of a technology-independent need to partition computations. Soccer-playing Experiments This section links theory to practice through a robot con- troller that has been constructed using reactive deliberation. The controller has been designed so that the robot can com- pete with another robot in a one-on-one game of soccer. In this section, the use of soccer is motivated as an appropri- ate domain for robotic experiments in dynamic domains. The testbed used to perform the experiments is briefly de- scribed. The experimental results are presented and their implications for robot architectures are discussed. Why soccer? Soccer has characteristics prevalent in the real-world that are absent from typical robot problem domains (Sahota & Mackworth, 1994). Soccer-playing is a dynamic environ- ment because the ball and the cars are all moving. A robot must deal with cooperating agents on the robot team, competing agents on the other team, and neutral agents such as the referee and the weather. The world is not com- pletely predictable: it is not possible to predict precisely where the ball will go when it is kicked, even if all the relevant factors are known. Continuous events such as a player running to a position and the ball moving through the air occur concurrently add further complexity. One advantage of the soccer domain is that there are objective performance criteria; the ability to score and prevent goals and the overall score of the game allow explicit comparisons of alternative controller designs. The ability to compare controller designs and draw conclusions from their strengths and weaknesses is a central feature of this domain. One problem with a direct comparison of robot con- trollers is that differences in performance may be the result of technical details (such as the length of time the designer spent tuning the controller) that may have nothing to do with the underlying architectures. However, implemented systems can provide a lower bound on the utility of an architecture since limitations in the architecture are often reflected in the functionality of a robot. For the experi- ments described in this paper, the problem is avoided by using the same program fragments in each controller with different organizational principles. Figure 2 Robot Players on the Soccer Field The Dynamite Testbed A facility called the Dynamite testbed has been designed to provide a practical platform for testing theories in the soccer domain using multiple mobile robots (Barman et al., 1993). It consists of a fleet of radio controlled vehicles that perceive the world through a shared perceptual system. In an integrated environment with dataflow and MIMD com- puters, vision programs can monitor the position and orien- tation of each robot while planning and control programs can generate and send out motor commands at 60 Hz. This approach allows umbilical-free behaviour and very rapid, lightweight fully autonomous robots. The mobile robot bases are commercially available radio controlled vehicles. We have two controllable l/24 scale racing-cars, each 22 cm long, 8 cm wide, and 4 cm high excluding the antenna. The testbed (244 cm by 122 cm in size) with two cars and a ball is shown in Figure 2. The cars have each been fitted with two circular colour markers allowing the vision system to identify their position and orientation. The ball is the small object between the cars. A feature of the Dynamite testbed is that it is based on the “ brain” approach to robotics. The testbed avoids the technical complexity of configuring and updating on-board hardware and makes fundamental problems in robotics and artificial intelligence more accessible. We have elected not to get on-board the on-board computation bandwagon, since the remote (but untethered) brain approach allows us to focus on scientific research without devoting resources to engineering compact electronics. A physics-based graphics simulator for the Dynamite world has been used for testing and developing reasoning and control programs. Results Several controllers based on reactive deliberation have been implemented to allow robots to compete in one-on-one games of soccer. Current functionality includes various simple offensive and defensive strategies, motion planning, ball shooting and playing goal. The robots can drive under accurate control at speeds up to 1 m/s, while simultaneously considering alternate actions. We have produced a 10 minute video that documents these features. A series of experiments, soccer games, called the Labo- ratory for Computational Intelligence (LCI) Cup were per- formed using the Dynamite testbed (Sahota, 1993). The 1306 Robotics Half-wit 11 6-3 1 5-5 No-wit II 8-2 I Table 1 Final Scores in the Soccer Tournament (11 - 1 means that the reactive deliberation controller scored 11 goals while the no-wit controller scored only 1.) most elaborated reactive deliberation controller competed with subsets of itself to provide, through the scores of the games, an objective utility measure for some of the archi- tectural features of reactive deliberation. The results of the soccer tournament that has been conducted in our labora- tory can be seen in Table 1. The versions of the controller used were: 0 Reactive Deliberation: the controller performs con- current deliberation and execution, as is intended of the architecture. * Half-wit: the executor yields control to the deliberator only when an action (activity) has been completed or a time-out occurs; this is equivalent to a GOFAIR controller. 0 No-wit: the controller alternates between offensive and defensive behaviours according to a fixed timer regardless of the current world state. There is an element of chance in these soccer games: the scores are a result of a complex set of interactions between the robots and their environment. These results are partially repeatable because the same general results will emerge, but the actual scores will be different. For a better estimate of the results, the duration of the soccer game could be extended from the current time of 10 minutes. Playing multiple games is equivalent to extending the duration of a single game. The rank of the controllers from best to worst is: reactive deliberation, half-wit, and no-wit. This ranking is probably reliable since the better controllers scored nearly twice as many goals (7-4 and 6-3 are the scores) as the controller ranked beneath it. The results of the games played with the same controller indicate that the better two controllers (reactive deliberation, half-wit) generate fairly constant per- formance, while the no-wit controller produces somewhat random performance. The scores (5-5 and 3-3) should be interpreted as close scores, rather than identical. They re- ally do not show the underlying randomness that is present as might be shown by a listing of when the goals were scored. The score 8-2 in the no-wit vs. no-wit game is a result of the almost random playing strategy of that con- troller. The reactive deliberation controller performs better than a human controlling the opposing robot. This is, however, somewhat of an unfair comparison since excellent motor skills are needed to even shoot the ball. Discussion The difference in score between the reactive deliberation and half-wit controllers is significant. The only differ- ence between these two controllers is that reactive delib- eration considers alternate actions all the time, while the half-wit controller does so only when an action schema ter- minates. The reactive deliberation controller selects goals as frequently as possible and can interrupt actions. The half-wit controller is like the traditional planning-based ar- chitectures: alternate actions are considered only when the current action has terminated. This is evidence that the fre- quent evaluation of goals and actions is critical to success in dynamic worlds. The level of performance that the robots were able to achieve is partially due to the use of internal world models. An internal model of the dynamics of the robot is used to provide feed-forward control. This is not a superfluous element; it really is necessary for the robots to operate at speeds of 1 m/s. Brooks argues that “the world is its own best model” and that internal models are inappropriate (Brooks, 199 1). Experiences with these soccer-playing robots suggest that Brooks’ slogan is misleading and that either explicit or implicit models are needed. The performance of the robots is largely a function of the action selection mechanism. It has been fine-tuned through an iteration cycle with observations of soccer games fol- lowed by incremental changes to the behaviours. A useful abstraction that helps with this is the routines of action from the concrete-situated approach (Agre & Chapman, 1987). The central idea is that the agent (or robot) interacts with the environment in a routine or typical way. One routine in soccer is: clear the ball, defend red line, shoot, etc. In the case of soccer-playing, the construction of successful robots does involve careful attention to patterns of activity. This is an emergent (and surprising) result of our experiments. The reactive deliberation controller plays a nice, although not flawless, game of soccer. The competitive nature of soccer places very strict time constraints on the robots and allows different controllers to be easily compared. The dy- namic and unpredictable nature of one-on-one robot soccer favours approaches that are concerned with the immediate situation and reactive deliberation takes advantage of this. Reactive deliberation is not a panacea for robotic archi- tectural woes. A further disclaimer is that it is an incom- plete robot architecture since it focuses on the issues related to dynamic domains and ignores a number of issues such as perceptual processing and the development of world mod- els. The proposal is orthogonal to those issues. Conclusions The theoretical contributions of reactive deliberation to the design philosophy of robot architecture for dynamic environments are the following: 0 A new split between reasoning and control is proposed Control 1307 since utility and hence action selection cannot always be suitably determined without detailed planning. 0 Goal-oriented behaviours are a useful abstraction that allow sharing of scarce computational resources and effective goal-arbitration through inter-behaviour bid- ding. A series of one-on-one soccer games have been con- ducted with real-world robots to evaluate reactive deliber- ation. The score of a soccer game provides an objective criterion for evaluating the success of a robot controller. The experimental results suggest that the architectural ele- ments in reactive deliberation are sufficient for generating real-time intelligent control in dynamic environments. Fur- ther, it has been experimentally demonstrated that the goals and actions of a robot need to be evaluated at a rate com- mensurate with changes in the environment. Future Work Future work can be classified as either testing or exten- sions. Possible testing procedures include comparing reac- tive deliberation with other architectures and testing it in other problem domains. It is not clear how general reactive deliberation is and it remains to be determined in which do- mains this style of architecture is preferable. One limitation of this research is that the experiment, from proposed solu- tions to testing, has been performed by the author; a more hands-off or double-blind procedure is needed to provide greater scientific rigour. It still remains to be demonstrated that our architecture is more appropriate than others even in the particular soccer-world that has been used. Some possible extensions to reactive deliberation are as follows: 0 incorporation of perceptual processing and world mod- eling into the architecture. * development of a more formal, yet practical, mecha- nism for estimating utility. 0 learning utility estimates and models of the robot’s dynamics. 0 ability to combine the preferences of different be- haviours. 0 support for inter-robot cooperation. Acknowledgments I am grateful to Rod Barman, Keiji Kanazawa, Stewart Kingdon, Jim Little, Alan Mackworth, Dinesh Pai, Heath Wilkinson and Ying Zhang for help with this. In partic- ular, Alan has provided deep insights and help revising drafts. This work is supported, in part, by the Canadian Institute for Advanced Research, the Natural Sciences and Engineering Research Council of Canada and the Institute for Robotics and Intelligent Systems Network of Centres of Excellence. References Agre, P., and Chapman, D. 1987. Pengi: An implementation of a theory of activity. In AAAI-87, 268-272. Agre, P., and Chapman, D. 1990. What are plans for? In Maes, P., ed., Designing Autonomous Agents: Theory and Practice from Biology to Engineering and Back. M.I.T. Press. 17-34. Barman, R.; Kingdon, S.; Little, J.; Mackworth, A. K.; Pai, D.; Sahota, M.; Wilkinson, H.; and Zhang, Y. 1993. Dy- namo: real-time experiments with multiple mobile robots. In Proceedings of Intelligent Vehicles Symposium, 261-266. Brooks, R. A. 1986. A robust layered control system for a mobile robot. IEEE Journal of Robotics and Automation RA-2: 14-23. Brooks, R. A. 1991. Intelligence without reason. In IJCAI- 91, 569-595. Chapman, D. 1991. Vision, Instruction, and Action. MIT Press. Firby, R. J. 1992. Building symbolic primitives with con- tinuous control routines. In First International Conference on Artificial Intelligence Planning Systems, 62-69. Gat, E. 1992. Integrating planning and reacting in a heterogeneous asynchronous architecture for controlling real-world mobile robots. In AAAI-92, 809-815. Haugeland, J. 1985. Arti$cial Intelligence: The Very Idea. Cambridge, Mass.: MIT Press. Kaelbling, L. P., and Rosenschein, S. J. 1990. Action and planning in embedded agents. In Maes, P., ed., Designing Autonomous Agents: Theory and Practice from Biology to Engineering and Back. M.I.T. Press. 35-48. Mackworth, A. 1993. On seeing robots. In Basu, A., and Li, X., eds., Computer Vision: Systems, Theory, and Applications. World Scientific Press. 1-13. Maes, P. 1990. Situated agents can have goals. In Maes, P., ed., Designing Autonomous Agents: Theory and Practice from Biology to Engineering and Back. M.I.T. Press. 49-70. Maes, P. 199 1. Learning behaviour networks from experi- ence. In Proceedings of the First European Conference on Artificial Life. M.I.T. Press. Minsky, M. 1986. The Society of Mind. Simon & Schuster Inc. Nilsson, N. 1984. Shakey the robot. Technical Report 323, SRI International. Collection of Earlier Technical Reports. Sahota, M. K., and Mackworth, A. K. 1994. Can situated robots play soccer ? In Proceedings of Canadian AI-94. Forthcoming. Sahota, M. K. 1993. Real-time intelligent behaviour in dynamic environments: Soccer-playing robots. Master’s thesis, University of British Columbia. Smith, G. 1980. The contract net protocol: High-level communication and control in a distributed problem solver. IEEE Transactions on Computing 29(12). 1308 Robotics | 1994 | 269 |
1,618 | Parsing Embedded Clauses with Distributed Neural Networks Risto Miikkulainen Dennis Bijwaard Department of Computer Sciences Department of Computer Science The University of Texas at Austin University of Twente Austin, TX 78712 USA 7500 AE Enschede, The Netherlands risto@cs.utexas.edu bijwaard@cs.utwente.nl Abstract A distributed neural network model called SPEC for processing sentences with recursive relative clauses is described. The model is based on sep- arating the tasks of segmenting the input word sequence into clauses, forming the case-role rep- resentations, and keeping track of the recursive embeddings into different modules. The system needs to be trained only with the basic sentence constructs, and it generalizes not only to new in- stances of familiar relative clause structures, but to novel structures as well. SPEC exhibits plausi- ble memory degradation as the depth of the center embeddings increases, its memory is primed by earlier constituents, and its performance is aided by semantic constraints between the constituents. The ability to process structure is largely due to a central executive network that monitors and con- trols the execution of the entire system. This way, in contrast to earlier subsymbolic systems, parsing is modeled as a controlled high-level pro- cess rather than one based on automatic reflex responses. The girl, who liked the dog, saw the boy’, and it will generalize to different versions of the same struc- ture, such as The dog, who bit the girl, chased the cat (Miikkulainen 1990). However, such a net- work cannot parse sentences with novel combina- tions of relative clauses, such as The girl, who liked the dog, saw the boy, who chased the cat. The problem is that distributed neural networks are pat- tern transformers, and they generalize by interpolating between patterns on which they were trained. They cannot make inferences by dynamically combining pro- cessing knowledge that was previously associated to dif- ferent contexts, such as processing a relative clause at a new place in an otherwise familiar sentence structure. This lack of generalization is a serious problem, given how effortlessly people can understand sentences they have never seen before. Introduction Reading an input sentence into an internal represen- tation is a most fundamental task in natural language processing. In the distributed (i.e. subsymbolic) neu- ral network approach, it usually involves mapping a sequence of word representations into a shallow seman- tic interpretation, such as the case-role assignment of the constituents. This approach offers several promises: it is possible to combine syntactic, semantic, and the- matic constraints in the interpretation, generate expec- tations automatically, generalize to new inputs, and process noisy sentences robustly (Elman 1990, 1991; McClelland & Kawamoto 1986; Miikkulainen 1993; St. John & McClelland 1990). To a limited extent, it is even possible to train such networks to process sentences with complex grammatical structure, such as embedded relative clauses (Berg 1992; Jain 1991; Miik- kulainen 1990; Sharkey & Sharkey 1992; Stolcke 1990). This paper describes SPEC (Subsymbolic Parser for Embedded Clauses), a subsymbolic sentence parsing model that can generalize to new relative clause struc- tures. The basic idea is to separate the tasks of seg- menting the input word sequence into clauses, form- ing the case-role representations, and keeping track of the recursive embeddings into different networks. Each network is trained with only the most basic relative clause constructs, and the combined system is able to generalize to novel sentences with remarkably complex structure. Importantly, SPEC is not a neural net- work reimplementation of a symbol processor. It is a self-contained, purely distributed neural network sys- tem, and exhibits the usual properties of such systems. For example, unlike symbolic parsers, the network ex- hibits plausible memory degradation as the depth of the center embeddings increases, its memory is primed by the earlier constituents in the sentence, and its per- formance is aided by semantic constraints between the constituents. However, it has been very difficult to build subsym- bolic systems that would generalize to new sentence structures. A network can be trained to form a case- role representation of each clause in a sentence like The SPEC Architecture SPEC receives a sequence of word representations as its input, and for each clause in the sentence, forms an output representation indicating the assignment of ‘In all examples in this paper, commas are used to indi- cate clause boundaries for clarity. 858 Neural Networks From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Figure 1: The SPEC sentence processing architecture. The system consists of the Parser (a simple recurrent the Stack (a RAAM network), and the Segmenter (a feedforward network). The gray areas indicate propagatio weights, t he solid lines stand for pattern transport, and the dashed lines represent control outputs (with gates). Input pars*Tl Segmenter Stack I Case-role vector I output words into case roles. The case-role representations are read off the system and placed in a short-term memory (currently outside SPEC) as soon as they are complete. SPEC consists of three main components: the Parser, the Segmenter, and the Stack (figure 1). Below, each component is described in detail. The Parser The Parser performs the actual transformation of the word sequence into the case-role representations, and like many other subsymbolic parsers, it is based on Elman’s (1990) simple recurrent network architecture (SRN; figure 2). The pattern in the hidden layer is copied to the previous-hidden-layer assembly and serves as input to the hidden layer during the next step in the sequence, thus implementing a sequence memory. The network is trained with examples of input/output sequences, adjusting all forward weights according to the backpropagation algorithm (Rumelhart, Hinton, & Williams 1986). Words are represented distributively as vectors of gray-scale values between 0 and 1. The component val- ues are initially assigned randomly and modified during learning by the FGREP method (Miikkulainen & Dyer 1991; Miikkulainen 1993). FGREP is a convenient way to form distributed representations for input/output items, but SPEC is not dependent on FGREP. The word representations could have been obtained through semantic feature encoding (McClelland & Kawamoto 1986) as well, or even assigned randomly. The case-role assignment is represented at the out- put of the Parser as a case-role vector (CRV), that is, a concatenation of those three word representation vec- tors that fill the roles of agent, act, and patient in the sentence2 (figure 2). For example, the word sequence “The representation was limited to three roles for simplicity. n etwork), n through the girl saw the boy receives the case-role assign- ment agent=girl, act=saw, patient=boy, which is rep- resented as the vector lgirl saw boy1 at the output of the Parser network. When the sentence consists of multiple clauses, the relative pronouns are replaced by their referents: The girl, who liked the dog, saw the boy parses into two CRVs: I girl liked dog1 and lgirl saw boy I. The Parser receives a continuous sequence of input word representations as its input, and its target pat- tern changes at each clause boundary. For example, in reading The girl, who liked the dog, saw the boy, the target pattern representing lgirl saw boy1 is maintained during the first two words, then switched to I girl liked dog1 during reading the embedded clause, and then back to lgirl saw boy I for the rest of the sentence. The CRV for the embedded clause is read off the network after dog has been input, and the CRV for the main clause after the entire sentence has been read. When trained this way, the network is not limited to a fixed number of clauses by its output representation. Also, it does not have to maintain information about the entire past input sequence in its memory, making it possible in principle to generalize to new clause struc- tures. Unfortunately, after a center-embedding has been processed, it is difficult for the network to remem- ber earlier constituents. This is why a Stack network is needed in SPEC. The Stack The hidden layer of a simple recurrent network forms a compressed description of the sequence so far. The Stack has the task of storing this representation at each center embedding, and restoring it upon return from the embedding. For example, in parsing The girl, who liked the dog, saw the boy, the hidden-layer Neural Networks 859 uence of input words Case-role assignment Figure 2: The Parser network. The figure depicts a snapshot of the network after it has read the first two words The and girl. The activity patterns in the input and output assemblies consist of word representations. The input layer holds the representation for the last word, girl, and the activity pattern at the output represents the (currently incomplete) case-role assignment of the clause. representation is pushed onto the stack after The girl, and popped back to the Parser’s previous-hidden-layer assembly after who liked the dog. In effect, the SRN can then parse the top-level clause as if the center em- bedding had not been there at all. The Stack is implemented as a Recursive Auto- Associative Memory (RAAM; Pollack 1990; figure 3). RAAM is a three-layer backpropagation network trained to perform an identity mapping from input to output. As a side effect, its hidden layer learns to form compressed representations of the network’s in- put;/output patterns. These representations can be re- cursively used as constituents in other input. patterns, and a potentially infinite hierarchical data structure, such as a stack, can this way be compressed into a fixed-size representation. The input/output of the Stack consists of the stack’s top element and the compressed representation for the rest of the stack. Initially the stack is empty, which is represented by setting all units in the “Stack” assem- bly to 0.5 (figure 3). The first element, such as the hidden-layer pattern of the Parser network after read- ing The girl, is loaded into the “Push” assembly, and the activity is propagated to the hidden layer. The hidden-layer pattern is then loaded into the “Stack” assembly at the input, and the Stack network is ready for another push operation. When the Parser returns from the center embedding, the stored pattern needs to be popped from the stack. The current stack representation is loaded into the hid- den layer, and the activity is propagated to the out- put layer. At the output, the “Pop” assembly contains the stored Parser-hidden-layer pattern, which is then loaded into the previous-hidden-layer assembly of the Parser network (figure 1). The “Stack” assembly con- tains the compressed representation for the rest of the stack, and it is loaded to the hidden layer of the Stack network, which is then ready for another pop operation. 860 Neural Networks The Segmenter The Parser+Stack architecture alone is not quite suffi- cient for generalization into novel relative clause struc- tures. For example, when trained with only exam- ples of center embeddings (such as the above) and tail embeddings (like The girl saw the boy, who chased the cat), the architecture generalizes well to new sentences such as The girl, who liked the dog, saw the boy, who chased the cat. How- ever, the system still fails to generalize to sen- tences like The girl saw the boy, who the dog, who chased the cat, bit. Even though the Stack takes care of restoring the earlier state of the parse, the Parser has to learn all the different transitions into relative clauses. If it has encountered center embed- dings only at the beginning of the sentence, it cannot generalize to a center embedding that occurs after an entire full clause has already been read. The solution is to train an additional network, the Segmenter, to divide the input sequence into clauses. The segmenter receives the current hidden-layer pat- tern as its input, together with the representation for the next input word, and it is trained to produce a mod- ified hidden-layer pattern as its output (figure 4). The output is then loaded into the previous-hidden-layer as- sembly of the Parser. In the middle of reading a clause, the Segmenter passes the hidden-layer pattern through without modification. However, if the next word is a relative pronoun, the segmenter modifies the pattern so that only the relevant information remains. In the above example, after boy has been read and who is next to come, the Segmenter generates a pattern similar to that of the Parser’s hidden layer after only The boy in the beginning of the sentence has been input. In other words, the Segmenter (1) detects transitions to relative clauses, and (2) changes the sequence mem- ory so that the Parser only has to deal with one type of clause boundary. This way, the Parser’s task be- Figure 3: The Stack network. This figure simultaneously illustrates three situations that occur at different times during the training and the performance of the Stack: (1) A training situation where the network learns to autoassociate an input pattern with itself, forming a compressed representation at the hidden layer; (2) A push operation, where a representation in the “Push” assembly is combined with the empty-stack representation (in the “Stack” assembly) to form a compressed representation for the new stack in the hidden layer; (3) A pop operation, where the current stack representation in the hidden layer generates an output pattern with the top element of the stack in the “Pop” assembly and the representation for the remaining stack (currently empty) in the “Stack” assembly. comes sufficiently simple so that the entire system can generalize to new structures. The Segmenter plays a central role in the architec- ture, and it is very natural to give it a complete control over the entire parsing process. Control is implemented through three additional units at the Segmenter’s out- put (figure 4). The units “Push” and “Pop” control the stack operations, and the unit “Output” indicates when the Parser output is complete and should be read off the system. The control implementation in SPEC empha- sizes an important point: although much of the struc- ture in the parsing task is programmed into the system architecture, SPEC is still a self-contained distributed neural network. In many modular neural network ar- chitectures control is due to a hidden symbolic super- visor. SPEC demonstrates that such external control mechanisms are not necessary: even a rather complex subsymbolic architecture can take care of its own con- trol and operate independently of its environment. Experiments The training and testing corpus was generated from a simple phrase structure grammar (table 1). Each clause consisted of three constituents: the agent, the verb and the patient. A relative who-clause could be attached to the agent or to the patient of the parent clause, and who could fill the role of either the agent or the pa- tient in the relative clause. In addition to who, the and “.” (full stop, the end-of-sentence marker that had its own distributed representation in the system just like a word), the vocabulary consisted of the verbs chased, liked, saw and bit, and the nouns boy, girl, dog and cat. Certain semantic restrictions were imposed on the sentences. A verb could only have certain nouns as its agent and patient, as listed in table 2. The gram- mar was used to generate all sentences with up to four ZP t NP VP “." + DET N I DET N RC E --f V NP + who VP I who NP V N + boy I girl I do I cat EET + chased I liked 7 saw I bit + the Table 1: The sentence grammar. Verb Case-role Possible fillers chased Agent: Patient: boy,girl,dog,cat cat liked Agent: Patient: boy ,girl boy,girl,dog saw bit Agent: Patient: boy,girl,cat boy,girl Agent: Patient: dog boy,girl,dog,cat Table 2: Semantic restrictions. clauses, and those that did not match the semantic re- strictions were discarded. The final corpus consisted of 49 different sentence structures, with a total of 98,100 different sentences. The SPEC architecture divides the sentence pars- ing task into three subtasks. Each component needs to learn only the basic constructs in its task, and the com- bined architecture forces generalization into novel com- binations of these constructs. Therefore, it is enough to train SPEC with only two sentence structures: (1) the two-level tail embedding (such as The girl saw the boy, who chased the cat, who the dog bit) and the two-level center-embedding (e.g. the girl, who the dog, who chased the cat, bit, saw the boy). The training set consisted of 100 randomly-selected sen- Neural Networks 861 Figure 4: The Segmenter network. The Segmenter receives the Parser’s hidden-layer pattern as its input together with the next input word, which in this case is who. The control outputs are 1, 0, 0, indicating that the Parser’s hidden-layer representation should be pushed onto the Stack, the current case-role representation is incomplete and should not be passed on to the output of the system, and the stack should not be popped at this point. In this case, the Segmenter output is identical to its input, because the girl is the smallest context that the Parser needs to know when entering a center embedding. tences of each type. In addition, the Stack was trained to encode and decode up to three levels of pushes and POPS. The word representations consisted of 12 units. Parser’s hidden layer was 75 units wide, Segmenter’s 50 units, and Stack’s 50 units. All networks were trained with on-line backpropagation with 0.1 learning rate and without momentum. Both the Parser and the Seg- menter developed word representations at their input layers (with a learning rate of 0.001). The networks were trained separately (i.e. without propagation be- tween modules) and simultaneously, sharing the same gradually-developing word and parser-hidden-layer rep- resentations. The convergence was very strong. Af- ter 400 epochs, the average error per output unit was 0.018 for the Parser, 0.008 for the Segmenter (0.002 for the control outputs), and 0.003 for the Stack, while an error level of 0.020 usually results in acceptable per- formance in’ similar assembly-based systems (Miikku- lainen 1993). The training took approximately three hours on an IBM RS6000 workstation. The final rep- resentations reflected the word categories very well. SPEC’s performance was then tested on the entire corpus of 98,100 sentences. The patterns in the Parser’s output assemblies were labeled according to the nearest representation in the lexicon. The control output was taken to be correct if those control units that should have been active at 1 had an activation level greater than 0.7, and those that should have been 0 had activa- tion less than 0.3. Measured this way, the performance was excellent: SPEC did not make a single mistake in the entire corpus, neither in the output words or in con- trol. The average unit error was 0.034 for the Parser, 0.009 for the Segmenter (0.003 for control), and 0.005 for the Stack. There was very little variation between sentences and words within each sentence, indicating that the system was operating within a safe margin. The main result, therefore, is that the SPEC ar- chitecture successfully generalizes not only to new in- 862 Neural Networks st,ances of the familiar sentence structures, but to new structures as well, which the earlier subsymbolic sen- tence processing architectures could not do. However, SPEC is not a mere reimplementation of a symbol pro- cessor. As SPEC’s Stack becomes increasingly loaded, its output becomes less and less accurate; symbolic sys- tems do not have any such inherent memory degrada- tion. An important question is, does SPEC’s perfor- mance degrade in a cognitively plausible manner, that, is, does the system have similar difficulties in process- ing recursive structures as people do’? To elicit enough errors from SPEC to analyze it,s limitations, the Stack’s performance was degraded by adding 30% noise in its propagation. Such an experi- ment can be claimed to simulate overload, stress, cog- nitive impairment, or lack of concentration situations. The system turned out to be remarkably robust against noise. The average Parser error rose to 0.058, but the system still got 94% of its output words right, with very few errors in control. ,4s expected, most, of t,lie errors occurred as a direct result of popping back from center embeddings with an inaccurate previous-hidden-layer representation. For example, in parsing The girl, who the dog, who the boy, who chased the cat, liked, bit, saw the boy, SPEC had trouble remembering the agents of liked, bit and saw, and patients of liked and bit. The performance depends on the level of the embedding in an interesting manner. It is harder for the network to remember the earlier constituents of shallower clauses than those of deeper clauses. For example, SPEC could usually con- nect boy with liked (in 80% of the cases), but it was harder for it to remember that it was the dog who bit (58%) and even harder that the girl who saw (38%) in the above example. Such behavior seems plausible in terms of human performance. Sentences with deep center embeddings are harder for people to remember than shallow ones (Foss & Cairns 1970; Miller & Isard 1964). It is easier to remember a constituent that occurred just recently in the sentence than one that occurred several embed- dings ago. Interestingly, even though SPEC was espe- cially designed to overcome such memory effects in the Parser’s sequence memory, the same effect is generated by the Stack architecture. The latest embedding has noise added to it only once, whereas the earlier ele- ments in the stack have been degraded multiple times. Therefore, the accuracy is a function of the number of pop operations instead of a function of the absolute level of the embedding. When the SPEC output is analyzed word by word, several other interesting effects are revealed. Virtually in every case where SPEC made an error in popping an earlier agent or patient from the stack it confused it with another noun (54,556 times out of 54,603; random choice would yield 13650). In other words, SPEC per- forms plausible role bindings: even if the exact agent or patient is obscured in the memory, it “knows” that it has to be a noun. Moreover, SPEC does not gen- erate the noun at random. Out of all nouns it output incorrectly, 75% had occurred earlier in the sentence, whereas a random choice would give only 54%. It seems that traces for the earlier nouns are discernible in the previous-hidden-layer pattern, and consequently, they are slightly favored at the output. Such priming effect is rather surprising, but it is very plausible in terms of human performance. The semantic constraints (table 2) also have a markecl effect on the performance. If the agent or patient that needs to be popped from the stack is strongly correlated with the verb, it is easier for the network to remember it correctly. The effect depends on the strength of the semantic coupling. For example, girl is easier to remember in The girl, who the dog bit, liked the boy, than in The girl, who the dog bit, saw the boy, which is in turn easier than The girl, who the dog bit, chased the cat. The rea- son is that there are only two possible agents for liked, whereas there are three for saw and four for chased. While SPEC gets 95% of the unique agents right, it gets 76% of those with two alternatives, G9% of those with three, and only G7% of those with four. A similar effect has been observed in human pro- cessing of relative clause structures. Half the subjects in Stolz’s (1967) study could not decode complex cen- ter embeddings without semantic constraints. Huang (1983) showed that young children understand embed- ded clauses better when the constituents are semanti- cally strongly coupled, and Caramazza 8~ Zurif (1976) observed similar behavior in aphasics. This effect is of- ten attributed to limited capability for processing syn- tax. The SPEC experiments indicate that it could be at least partly due to impaired memory as well. When the memory representation is impaired with noise, the Parser has to clean it up. In propagation through the Parser’s weights, noise that does not coincide with the known alternat>ives cancels out. Apparently, when the verb is strongly correlated with some of the alterna- tives, more of the noise appears coincidental and is fil- tered out. Discussion Several observations indicate that the SPEC approach to subsymbolic parsing should scale up well. First, as long as SPEC can be trained with the basic constructs, it will generalize to a very large set of new combinations of these constructs. Combinatorial training (St. John 1992) of structure is not necessary. In other words, SPEC is capable of dynamic inferencing, previously postulated as very difficult for subsymbolic systems to achieve (Touretzky 1991). Second, like most subsym- bolic systems, SPEC does not need to be trained with a complete set, of all combinations of constituents for the basic constructs; a representative sample. like the 200 out of 1088 possible training sentences above, is enough. Third, with the FGREP mechanism it is pos- sible to automatically form meaningful distributed rep- resentations for a large number of words, even to ac- quire them incrementally (Miikkulainen 8~ Dyer 1991: Miikkulainen 1993), and the network will know how to process them in new situat,ions. Fourth, SPEC is quite insensitive to configuration and simulation parameters, suggesting that the approach is very st,rong, and there should be plenty of room for adapting it to more chal- lenging experiments. The most immediate direction for future work is to apply the SPEC architecture to a wider variety of grammatical constructs and to larger vocabularies. The Segmenter is perhaps the most significant new feature of the SPEC architecture. It, can be seen as a first step toward implementing high-level control in the connectionist framework (see also Jacobs. Jordan, & Barto 1991: Jam 1991: Schneider 8~ Detweiler 198’7: Sumida 1991). The Segmenter monitors the input se- quence and the state of the parsing network, and is- sues I/O control signals for the Stack memory and the Parser itself at appropriate times. The Segmenter has a high-level view of the parsing process. and uses it to assign simpler tasks to the other moclules. In that sense, the Segmenter implements a strategy for parsing sentences with relative clauses. Such control networks could play a major role in future subsymbolic models of natural language processing and high-level reasoning. Conclusion SPEC is largely motivated by the desire to build a sys- tem that (1) would be able to process nontrivial input like symbolic systems, and (2) woiild make use of the unique properties of distributed neural networks slrch as learning from examples, spontaneous generalization, robustness, contest> sensit,ivity, and integrating statisti- cal evidence. Alt,hough SPEC does not address several important issues in connectionist natural language pro- cessing (such as processing exceptions and representing flexible structure), it, does indicate that learning and Neural Networks 863 applying grammatical structure for parsing is possible with pure distributed networks. However, even more than an AI system aiming at best possible performance, SPEC is an implementa- tion of a particular Cognitive Science philosophy. The architecture is decidedly not a reimplementation of a symbol processor, or even a hybrid system consisting of subsymbolic components in an otherwise symbolic framework. SPEC aims to moclel biological information processing at a specific, uniform level of abstraction, namely that of distributed representation on modular networks. SPEC should be evaluated according to how well its behavior matches that produced by the brain at the cognitive level. The memory degradation ex- periments indicate that SPEC is probably on the right track, and the success of the high-level controller net- work in generating high-level behavior opens exciting possibilities for future work. References Berg, G. 1992. A connectionist parser with recursive sentence structure and lexical disambiguation. In Proceedings of the 10th National Conference on Artijkxl Intelligence, 32-37. Cambridge, MA: MIT Press. Caramazza, A., and ‘Zurif, E. B. 1976. Dissociation of algorithmic and heuristic processes in language comprehension: Evidence from aphasia. Bruin and Language 3~572-582. Elman, J. L. 1990. Finding structure in time. Cognitive Science 14:179-211. Elman, J. L. 1991. Distributed representations, sim- ple recurrent networks, ancl grammatical struc- ture. Muchine Leurning 7:195-225. Foss, D. J., and Cairns, H. S. 1970. Some effects of memory limitation upon sentence comprehension and recall. Journal of Verbal Learning and Verbal Behavior 91541-547. Huang, M. S. 1983. A developmental study of chil- dren’s comprehension of embedded sentences with and without semantic constraints. Journal of Psy- chology 114351-513. Jacobs, R. A.; Jordan, M. I.; and Barto, A. G. 1991. Task decomposition through competition in a modular connectionist architecture: The what and where vision tasks. Cognitive Science 15:219- 250. Jain, A. N. 1991. Parsing complex sentences with struc- tured connectionist networks. Neural Computation 3:110-120. McClelland, J. L., and Kawamoto, A. H. 1986. Mech- anisms of sentence processing: Assigning roles to constituents. In McClelland, J. L., and Rumel- hart, D. E., eds., Purullel Distributed Processing. Cambridge, MA: MIT Press. 272-325. 864 Neural Networks Miikkulainen, R. 1990. A PDP architecture for pro- cessing sentences with relative clauses. In Karl- gren, H., ed., Proceedings of th,e 13th Internn- tional Conference on Computational Linguistics, 201-206. Helsinki, Finland: Yliopistopaino. Miikkulainen, R. 1993. Subsymbolic Natural Languuge Processing: An Integrated Model of Scripts, Lezi- con, and Memory. Cambridge, MA: MIT Press. Miikkulainen, R., and Dyer, M. G. 1991. Natural language processing with modular neural networks and distributed lexicon. Cognitive Sciewe 15:343- 399. Miller, G. A., and Isard, S. 1964. Free recall of self-embedded English sentences. Inform&ion nn,d Control 7:292-303. Pollack, J. B. 1990. Recursive clistributed representa- tions. Art$cial Intelligence 46:77-105. Rumelhart, D. E.; Hinton, G. E.; and Williams, R. J. 1986. Learning internal representations by error propagation. In Rumelhart, D. E., and I\IcClel- land, J. L., eds., Par&lel Distributed Processing. Cambridge, MA: MIT Press. 318-362. Schneider, W., and Detweiler, M. 1987. A connec- tionist/control architecture for working memory. In Bower, G. H., ed., The Psychology of Learning and Motivation, volume 21. New York: Academic Press. 53-119. Sharkey, N. E., and Sharkey, A. J. C. 1992. A modu- lar design for connectionist parsing. In Drossaers. M. F. J., and Nijholt,, A., eds., T,wente TVorksh.op on Language Tech,nology $. 87-96. Department of Computer Science. University of Twente, the Netherlands. St. John, R/I. F. 1992. The story gestalt: A model of knowledge-intensive processes in text comprehen- sion. Cognitive Science 163271-306. St. John, M. F., and McClelland, J. L. 1990. Learning and applying contextual constraints in sentence comprehension. Artificial Intelligence 463217-258. Stolcke, A. 1990. Learning feature-basecl semantics with simple recurrent networks. Technical Report TR-90-015, ICSI, Berkeley, CA. Stolz, W. S. 19G7. A study of the ability to decode grammatically novel sentences. Journal of Verbal Learning and Verbal Beh,nvior 6:867-873. Sumida, R. A. 1991. Dynamic inferencing in parallel distributed semantic networks. In Proceedings of the 13th Annuul Conference of the Cognitzve Scz- ence Society, 913-917. Hillsdale, NJ: Erlbaum. Touretzky, D. S. 1991. Connectionism and composi- tional semantics. In Barnden, J. A., and Pollack, J. B., eds., High-Level Connectionist Models. Nor- wood, NJ: Ablex. 17-31. | 1994 | 27 |
1,619 | Structure in Genetic Algorithms Scott H. Clearwater and Tad Hogg Xerox Palo Alto Research Center 3333 Coyote Hill Road Palo Alto, CA 94304, U.S.A. clearwat@parc,xerox.com, hogg@parc.xerox.com Abstract Recent empirical and theoretical studies have shown that simple parameters characterizing the structure of many con- straint satisfaction problems also predict the cost to solve them, on average. We apply these observations to improve the performance of genetic algorithms. In particular, we use a simple cost measure to evaluate the likely solution difficulty of the different unsolved subproblems appearing in the population. This is used to determine which indi- viduals contribute to subsequent generations and improves upon the traditional direct use of the underlying cost func- tion. As a specific test case, we used the GENESIS genetic algorithm to search for the optimum of a class of random Walsh polynomials. We also discuss extensions to other types of machine learning and problem solving systems. Introduction Several recent studies of NP-hard search problems have shown that easily computable characteristics of their structure determine, on average, their hardness, i.e., the cost to solve them with a variety of heuristic search methods [Cheeseman et al., 1991, Mitchell et al., 1992, Williams and Hogg, 1992a, Williams and Hogg, 1992b]. While these results provide insight into the nature of NP- hard problems, there remains the issue of whether they can also be used to improve search methods. If possible, an improvement based on these results would be a sig- nificant domain-independent heuristic. At first sight this might appear difficult since the relation between problem structure and hardness only holds on average: the large observed variances indicate that any individual problem instance can deviate significantly from the average behav- ior. Thus these results cannot be expected to give detailed guidance for sophisticated domain-specific heuristics. However, some search methods, such as genetic algorithms [Holland, 1975, Goldberg, 1989, Forrest, 19931 (GAS), rely on a statistical sample of search states. Evaluating these states with respect to the overall goal is then used to guide the selection of further states. To the extent that the selection method is able to focus the search toward solution states, on average, these methods can be effective. Such methods are natural candidates for exploiting an improved understanding of average problem hardness. 1310 Genetic Algorithms The novel contribution of this paper is using a theory relating problem structure to hardness to help select in- dividuals within the context of a genetic algorithm, and comparing this improvement with the traditional approach. We do this for a particular class of constraint satisfac- tion problems. We also discuss how this specific example may be generalized to learning programs and other search problems. Our results suggest that the relation between problem structure and hardness can indeed be exploited to give improved domain-independent heuristics. Genetic Algorithms for Constraint Satisfaction Genetic algorithms are a general optimizing search method. They use analogs of evolutionary operators on a population of states in a search space to find those states that minimize the value of a given cost function. Equivalently, they can be viewed as maximizing a fitness function. We used the search space consisting of bit- strings of length ,Y, commonly employed with GAS. Each particular search problem was defined by a cost function on these states, with a known optimal state. By contrast, the studies of problem structure and hardness have fo- cused mainly on constraint satisfaction problems (CSPs). In these problems, one is given a set of constraints and attempts to find a state in a search space that satisfies all of them (i.e., a solution to the CSP), or prove no such state exists. In our work, we used a simple class of opti- mization problems that can also be viewed as CSPs, thus allowing for the most direct use of the hardness theory. Specifically, our cost function can be expressed as a type of Walsh polynomial, i.e., a sum of discrete Walsh functions with coefficients. The Walsh functions form a basis set for functions defined on bit-strings. These polynomials, which are thus much like Fourier series, have been studied previously with GAS [Forrest and Mitchell, 19931. Each such Walsh function is specified by a bit- string ,O and maps bit-strings b in the search space to f 1 aS: if b A ,8 has even parity (even no. of l’s) (1) From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. where A is the bitwise AND operator. The number of I’s in @’ is referred to as the order of the Walsh function. Example values for an order-2 function are $Q~OO ( 1110) = 1 and ~1100(1010) = - 1. A function defined on bit- strings of length 1-1 is expressed as a Walsh polynomial as: 2p-1 F(b) = ‘Tr3 whdb) p=o (2) where wp are real coefficients. Here the sum is over all possible bit-strings ,0 of length ~1. The number of terms in F(b) is defined to be the number of nonzero coefficients WP appearing in the sum. For our experiments, we defined a class of optimization problems by selecting the Walsh polynomials randomly according to specified parameters to correspond to the simplest CSPs studied with the theory. First, we only included Walsh functions of a specified order k. And among these, we selected randomly exactly n terms to include in the Walsh polynomial, i.e., from among the (z) Walsh functions of order k, we randomly selected n to use. Second, for each problem we selected a random bit-string B and chose the sign of each coefficient so that wp+p (B) > 0, with the magnitude of the coefficient a random integer in the range [l, 51. With this choice of signs, the maximum value of F is: (3) and is achieved by the state B. Finally, the optimization problem presented to the GA in our experiments was to find a bit-string b which minimized the cost function c(b) = F,,, - F(b). (4) The minimum of this cost is zero, so we can readily determine how close to optimal the GA gets. The optimization problem defined this way can also be viewed as a constraint satisfaction problem (CSP) with a prespecified solution. Specifically, we can view each po- sition in the bit-string as a variable which can be assigned one of two values (0 or 1). Moreover, each term wp& in the Walsh polynomial corresponds to a constraint. A given bit-string b satisfies the constraint if and only if up$p(b) > 0. By our choice of signs for the wp the min- imum value of the cost function is achieved only when all terms are positive, so a minimum cost state corresponds to a solution to the CSP, i.e., a state in which all constraints are satisfied. In particular, the state B is a solution. Theory By viewing the optimization problem as a CSP, we can apply recently developed theories [Williams and Hogg, 1 p 1 number of variables and bits in the state I 1 k 1 size of constraints = order of Walsh functions 1 I I number of constraints and terms in Walsh n polynomial I I m I number of minimized nogoods, n2”-l I Table 1. Map ing between theory parameters and the experi- bedp mental test . 1992b] to characterize the difficulty of searching for a solution. In this work, a CSP is characterized by the number of variables b), the domain size of each variable (2 for our case of binary variables), and the number and size of the minimized nogoods of the constraints. These nogoods are simply those smallest subsets of all possible states in the problem that violate at least one constraint. Their size is just the number of variables involved. For example, consider a Walsh polynomial with one term, F(b) = 2$1100(b). The corresponding CSP has p=4, k=2, and n=l. Since only the non-zero bits are important in determining the value of the Walsh polynomial there are at most two variables we need to be concerned about, in this particular example the first and second positions. For these two variables there are two ways to obtain IhlOO = +l and hence a positive contribution to F since wr 100 = 2 is positive (the “goods”), { bl = 0, b2 = 0) and (h = 1, b2 = 1). There are also two ways to obtain a -1 (the “nogoods”), {bl = 1, b2 = 0) and {bl = 0, b2 = 1) where bi = s denotes the assignment of value s to variable i, i.e., value s appearing at position i in the bit-string 6. More generally, a Walsh function of order k will involve exactly k variables, so the corresponding nogoods will have size k. Moreover, of the 2” possible assignments to these variables, exactly half will have even parity giving @p(b) > 0. Thus, for either choice of the sign of the coefficient wp, exactly half the assignments will violate the constraint associated with this term, i.e., will be nogood. So each term in the Walsh polynomial will contribute 2”-l minimized nogoods. Moreover, these will be distinct from those contributed by other terms since each term has a distinct subset of the variables in the problem. From this argument we see that our CSP’s, in which the Walsh polynomial has n terms, have n2k-1 minimized nogoods, all of size k. This mapping between the parameters in the theory and our problem class is summarized in Table 1. For simple backtrack search, the theory [Williams and Hogg, 1992a, Eq. lo] estimates that the search cost, on average, as a function of p, k and n is f es% c i=O theory = max(l,eg*) (5) Genetic Algorithms 1311 with gi = iln2 + n2”-l h(1- ($-,*). (6) Note that gi decreases as more terms are added, i.e., as n increases, and this decrease is more rapid for larger values of i. This means that, for fixed ~1 and k, ctheory first increases with n, eventually reaches a peak at a value n = n,,.it (which depends on ~1 and k), and then decreases, as shown in Fig. 1 for parameter values used in some of our experiments. ok. . . _ * . . . . . .A 0 50 100 150 200 Fig. 1. In (Ctheory ) versus n, the number of constraints, for p = 25 and k = 4. The maximum hardness occurs for n = 34. A Hardness-Based Cost Measure As it stands, this theory evaluates the expected search difficulty of an entire problem. Applied in the context of a GA, we need to evaluate the usefulness of different individual states in the population. That is, some states are more likely than others to lead readily to a solution, and hence should have an enhanced number of offspring in the next generation. The traditional fitness function approach simply equates usefulness of a state with the value of the function to be optimized applied to that state, where the function to be optimized may be either maximized or minimized. We now describe how we applied the theory to evaluate individual states and used this evaluation to define a new cost measure for use with the GA. For an individual state b some constraints in the problem will be satisfied while oth- ers are violated. Thus one way to apply the problem hard- ness measure of Eq. 5 is to view the violated constraints as forming a subproblem and use this subproblem’s hard- ness measure as the hardness associated with the state b. While there are several specific ways one could do this, our particularly simple approach is to replace the value of n in Eq. 5 with the number of constraints (i.e., terms in the Walsh polynomial) that are violated by the state. The potential advantage of using hardness-based cost is that we can exploit hard and easy parts of the search space and either seek out or avoid those areas as nec- essary. When applied to GAS this implies we can bias the population in one direction or the other via reproduc- tion operations. For example, if a particular individual had a cost to the right of the maximum hardness peak of Fig. 1 and the next generation had a cost to the left, then we would want to exploit that discovery by heavily in- creasing that individual’s number of offspring for the next generation. Note that this is the case even if the hardness to the left of the maximum is higher than the hardness to the right. This is because a problem becomes easier very rapidly to the left of the peak. Thus, in our experiments we sought to decrease the number of violated terms, with- out considering the weights given to the various terms by the coefficients, unlike the traditional approach. To do this within the context of a GA, we need to re- late the hardness measure we defined for an individual state to an appropriate cost function. In this context we note that the standard cost measure of Eq. 4 monotonically decreases as the state gets close to the optimum. The situ- ation is more complicated for the non-monotonic hardness function of Eq. 5. The region to the left of the maximum peak is monotonically decreasing as n decreases, which is fine. The problem is that the hardness function is mono- tonically increasing to the right of the maximum hardness peak as n decreases. Instead, we need to find a func- tion of hardness which decreases even though hardness itself increases. There are a plethora of ways to define an appropriate cost function. One way that systematically produces better results is as follows. If the state b, with n violated constraints, is “to the right” of the maximum hardness peak, i.e., n > n,,it, then reducing the cost re- quires first solving harder problems closer to the peak on the way towards the steeply dropping part of the hardness curve “to the left” of the peak. Thus, to encourage the GA to reduce the number of violated constraints, a func- tion inversely proportional to the hardness can be used. Similarly, when n < n c,.it a function proportional to the hardness can be used. Moreover, to stress the importance of states to the left of the hardness peak, a resealing of hardness is done to cause a “stampede” across the hard- ness peak that might otherwise take a long time. Since the hardness theory is an approximation, the exact location of the peak is uncertain, but on the average it should, like the GA procedure itself, lead to better performance. The cost function we chose was one based on simplicity, namely: Char&, k, n) = In (Ctheory) 400/ In (Ctheory ) if 7-2 < b-it. c7J otherwise Finally, the cost for given bit-string b was chard(b) = Cha,.d(p, k, n) where n was the number of constraints that conflict with the state b. This cost is minimized when all constraints are satisfied, i.e., when n = 0, corresponding 1312 Genetic Algorithms to a solution. To distinguish this use of n for a state 6, we use no to denote the total number of terms in the Walsh polynomial of the problem. This remains fixed while the n values associated with a population of states varies as states are modified by the GA. 0.8 xO.6 2 k "0.4 0.2 0 L 0 50 100 150 200 n Fig. 2. Comparison of standard (dashed) and hardness-based (solid) cost measures as a function of the number of violated constraints n for p = 25 and L = 4. Both values are normalized to their maximum value in the range considered. Note that the standard measure depends on the values of the coefficients and hence the line represents a hardness averaged over many problems with this structure. Note the abrupt change in the hardness at the transition point ncrtt = 34 which acts to initiate a stampede of individuals across the critical region. To illustrate our application of the theoretical measure to individual states, we can examine the number of con- straints that are violated by individual randomly chosen initial states. It is important to realize that most such states will already satisfy many constraints. Thus, if we assume the constraints are independent, one would expect that the number of terms in conflict with a random initial state would be n = $no. In fact, we observe somewhat more initial conflicts, and further, there is a wide variation in the initial number terms to be solved. This of course leads to a spread in the initial hardness of the problem to be solved. Experimental Setup Does the Theory Apply to We used a publicly available genetic algorithm called Before presenting our evaluation of the new fitness func- GENESIS for GENEtic Search Implementation System tion, we first used the standard GA to see whether the version 5.0 [Grefenstette, 19901. The program provides a theory applies at all to GAS. Although a relation between standard genetic algorithm implementation with bit-string problem structure and hardness has been observed for a or floating point vector representation. The user provides variety of search methods, it is important to check that it an evaluation function for determining the fitness of the also applies to our problems solved by GAS. More gen- individuals in the population. The user also provides the erally, instead of examining the time required to reach crossover and mutation rates. There is also an elitist an optimal state, we considered near-optimal states as mechanism for guaranteeing that a number of the fittest well. Fig. 3 shows how the search cost varies with prob- individuals from one generation will survive to the next. lem size and closeness to optimality. We see the de- In all the experiments reported here a fitness proportionate velopment of a peak indicating a region of particularly reproduction was used where the number of offspring from hard problems, in qualitative agreement with the theoret- an individual was proportional to its fitness (which means ical prediction and empirical observations of other search how well it minimizes cost) in the overall population. methods. This generalizes and “explains” more generally 80 20 0’ I 50 100 150 200 250 300 mu Fig. 3. Generation versus p with k=4, -3, using the standard cost measure. The lowest curve (solid black) is the distribution of time to reach 80% of the optimal solution avera ed over 10 runs, i.e., the time required to ftrst find a state with F B 21)/p,,, 2 0.8. Similar curves follow u ward and become more dashed are for 85%,. 90%, 92%, 94%, 8 6%, and 98%. Curves that do not. have certam Jo values did not reach the s r cified level of opttmum within 100 generations. This is in qua itative agreement with the theory which states that the hardest problems are in the regions of intermediate p. A similar eas -hard-easy pattern of problems is seen when n is varied at a f! xed value of ,u, in qualitative agreement with the behavior shown in Fig. 1. All of the experiments used 250 individuals with a mutation rate of .02 per bit and a crossover rate of 0.5 per individual. At each generation, the best 10 individuals were guaranteed to survive. Typically 100 runs were made under the same conditions. Each run ran for 100 generations. With our choice of parameters p, k and n describing the class of problems, the initial hardness was in the overconstrained part of the space. Thus, the individual had to move through the maximum hardness peak to solve the problem. Further, the polynomials were easy enough to be solved in a reasonable amount of time so that decent statistics could be obtained. Still, not every problem was solved within the allotted time. Thus we have a choice of performance metrics: fraction of time the problem was solved within a given number of generations, and fraction of the optimal solution found at a given generation. Genetic Algorithms 1313 0 0 20 40 60 80 100 Generation Fig. 4. Fraction of optimum as a function of generation, i.e., the largest value of F(b)/F,,, for states b in the population. For this plot p = 25, k = 4, no = 150. Black points are the hardness-based cost results and the gray points are the standard fitness results. The error bars are the standard error of the mean for the generation. All 100 runs are plotted. Much of the displayed variance is due to the different problem instances. A more precise comparison of the two algorithms is given by Hotelling’s multivariate paired T test [Johnson and Wichem, 19921. This test on the differences in the two methods on 400 problems, rejects the hypothesis that they have the same behavior at a significance level of less than 10s4. two observations Forrest and Mitchell, 19931 where what naively seems to be a harder problem (since it involves more variables) is actually easier. Search Performance We compare the hardness-based cost measure with a stan- dard measure in Fig. 4. Note that in the figure the hardness-based cost led to superior performance. Addi- tionally, the hardness-based cost found the optimum on 63 out of 100 runs versus 58 with the standard fitness. Each run consisted of a randomly generated Walsh polynomial, which was used with both the hardness-based and stan- dard cost functions. By using the same problem instances with both methods we obtain a more discriminating com- parison between the methods than if we had used separate random samples for each case. It is also worthwhile looking at the finishing time of the runs that actually finished, shown in Fig. 5. As can be seen from the figure the hardness based fitness measure is significantly faster at finishing than the standard fitness. Thus not only is the hardness measure better at finding solutions, it is also finds those solutions faster. Finally, we mention the computational resources re- quired for our new method. There is no extra storage cost incurred using this implementation. Further, although the hardness computation is not optimized, its use adds only about 13% to the CPU time to evaluate each generation on a SUN SparcStation 2. This modest increase is more than offset by the large reduction in the problem solving steps, from an average of 49&l generations using the standard fitness measure to 28+1 using the hardness-based measure (where the 1 is the standard error of the mean), so that / 0 0 20 40 60 80 100 Generation Fig. 5. Probability of finishing as a function of generation averaged over 400 runs. For this plot p = 25 and k = 4, Q = 150. The solid line the hardness-based fitness results (224 finishers) and the dotted line is the standard fitness results (201 finishers). The chance that the two distributions are the same is rejected at a significance level of a few parts per million using the Kolmogorov-Smimov test [Press et al., 19861. our method uses 1.75 times fewer generations, on average, and thus runs 1.52 times faster in CPU time. iversity One important characteristic of GAS is the diversity of the individuals in the population. The mutation rate is a force acting to increase diversity and the crossover operation is a force acting to reduce diversity. Diversity can be a good or bad depending on when it occurs during problem solving. During the early part of a search we would like to have a high diversity so as to reap the benefits of having many individuals exploring different parts of the search space. On the other hand, once a promising region of the space has been found we would like to focus our resources on that area which necessitates a reduction of the diversity. We defined the diversity of the GA as the average over the population of the fraction of the least prominent value for a particular bit location in the state, averaged over all the locations. Thus, the maximum diversity of 0.5 means that O’s and l’s are evenly distributed, and the minimum diversity of 0 means that each member of the population is identical at each location. The evolution of diversity is shown in Fig. 6. As seen in the figure the diversity for the hardness-based runs is lower than for the standard runs in the region where the hardness-based runs typically finish. This means that the hardness switchover that occurs at maximum theoretical hardness is having the desired effect of focussing the individuals into easier regions of the problem and thereby speeding problem solving. Extensions In this paper we have shown how the simple use of a theoretically motivated measure of problem difficulty provides a useful heuristic for evaluating a population of search states. Within this context there are a variety of extensions that could also be tried. For instance, instead of focusing on how hard the remaining part of the problem 1314 Genetic Algorithms 0.4 I 80 IP . fb 50.3 -4 :: .E 0.2 ’ P 0 . , . . . . . . _ . . . . . 0 20 40 60 80 100 Generation Fig. 6. Diversity as a function of generation for 400 runs. For this plot fl = 25 and k = 4, no = 150. The black points are for the hardness-based fitness result and the gray points are for the standard fitness result. is to solve (favoring easier cases), we could also examine how hard a subproblem has already been solved. There are also more sophisticated ways to define the subproblem hardness. In particular, one could vary not only the number of constraints as we did, but also the number of variables. That is, only count those variables that are involved in at least one conflicting constraint. This would focus more precisely on the remaining subproblem, but ignores any interaction with the remaining constraints, which are already satisfied by the given state. If these remaining constraints greatly restrict the allowed choices for solving the subproblem, that subproblem will in fact be much more difficult than it appears on its own. This can be addressed to some extent by including the overlap of the remaining constraints with the subproblem as additional constraints for the subproblem. Including this level of detail requires using an extension of the basic theory that applies to minimized nogoods of differing sizes [Williams and Hogg, 1992a]. The idea of using general statistical knowledge of the problem may be extended to other types of problem solv- ing techniques. For example, we may be able to use the hardness criteria to better adjust the cooling schedule in simulated annealing [Kirkpatrick et al., 19831. Neural net- work learning may also benefit by using a hardness mea- sure to automatically adjust the learning rate of the net- work as it learns. Heuristic search, such as beam search or heuristic repair [Minton et al., 19901 may also benefit. A more intriguing possibility exploits the diversity be- havior we found using the “stampede” across the critical region. In nature, this kind of high diversity to low diver- sity activity is seen with ants who initially forage over a wide area but become highly localized once a food source has been found. Similarly, one could imagine a collec- tion of mobile robots [Brooks, 19911 trying to solve some kind of constraint satisfaction problem. Initially the robots would be highly dispersed but would become much more clustered as one of them informed the others that it had found something interesting to investigate. This would correspond to the genetic stampede we have observed. eferences Brooks, R. A. (1991). New approaches to robotics. Sci- ence, 253: 1227-1232. Cheeseman, P., Kanefsky, B., and Taylor, W. M. (1991). Where the really hard problems are. In Mylopoulos, J. and Reiter, R., editors, Proceedings of IJCAI91, pages 331- 337, San Mateo, CA. Morgan Kaufmann. Forrest, S. (1993). Genetic algorithms: Principles of nat- ural selection applied to computation. Science, 261:872- 878. Forrest, S. and Mitchell, M. (1993). What makes a problem hard for a genetic algorithm? Some anomalous results and their explanation. Machine Learning, 13:285-319. Goldberg, D. E. (1989). Genetic Algorithms in Search, Qptimization and Machine Learning. Addison-Wesley, NY. Grefenstette, J. (1990). A User’s Guide to GENESIS Version 5.0. Navy Center for Applied Research in AI, Naval Research Laboratory. Holland, J. H. (1975). Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI. Johnson, R. A. and Wichern, D. W. (1992). Applied Multivariate Statistical Analysis. Prentice Hall, Englewood Cliffs, NJ, 3rd edition. Kirkpatrick, S., Gelatt, C. D., and Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220:671- 680. Minton, S., Johnston, M. D., Philips, A. B., and Laird, P. (1990). Solving large-scale constraint satisfaction and scheduling problems using a heursitic repair method. In Proceedings of M-90, pages 17-24, Menlo Park, CA. AAAI Press. Mitchell, D., Selman, B., and Levesque, H. (1992). Hard and easy distributions of SAT problems. In Proc. of IOth Natl. Conf. on Artificial Intelligence (AAAI92), pages 459- 465, Menlo Park. AAAI Press. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. (1986). Numerical Recipes. Cambridge Univ. Press? Cambridge. Williams, C. P. and Hogg, T. (1992a). Exploiting the deep structure of constraint problems. Technical Report SSL92- 24, Xerox PARC, Palo Alto, CA. Williams, C. P. and Hogg, T. (1992b). Using deep structure to locate hard problems. In Proc. of IOth Natl. Conf. on Artifkial Intelligence (AAAl92), pages 472-477, Menlo Park, CA. AAAI Press. Genetic Algorithms 1315 | 1994 | 270 |
1,620 | Increasing The Efficiency of Simulated Annealing Search Learning to Recognize (Un)Promising Runs * Yoichiro Nakakuki Norman Sadeh C&C Research Laboratories, NEC Corp. The Robotics Institute, Carnegie Mellon University 4- l- 1 Miyazaki, Miyamae-ku Kawasaki 216, JAPAN nakakuki@swl.cl,nec.co.jp Abstract Simulated Annealing (SA) procedures can poten- tially yield near-optimal solutions to many diffi- cult combinatorial optimization problems, though often at the expense of intensive computational ef- forts. The single most significant source of inef- ficiency in SA search is its inherent stochasticity, typically requiring that the procedure be rerun a large number of times before a near-optimal solu- tion is found. This paper describes a mechanism that attempts to learn the structure of the search space over multiple SA runs on a given problem. Specifically, probability distributions are dynami- cally updated over multiple runs to estimate at dif- ferent checkpoints how promising a SA run appears to be. Based on this mechanism, two types of cri- teria are developed that aim at increasing search efficiency: (1) a cuto$ criterion used to determine when to abandon unpromising runs and (2) restart criteria used to determine whether to start a fresh SA run or restart search in the middle of an ear- her run. Experimental results obtained on a class of complex job shop scheduling problems show (1) that SA can produce high quality solutions for this class of problems, if run a large number of times, and (2) that our learning mechanism can signif- icantly reduce the computation time required to find high quality solutions to these problems. The results further indicate that, the closer one wants to be to the optimum, the larger the speedups. 1 Introduction Simulated Annealing (SA) is a general-purpose search procedure that generalizes iterative improvement ap- proaches to combinatorial optimization by sometimes accepting transitions to lower quality solutions to avoid getting trapped in local minima (Kirkpatrick 83; Cerny 85). SA procedures have been successfully ap- plied to a variety of combinatorial optimization prob- lems, including Traveling Salesman Problems (Cerny *This research was supported, in part, by the De- fense Advanced Research Projects Agency under contract F30602-91-C-0016 and, in part, by an industrial grant from NEC. The research was carried out while the first author was a visiting scientist at Carnegie Mellon University. 1316 Genetic Algorithms 5000 Forbes Avenue Pittsburgh, PA 15213, U.S.A. sadeh@cs.cmu.edu 85), Graph Partitioning Problems (Johnson et al. 89), Graph Coloring Problems (Johnson et al. 91), Ve- hicle Routing Problems (Osman 92), Design of Inte- grated Circuits, Minimum Makespan Scheduling Prob- lems (Matsuo et al. 88; Osman & Potts 89; Van Laarhoven et al. 92) as well as other complex schedul- ing problems (Zweben et al. 92), often producing near- optimal solutions, though at the expense of intensive computational efforts. The single most significant source of inefficiency in SA search is its inherent stochasticity, typically requir- ing that the procedure be rerun a large number of times before a near-optimal solution is found. Glover et al. developed a set of “Tabu” mechanisms that can help increase the efficiency of SA and other neighborhood search procedures by maintaining a selective history of search states encountered earlier during the same run (Glover & Laguna 92). This history is then used to dy- namically derive “tabu restrictions” or “aspirations”, that guide search, preventing it, for instance, from re- visiting areas of the search space it just explored. This paper describes a complementary mechanism that at- tempts to learn the structure of the search space ozler multiple runs of SA on a given problem. Specifically, we introduce a mechanism that attempts to predict how (un)promising a SA run is likely to be, based on probability distributions that are refined (“learned”) over multiple runs. The distributions, which are built at different checkpoints, each corresponding to a dif- ferent value of the temperature parameter used in the procedure, approximate the cost reductions that one can expect if the SA run is continued below these tem- peratures. Two types of criteria are developed that aim at increasing search efficiency by exploiting these distributions: o A Cut08 Criterion: This criterion is used to detect runs that are unlikely to result in an improvement of the best solution found so far and, hence, should be abandoned; e Restart Criteria: When completing a run or aban- doning an unpromising one, these criteria help de- termine whether to start a fresh SA run or restart search in the middle of an earlier promising run. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. The techniques presented in this paper have been applied to a class of complex job shop scheduling prob- lems first described in (Sadeh 91)l. Problems in this class require scheduling a set of jobs that each need to be completed by a possibly different due date. The objective is to minimize the sum of tardiness and in- ventory costs incurred by all the jobs. This class of problems is known to be NP-complete and is repre- sentative of a large number of actual scheduling prob- lems, including Just-In-Time factory scheduling prob- lems (Sadeh 91; 93). Experimental results indicate (1) that SA can produce high quality solutions for this class of problems, if run a large number of times, and (2) that our learning mechanism can yield significant reductions in computation time. The results further indicate that, the closer one wants to be to the opti- mum, the larger the speedups. The remainder of this paper is organized as follows. Section 2 quickly reviews fundamentals of SA search. Section 3 analyzes the behavior of typical SA runs and introduces a mechanism that aims at learning to recog- nize (un)promising runs on a given problem, using the concept of Expected Cost Improvement Distributions (ECID). I n ec ion s t 4, we use ECID distributions to develop a cuto$ criterion to determine when to aban- don unpromising runs. Section 5 presents three restart criteria based ECID distributions. Experiments ob- tained on a set of benchmark job shop scheduling prob- lems with tardiness and inventory costs are reported in Section 6. A summary is provided in Section 7. 2 Simulated Annealing Search Figure 1 outlines the main steps of a SA procedure designed to find a solution x E S that minimizes a real- valued function, cost(x). The procedure starts from an initial solution x0 (randomly drawn from S) and iter- atively moves to other neighboring solutions, as deter- mined by a neighborhood function, neighbor(z), while remembering the best solution found so far (denoted by s). Typically, the procedure only moves to neigh- boring solutions that are better than the current one. However, the probability of moving from a solution x to an inferior solution x’ is greater than zero, thereby allowing the procedure to escape from local minima. rund() is a function that randomly draws a number from a uniform distribution on the interval [0, l]. The so-called temperature, T, of the procedure is a parame- ter controlling the probability of accepting a transition to a lower quality solution. It is initially set at a high value, TO, thereby frequently allowing such transitions. If, after N iterations, the best solution found by the procedure has not improved, the temperature param- eter 2’ is decremented by a factor Q (0 < o < 1). One motivation for progressively lowering the temper- ‘These optimization problems should not be confused with the set of Constraint Satisfaction problems also intro- duced in this dissertation. ature is to obtain convergence. Additionally, as t,he procedure slowly moves towards globally better solu- tions, accepting transitions to lower quality solutions becomes increasingly less attractive. When the tem- perature drops below a preset level Tl, the procedure stops and s is returned (not shown in Figure 1). T = TO; x = x0 (E S); min = co; while (T > Tl) { for i = 1,N 1 x’ = neighbor(x); if (co&(x’) < cost(x)); ‘. x=x, else if (r,und() < exp{(cost(x) - cost(x’))/T}); x=x; if(cost(x) < min) min = cost(x), s = 2; I if (Min was not modified in the above loop); T=T*cr; Fig. 1 Basic Simulated Annealing Procedure. Fig. 2 depicts the cost distribution of the best solu- tions returned by 300 SA runs on a typical combina- torial optimization problem - a job shop scheduling problem Section arks to be -described iI‘; from a set of benchm 6. Frequency 30 CO& 1ooQo 15000 20000 25ooo 3ooQo Fig. 2 Cost Distribution of the Best Solutions Found by 300 SA Runs. The optimal solution for this problem is believed to have a cost around 11,500 - the value in itself is of no importance here. Figure 2 indicates that, if run a large number of times, SA is likely to eventually find an optimal solution to this problem. It also shows that,. in many runs, SA gets trapped in local minima with costs much higher than the global minimum. For in- stance, 60% of the runs produce solutions with a cost at least 30%) above the global minimum. This suggests that, if rather than completing all these unsuccessful runs, one could somehow predict when a run is likely to lead to a highly sub-optimal solution and abandon it, the efficiency of SA could be greatly enhanced. The following section further analyzes the behavior of typi- cal SA runs and proposes a mechanism which, given a problem, aims at learning to recognize (un)promising SA runs. Genetic Algorithms 1317 3 Learning To Recognize (Un)Promising SA Runs Figure 3 depicts the behavior of a SA procedure on two different scheduling problems (from the set of bench- marks used in Section 6). For each problem, the figure depicts five SA runs, plotting the cost of the best solu- tion, s, as the temperature of the procedure is progres- sively lowered - temperatures are shown in log scale, which is almost equivalent to computation time in lin- ear scale. SA behaves very differently on these two problems. For instance, in Problem #l, the range of final solutions is relatively narrow, while in Problem #2 it is much wider. Another differentiating factor is the behavior of the procedure at low temperatures. It seems that for Problem #l, the quality of a run can already be estimated quite accurately at T = 50 (e.g. the best run at T = 50 remains best at lower temper- atures), while this is less so for Problem #2. Formally, given a combinatorial optimization prob- lem and a SA procedure for that problem, we define ci as the cost of the best solution, s, at check point t in the i-th run and cp as the cost of s at the end of the same run (i.e., at temperature T = Tl) When the (n + 1)-st run reaches a checkpoint temperature t, the ECID below t is approximated as a normal dis- tribution N[pk, ~$1 , whose average, PC”,, and standard deviation, a:, are given by: 25000 25000 20000 -2500 t 15000 I...... l TfJrnD. 260 l&I 50 25 12.5 6.25 . --..I- 200 100 50 26 12.5 6.25 (a) Problem 1 (b) Problem 2 Fig. 3 Cost reductions in five SA runs on two different problems. Clearly, such properties are not intrinsic to a prob- lem itself. They could change if a different neighbor- hood structure or a different cooling profile was se- lected, as these parameters can affect the types of local optima encountered by the procedure and the chance that the procedure extricates itself from these local op- tima below a given temperature. While, in general, it may be impossible to find a SA procedure that re- liably converges to near-optimal solutions on a wide class of problems, we can try to design adaptive SA procedures which, given a problem, can learn to rec- ognize (un)promising runs and improve their perfor- mance over time. Below, we present a mechanism, which, given a problem, attempts to “learn” at dif- ferent checkpoint temperatures the distribution of cost improvements that one can hope to achieve by contin- uing search below these temperatures. Specifically, we postulate that, given a problem and a checkpoint temperature T = t, the distribution of the cost improvement that is likely to be achieved by continuing a run below t can be approximated by a normal distribution. Using performance data gathered over earlier runs on a same problem, it is possible to approximate these Expected Cost Irnprovekent Distri- butions (ECID) for a set C of checkpoint temperatures and use‘these distributions to identify (un)promising By incrementally refining these estimators over mul- tiple runs, this mechanism can in essence “learn” to recognize (un)promising SA runs. The following sec- tions successively describe a cutoff criterion and three restart criteria based on ECID distributions. 4 A Cutoff Criterion Suppose that, in a sixth run on Problem #l, the best solution obtained at checkpoint T = 100 is solution A - Figure 4(a). At this checkpoint, the distribution of c; - the cost of the best solution that will have been found if the run is completed - can be approximated by the normal distribution N[cioo - yioo, ,:“]. This distribution, represented in Fig. 4(a), suggests that, if continued, the current, run has a good chance of im- proving the current best’ solution, x. Cpt 25000 i 200 100 I I I I “Temp. 50 25 12.5 6.25 Expected Distribution 8 LTemp. 200 100 60 25 12.5 6.25 (b) Fig. 4 Expected Cost Improvement Distributions at T=lOO and T=50. Suppose that based on this analysis, the run contin- ues until the next checkpoint, T = 50, and that the best solution found by the run when it, reaches that temperature is A’. At this point, a new distribution of ci can be computed to check how the run is doing. This distribution, N[ciO - pg”, a:‘] is shown in Figure runs. 1318 Genetic Algorithms 4(b). It appears much less promising than the one at 2’ = 100. Now, the chances of improving the current best solution, x, appear remote: it probably does not make sense to continue this run. Formally, when the (n + 1)-st run reaches a check- point temperature t, a cutoff criterion is used to deter- mine whether or not to continue this run. In the study reported in Section 6, we use a cutoff criterion of the form: (42+1 - Pft) - Xn 1 > threshold where x, is the cost of the best solution found during the previous n runs and threshold is a threshold value. If the inequality holds, the current run is abandoned. For example, if threshold = 3 (the value used in our experiments) and the cutoff inequality holds at a given checkpoint temperature t, the probability of improving Z, by continuing the run below t is expected to be less than 1% (Beyer 87). 5 Three Restart Criteria Whenever a run is completed or abandoned, two op- tions are available: either start a fresh new annealing run or, instead, restart an earlier (promising) run, us- ing a different sequence of random numbers (“reanneal- ing”), i.e. restart from an intermediate temperature, using the solution x obtained at that temperature in an earlier run. In total, if reannealing is constrained to start from one of the checkpoint temperatures, there are up to n . ICI + 1 possible options, where n is the number of earlier runs and ICI the number of check- points in set C. Below, we describe three “restart cri- teria” that aim at selecting among these options so as to maximize the chances of quickly converging to a near-optimal solution. 5.1 Maximum Cost Reduction Rate Criterion When considering several points from which to restart search, two factors need to be taken into account: (1) the likelihood that restarting search from a given point will lead to an improvement of the current best solu- tion and (2) the time that it will take to complete a run from that point. Restarting from a low temperature will generally bring about moderate solution improve- ments, if any, while requiring little CPU time. Starting fresh new runs or restarting from higher temperatures can lead to more significant improvements, though less consistently and at the cost of more CPU time. In gen- eral, the cost improvements that can be expected from different temperatures will vary from one problem to another, as illustrated in Figure 3 (and as formalized by ECID distributions). A natural restart criterion is one that greedily picks the restart point expected to maximize the rate at which the cost of the current best solution will im- prove. For each restart candidate 01, (fresh annealing or reannealing), this can be approximated as the ex- pected cost reduction (in the best solution), if search is restarted from Ok, divided by the expected CPU time required to complete a run from that restart point. Be- low, we use R(Oh) t o d enote this approximation of the expected cost reduction rate, if search is restarted from Ok: ._ R(Ok) = expected-reduction(Ok) expected-CPU(Ok) where expected-reduction(Ok) is the expected cost re- duct(ion at the end of a ‘run starting-from Ok and expected-CPU(Ok) is the CPU time that this run is ex- pected to require. eXpeCted-CPU(Ok) can be approxi- mated as the average time required to complete earlier runs from Ok’s temperature. expected-reduction(Ok) can be evaluated using ECID distributions, as detailed below. Given a reanneahng point 01, at’ checkpoint tempera- ture t and n. earlier SA runs completed from t or above, expected-reduction(Ok) can be approximated as: expected-reduction(Ok) = J -{P;k(x) - (X, - x)}dx LB where P,$ (x) is the density function of the normal dis- tribution N[Ck - solution2, pk, a:], ck is the cost of Ok’s best x, is the cost of the best solution obtained over the first n runs, and LB is a lower-bound on the optimal solution3 If Ok is a fresh SA run, expected-reduction(Ok) can similarly be approximated as: \ , expected-reduction(Ok) = J zn{Pn(x). (I,, - x)}dx LB where P,(x) is the density function of the normal dis- tribution N[&, cri], with 5.2 One high dl = CL 4 oo n ’ n = J z--l (4 - PO, I2 n- 1 * Randomized Criterion possible problem with the above criterion is its sensitivity to possible inaccuracies in approxima- tions of ECID distributions (e.g., when the number of earlier runs is still small). When inaccurate ECID distributions lead the crit.erion to choose a poor restart point, the procedure may take a long time before it improves the quality of the current best solution. In the meantime, it may keep on coming back to the same poor restart point. For this reason, it is tempting to use a randomized version of the criterion. One such varia- tion involves randomly picking from a set, of promising restart points, H = {oZIR(OZ) > P ’ M(=‘{R(Ok)}}, while assuming that each element in H has the same probability, l/j HI, of being selected. 0 is a constant whose value is between 0 and 1. 2To be consistent, if 01, corresponds to the i-th SA run, ck = cf , as defined in Section 3. 31n the experiments reported in this paper, LB was sim- ply set to 0. Genetic Algorithms 1319 5.3 Hybrid Criterion A third alternative involves keeping some level of stochasticity in the restart criterion, while ensuring that more promising restart points have a higher chance of being selected. This can be done by selecting restart points in H according to a Boltzmann distribu- tion that assigns to each element 01 E H a probability Here, r is a positive constant. If r is very large, this method becomes equivalent to the randomized crite- rion described in subsection 5.2. If r = 0, this cri- terion becomes similar to the criterion of subsection 5.1. A similar distribution is used in the Q-learning algorithm described in (Watkins 89). 6 Performance Evaluation 6.1 The Job Shop Scheduling Problem with Tardiness and Inventory Costs To evaluate performance of our cutoff and restart cri- teria, we consider a set of complex job shop schedul- ing problems first introduced in (Sadeh 91). The problems assume a factory, in which a set of jobs, J = (ji, j,, ‘9 . , jn}, has to be scheduled on a set of re- sources, RES = (RI, Ra,. l l , R, . Each job requires performing a set of operations 0 1) = {Oi, Oi, . . l OL, ) and, ideally, should be completed by a given due date, ddl, for delivery to a customer. Precedence constraints specify a complete order in which operations in each job have to be performed. By convention, it is as- sumed that operation 0: has to be completed before operation Oi,, can start (i = 1,2,. . . , nl - 1). Each operation Of has a deterministic duration duf and re- quires a resource Rf E RES. Resources cannot be assigned to more than one operation at a time. The problem is to find a feasible schedule that minimizes the sum of tardiness and inventory costs of all the jobs (“Just-In-Time” objective). This problem is known to be NP-complete (Sadeh 91) and is representative of a large number of actual factory scheduling problems where the objective is to meet customer demand in a timely yet cost effective manner. Experimental results reported below suggest that a good neighborhood function for this problem can be obtained by randomly applying one of the following three operators to the current schedule4: 41n the scheduling jargon, the Just-In-Time objective considered in this study is known to be irregular(Morton & Pentico 93). Prior applications of SA to job shop scheduling have only considered regular objectives such as Minimum Makespan. It can be shown that the neighborhoods used in these earlier studies are not adequate to deal with irreg- ular objectives such as the one considered here (Sadeh & Nakakuki 94). SHIFT-RIGHT: randomly select a “right-shiftable” operation and increase its start time by one time uriit5. SHIFT-LEFT ( mirror image of SHIFT-RIGHT): randomly select a “left-shiftable” operation and de- crease its start time by one time unit. EXCHANGE: randomly select a pair of adjacent op- erations on a given resource and permute the order in which they are processed by that resource. Specif- ically, given two consecutive operations, A and B on a resource R, with A preceding B in the current so- lution, the exchange operator sets the new start time of B to the old start time of A and the new end time of A to the old end time of B 6. In our experiments, the probability of picking the EX- CHANGE operator was empirically set to 3/7 while the probabilities of picking SHIFT-RIGHT or SHIFT- LEFT were each set to 2/7. Additionally, the values of parameters in the SA procedure (see Figure 1) were set as follows: To = 700, 2’1 = 6.25, N = 200,000 and a = 0.85. The performance of this SA procedure has been eval- uated in a comparison against 39 combinations of well- regarded dispatch rules and release policies previously used to assess the performance of the Sched-Star (Mor- ton 88) and Micro-Boss (Sadeh 91; 93) systems on a set of 40 benchmark problems similar to the ones de- scribed in (Sadeh 91). The 40 benchmarks consisted of 8 problem sets obtained by adjusting three parameters to cover a wide range of scheduling conditions: an aver- age due date parameter (tight versus loose average due date), a due date range parameter (narrow versus wide range of due dates), and a parameter controlling the number of major bottlenecks (in this case one or two). For each parameter combination, a set of 5 scheduling problems was randomly generated, thereby producing a total of 40 problems. Each problem involved 20 jobs and 5 resources for a total of 100 operations. On av- erage, when compared against the best solution found on each problem by the 39 combinations of dispatch rules and release policies, SA reduced schedule cost by 22% (average over 10 SA runs). When compar- ing the best solution obtained in 10 SA runs against the best solution obtained on each problem by the 39 combinations of dispatch rules and release policies, SA produced schedules that were 30% better. However, while running all 39 combinations of dispatch rules and release policies on a given problem takes a few CPU seconds, a single SA run takes about 3 minutes 5An operation is said to be “right(left)-shiftable” if its start time can be increased (decreased) by one time unit without overlapping with another operation. 61n our implementation, exchanging two operations is allowed even if a precedence constraint is violated in the process. Precedence constraint violations are handled using large artificial costs that force the SA procedure to quickly get rid of them (Sadeh & Nakakuki 94). 1320 Genetic Algorithms (on a DECstation 5000/200 running C). Additional de- tails on these experiments can be found in (Sadeh & Nakakuki 94). 6.2 Empirical Evaluation of Cutoff and Restart Criteria We now turn to the evaluation of the cutoff and restart criteria presented in this paper and compare the perfor- mance of five variations of the SA procedure presented in 6.1: N-SA: regular SA, as described in 6.1 (no learning). P-SA: SA with cutoff criterion. B-SA: SA with cutoff and Maximum Cost Reduc- tion Rate restart criteria. R-SA: SA with cutoff and randomized restart crite- ria (p = 0.5). H-SA: SA with cutoff and hybrid restart criteria (p = 0.5 and r = 1). When running P-SA, B-SA, R-SA, and H-SA, the cut- off and/or restart criteria were only activated after 5 complete SA runs to allow for the construction of meaningful ECID distributions. All four of these pro- cedures used the same set of checkpoints, C = (200, 100, 50, 25, 12.5). The five procedures were compared on the same 40 benchmark problems described in subsection 6.1. Each SA procedure was run for 2 hours on each bench- mark problem. cost b 9 0 N-SA o P-SA q B-SA A R-SA * H-SA 7500' . . 1 bTime (min.) 30 60 so 120 Fig.5 Improvement of the best solution over time. Fig. 5 depicts the performance of the five SA proce- dures on a typical benchmark problem. It shows that throughout its run, N-SA was dominated by the other four procedures. It also indicates that both the cut- off criterion and the restart criteria contributed to this performance improvement. Among the three restart criteria, H-SA appears to perform best. Figure 5 fur- ther suggests that the restart criterion in H-SA im- proves performance through the entire run, as the gap between H-SA and N-SA widens over time. These ob- servations are confirmed by results obtained on the 8 problem sets of the study, as depicted in Figure 6. Fig. 6(a) shows the average cost reductions yielded by P-SA, B-SA, R-SA and H-SA over N-SA at the end of the two-hour runs. Figure 6(b) gives the average CPU time reductions obtained by each of these four procedures (over N-SA), when required to produce a solution of quality equal to or better than that of the best solution found by N-SA in 2 hours. It can be seen that H-SA requires between 25% and 70% less CPU time than N-SA. Cost ryluction (?h) 4.0 0 P-SA m B-SA 3.0 12345678 (a) Cost reduction (fixed CPU time) Set 0 II A e 0 00 . Problem Set 12345678 (b) Speedup (fixed cost) Fig. 6 Empirical comparison. A finer analysis indicates that performance improve- ments produced by our cutoff and restart criteria in- crease as one requires higher quality solutions. Figure 7, compares the average CPU time of each of the five procedures as the required quality of solutions is in- creased. While all five procedures take about as long to find a solution with cost below 9000 or 8800, the time required to find a solution below 8500 varies sig- nificantly (e.g. H-SA can find such a solution in 3500 seconds while N-SA requires close to 10,000 seconds). Time (eec) t ; loo00 :. I\ ; : : : : N-SA P-SA B-SA R-SA H-SA Fig. 7 Speedups as a function of required solution quality. As already indicated in Section 5, the difference in performance between B-SA, R-SA and H-SA suggests that a deterministic use of ECID distributions to de- cide where to restart search can be tricky, as these dis- Genetic Algorithms 1321 tributions may not be accurate, especially when only a small number of runs has been completed. By in- jecting non-determinism in the restart criterion, R-SA and H-SA ensure that the procedure will not always restart from the same point. The procedure is forced to sample a wider area and in the process gets a chance to refine ECID distributions. From this point of view, B-SA is a procedure that places more emphasis on us- ing existing knowledge of the search space than on ac- quiring new one, while R-SA places more emphasis on learning and less on exploiting already acquired infor- mation. H-SA appears to provide the best compromise between these two requirements. Finally, it should be obvious that the CPU time and memory overheads of our cutoff and restart criteria are very moderate. All in all, in our experiments, the CPU time required to learn ECID distributions and apply the cutoff and restart criteria was well under 1% of total CPU time. 7 Summary In summary, we have developed a mechanism that learns to recognize (un)promising SA runs by refining “Expected Cost Improvement Distributions” (ECIDs) over multiple SA runs, and have developed search cut- off and restart criteria that exploit these distributions. These mechanisms can be applied to any SA procedure and have been validated on complex job shop schedul- ing problems with tardiness and inventory costs, where they have been shown to dramatically reduce the com- putational requirements of a competitive SA proce- dure. Experiments presented in this paper further in- dicate that the closer one seeks to be to the optimum, the larger the speedups. Acknowledgments The first author would like to thank Masahiro Ya- mamoto, Takeshi Yoshimura and Yoshiyuki Koseki of NEC Corporation for giving him the opportunity to spend a year at Carnegie Mellon University. References Cerny, V., “Thermodynamical Approach to the Traveling Salesman Problem: An Efficient Simulation Algorithm,” J. Opt. Theory Appl., Vol. 45, pp. 41-51, 1985. Beyer, W.H. “CRC Standard Mathematical Tables, 28th Edition,” CRC Press, Inc., Boca Raton, FL, 1987. Garey, M. R. and Johnson, D. S. “Computers and In- tractability: A Guide to the Theory of NP-Completeness,” Freeman and Co., 1979 Glover, F. and Laguna M. “Tabu Search,” Chapter in Modern Heuristic Techniques for Combinatorial Prob- lems, pp. 70-150, Cohn Reeves (Ed.), Blackwell Scientific Publications, Oxford, 1993 Graves, S. C. “A Review of Production Scheduling,” Op- erations Research Vol. 29 no. 4, pp. 646-675, 1981 Johnson, D. S., Aragon, C. R., McGeoch, L. 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1,621 | Imtxovinrr Search through 1. ” Peter Shell Juan Antonio Hernandez Rubio Center for Machine Translation Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213 pshell@cmu.edu Abstract Adding diversity to symbolic search techniques has not been explored in artificial intelligence. Adding a diversity criterion provides us with a powerful new mechanism for finding global maxima in complex search spaces and helps to alleviate the problem of premature convergence to local maxima. A theoretical analysis is presented of issues in diversity searching which previously haven’t been addressed, and a domain-independent diversity-search algorithm for practical breadth-first searching is devel- oped. Empirical results of an implementation in the CRE- SUS expert system for intelligent cash-management con- firm that diversity can significantly improve the solution quality of symbolic searchers. Introduction This paper presents a new symbolic technique for tack- ling a fundamental problem found in all search techniques used in complex domains: converging to a local maxi- mum at the expense of not finding a global optimum. In large and complex search problems where it is impossible to visit a significant fraction of the possible states, heuris- tic evaluation functions must be used to decide which intermediate solutions to reject and which to pursue. This can cause pruning of locally suboptimal intermediate states even though they may have led to a better global solution. This recurring problem has not been studied in depth and thus there are not many good solutions to it. This problem manifests itself in all heuristic search paradigms. In genetic algorithms (Holland 1975) one of the main problems affecting search performance is “premature convergence”, where most of the members of the “population” end up being very similar to each other and many potentially useful “genes” are lost. This results in suboptimal solutions when the best solution included one of the lost genes. A similar problem occurs in breadth-first search as we will see. In depth-first search such as game-trees, there is a simi- lar problem called the “horizon effect”. The evaluation function gives an inaccurate estimation of the cost of a state because it was at an unstable local maximum or minimum (for example threatening the king in chess), thereby misleading the search to prefer that state even though it may not ultimately lead to an optimum. Gonzalo Quiroga Barro Union Fenosa Capitsn Haya, 53 28020 Madrid (Spain) gquiroga@uef.es This paper develops and evaluates a method I call “diversity search”. Diversity search maintains the unique- ness of intermediate states and operators in order to increase the coverage of the space searched. It promises to improve the performance of many types of searchers by alleviating the local-minimum problem. Although it can augment most search techniques, it has received little attention in artificial intelligence. The idea has been used in genetic algorithms (Mauldin 1984) and simulated annealing (Kirkpatrick, Gelatt & Vecchi 1983) but hasn’t been attempted in symbolic search methods such as depth-first or breadth-first search. This paper reports work which has combined ideas found in genetic algorithms and simulated annealing with symbolic search techniques. I address some issues surrounding diversity search which haven’t previously been considered, then develop a domain-independent algorithm for diversity-search in a breadth-first searcher. An implementation is presented in CRESUS (Shell et al. 1992), a working expert-system in the complex domain of cash-management, with empirical results that show that diversity search can significantly improve global search performance. Related Work Here we consider related solutions to the local maximum problem in different search formalisms and contrast them to diversity search. Although diversity search hasn’t been addressed in symbolic search, it has been addressed in genetic algorithms. Genetic algorithms simulate natural evolution to optimize an evaluation function. They are analogous to breadth-search where the intermediate states are called “genomes”; sets of states correspond to popula- tions; and the evaluation function corresponds to the physical environment. New states are generated by apply- ing genetic operators such as crossover or mutation to single or pairs of parent genomes. Genomes with the highest evaluation function have the best probability of “reproducing.” Search proceeds by reproducing and replacing genomes for typically several thousands of generations, and picking the most fit genomes from the resulting population. Genetic algorithms are mostly used in machine learning (DeJong 1990). Genetic Algorithms 1323 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. DeJong (DeJong 1975) recognized early on that prema- ture convergence in genetic algorithms adversely affected performance and attempted to alleviate it. He employed probabilistic reproduction and operator mutation so that the locally favored genes wouldn’t dominate the pool. Although this increased the diversity of the population it didn’t significantly improve performance. Adding a “crowding factor”, which limited the number of geno- types similar to the favored genotype, helped his system on his hardest test case (F5). Mauldin (Mauldin 1984) later introduced an explicit diversity criterion into genetic search and showed that diversity significantly improved performance using DeJong’s 5 polynomial test functions. Booker (Booker 1987) developed several new crossover strategies (such as using two crossover points and strate- gically varying the crossover rate) which gave similar improvement without explicitly introducing diversity. For several reasons, diversity in genetic algorithms doesn’t transfer easily to symbolic search methods. Genetic algorithms usually require several thousand itera- tions to find an optimized solution. This works well for the simple polynomial functions used in much of the genetic-algorithms literature where the evaluation is fast and states are represented in few bits, but isn’t feasible in knowledge-rich systems where the evaluation function takes longer to compute and the states are more complex. Furthermore, the two orthogonal criteria of diversity and primary evaluation cannot be combined in the same way by symbolic searchers, as we will see. Finally, the metric used to evaluate diversity in genetic algorithms is simply the “Hamming distance” between the bit-strings repre- senting each genome. Since symbolic search methods don’t usually use a bit-string representation this metric is not transferrable. Simulated annealing (Kirkpatrick, Gelatt & Vecchi 1983) is a stochastic search technique designed to find minimum-cost solutions to large optimization problems without converging to a local minimum. It is based on an analogy with statistical mechanics. It has been used in such tasks as graph bisection (Jerrum & Sorkin 1993) and connectionistic networks such as the Boltzman machine (Ackley, Hinton & Sejnowski 1985) However, simulated annealing is a slow process which requires fast evaluation and generation functions (Davis & Steenstrup 1987) and so wouldn’t be feasible for most knowledge-based expert- systems. Furthermore, as Mauldin (Mauldin 1984) pointed out, it is not intrinsically parallel like genetic algorithms. Techniques have been developed for alleviating a simi- lar problem in depth-first search. Quiescence search (Beal 1990), used largely in game programs to handle the hori- zon effect, identifies local maxima with respect to the (sometimes inaccurate) evaluation function by situations of instability such as checking a king in chess. Such situa- tions are likely to “fool” the evaluation function into giving an inaccurate cost. When they occur the algorithm continues searching until a stable, or quiescent, state is reached. Depth-first searchers can’t incorporate the diver- sity of states into their algorithms because they only retain one state at a time, and they need to compare the states to determine their diversity. Berliner (private communication) has experimented with increasing the diversity of operators in depth-first searchers by grouping operators by similarity and ensur- ing that several different groups of operators are gener- ated at each step in the search. This may encourage diver- sity at the operator-generation level but lacks the ability to ensure diversity among states. Motivation The introduction described the need for a technique to avoid convergence to a local maximum in order to find the global maximum, and noted the lack of research into diversity search in symbolic domains. Here we examine the behavior of a specific breadth-first searcher which will motivate introducing diversity into searching techniques. Our breadth-first searcher is part of CRESUS (Shell et al. 1992), a cash-management expert-system used by the treasury department of Union Fenosa, an electric company serving greater Madrid in Spain. This expert system could be used by any medium or large-sized company to automate and improve their treasury. The task of the treasurer is to manage the daily cash-flow and cover the company’s financial needs by borrowing money from some subset of the numerous company credit lines, balance several bank accounts, allocate payments and collections and invest any excess funds. Each such opera- tion involves commissions and interest payments which vary depending on the amount of money and the associ- ated financial instrument (e.g., check or wire), credit-line or bank-account. The goal is to minimize the global cost of all of these operations. An artificial intelligence approach was developed after it was realized that non-heuristic algorithms such as linear programming couldn’t find a solution in a reasonable amount of time due to the large number of variables in the problem. In the CRESUS searcher, an operator is a cash- management operation such as moving $1000 from account A to account B using a wire transfer. A state is defined by the current balance of all the bank accounts and amounts available in the credit lines. The evaluation function computes the total cost of the current operations plus the estimated cost of the remaining operations. A solution is a sequence of operations which balance all of the bank accounts. CRESUS is implemented in Common- Lisp and currently runs on Sun Sparcstations. It uses the PARMENIDES (Shell & Carbonell 1988) frame language as its knowledge representation and FRULEKIT (Shell & Carbonell 1986) for the inference engine. 1324 Genetic Algorithms An experienced treasurer requires several hours to manually complete the task. The searcher automates the decision-making and performs it in about 5 minutes with a hybrid beam-search (Newell 1978) algorithm. Further, the searcher usually outperforms the treasurer, finding solutions which cost about 20% less than the treasurer’s. The cash-management task is extremely complex. For each state in the search space, about 100 operators may apply, and solutions typically consist of a sequence of about 100 operators. Thus the search space contains about 10200 states. Furthermore, it is multi-modal; of high dimensionality and has a high degree of “epistasis”: one part of a solution can be inhibited or modified by another part. This space is made tractable by encoding expert knowledge into the operator evaluation and generation functions, and by partitioning it into minimally interact- ing subspaces. These subspaces correspond to the daily solution versus the global, or period, solution of 2 to 4 weeks and the space of operators of a particular type. Although the beam-searcher usually finds solutions which the human expert can’t improve, occasionally it constructs suboptimal solutions corresponding to local maxima. It is important to avoid such solutions because the treasury department has started to rely on the searcher on a daily basis; and since the searcher usually finds good solutions, the expectations of the users have been raised. Furthermore, the company plans to market the system and would like it to perform consistently well. Examining the states at which the searcher arrived at the end of the search illustrates the problem. The final states are extremely similar to each other. Table 1 shows the average number of operators constituting each state which are unique to that state, i.e. which don’t appear in any other state. For example, if state I were created by the application of operators {A,B,CJ and state 2 by operators {B,D,A] then those states would each have two unique operators, C and D, respectively (the computation of operator uniqueness is discussed in more detail in the next section). The beam-searcher was run over 5 days in Octo- ber 1993 with a beam-width of 20. Similar results are obtained when the intermediate states are examined, for example after 10 or 20 iterations. Table 1: Average numberofuniqueandcommon beamsearcherstates operators in the Intuition explains the high similarity between the state:. When any type of searcher tries to find an optimal state in a large search space it will only be able consider a tiny subset of those nodes. For example a beam searcher might keep a set of on the order of the 20 best states and generate 10 potential successors to each state. If the aver- age depth of a space is 100, then the searcher will only have considered 20 x 10 x 100 or 20,000 states. Because the number of states visited by the searcher is so small compared to the number in the space (lo4 versus 10200), intuition tells us that the states which have the highest evaluation will end up being very similar to each other. This is because the states which only differ from the preferred state by one operator or by a small change in an operator, will likely have one of the highest evaluations as well. This isn’t due to an inaccurate evaluation function because the evaluation function had been finely tuned - it performs miniature searches of its own to accurately esti- mate the cost of the remaining operations. These observa- tions led me to develop the diversity search algorithm. The Diversity-search Algori The heuristic of diversity search is that by increasing the “diversity” of the intermediate states in a breadth-first searcher, we may be able to improve the final results. By retaining some states not only because they have a desir- able primary evaluation (such as cost) but also because they are sufficiently different from the other states, we can avoid converging on local maxima which can mislead the global searcher. A formalization of the standard beam- search algorithm is presented, followed by the diversity- based algorithm. Next two issues in diversity searching which haven’t been sufficiently considered are addressed: how to define diversity of states and how to combine the primary evaluation with the diversity evaluation. The Standard Beam-search Algorithm To compare diversity-search with a more traditional algo- rithm and to introduce notation, the standard beam-search algorithm used in CRESUS is first presented. a. Initialize set-of-states to a set containing one state which is the current problem's state. b. REPEAT until no more states can be expanded: 1. Expand set-of-states using generation function G. 2.Evaluate the expanded states using primary evaluation function E. 3.Pick the K highest-evaluated states as the next set of states. The generation and evaluation functions are as follows: Genetic Algorithms 1325 G: State0 * {StateI, State2, . . . State,) Statei is derived by applying an operator to Stateg. E: State ) Evaluation Evaluation is the estimated cost of the given state. K, the beam width, is the number of states retained at each step. The Diversity Beam-search Algorithm The diversity beam-search algorithm augments steps b.2 and b.3 to include an evaluation of the diversity of states as well as primary evaluation: a. Initialize set-of-states to a set containing only the current problem's state. b. REPEAT u expanded ntil no more states can be 1. Expand set-of-states using generation function G. 2.Evaluate the expanded states using primary evaluation function E. 2'.Evaluate the diversity of the expanded states using diversity evaluation function D. 3.Pick the K highest-evaluated states into the next set of states. 3'.Add the _Kf states which maximize the function C(E,D) to the next set of states. Where: D: State * Diversity-evaluation where Diversity-evaluation is the estimated diversity of the given state relative to the other states and: c: Cost-eval, Diversity-eval * Combined-eval K’ is the diversity beam width, i.e., the number of states to keep at each step based on their diversity in addi- tion to the K cost-wise best states. The diversity-computation function D and combination function C are discussed next. Computing the Diversity Because diversity search hasn’t previously been attempted in symbolic search techniques, the issue of computing the diversity of states hasn’t been adequately addressed. An intuitive method would be to compare states directly using domain-specific functions. For exam- ple, in the cash-management domain, one might compare how many bank accounts are balanced and how much 1326 Genetic Algorithms money is available in each credit-line. However, this requires domain-specific comparison functions and doesn’t take into account that different sequences of oper- ators with different costs could have led to the same state. A more accurate way to compare states is to count how many constituent operators - independent of order - that they have in common, since it is the constituent operators which comprise the solution. In symbolic searchers where operators are applied to generate new states, the sequence of operators leading to each state can be associated with each state. To calculate the closeness between two states S1 and S2, we will define State-match(S1,&) to be: Len (SJ c Op-state-match (Op-num (i, S,) , S,) (EQ 1) i=l where Op-state-match(Op,S) is defined as: Max(Op-match(Op,Op-num (i, S) ) Vi < Len (S) (EQ 2) where Op-num(i,S) returns the izh operator in state S. Note that if the search technique compared states at different depths, such as A*, State-match would have to return a percentage instead of a count of matches. The function Op-match should return a number 0 through 1, where 0 means that the operators are completely different and 1 means that they are identical. To simplify and to make the comparison domain-indepen- dent, we can define Op-match to return 1 only if the oper- ators are identical and to otherwise return 0. Under this definition, State-match(S1&) tells us how many opera- tors associated with St are also associated with S2. Finally, to compute the degree of match of a state rela- tive to a set of states, a logical method would be to compute the maximum match between the state in ques- tion and the rest of the states in the state-set. Thus Match- in-Set(S,Set) is: Max(State-match(S,State-num(i,Set)) ) Vi < Len(S) (EQ 3) State-num(i,Set) gives the ilh state in the set of states Set. The diversity of a state is then the number of operators in the state minus the Match-in-Set of that state. Combining Primary and Diversity Evaluation A harder question is how to combine the orthogonal crite- ria of primary cost-evaluation and diversity evaluation. We want to retain some states because of their diversity, but we should also retain some of the best cost-evaluated states so that the search proceeds towards the global mini- mum. In genetic algorithms, Mauldin (Mauldin 1984) limited the population size by requiring that all intermedi- ate states have a minimum diversity from the others, and probabilistically “reproduced” the state with the highest cost-evaluation. However, these two steps are merged in beam search and there is no analog to “reproduction” in symbol search, so a different technique is needed. A simple method would be to maintain two different sets of states: one for the states which minimize the cost and one for the states which maximize the diversity func- tion. This would cause combination function C to simply return the diversity and ignore the cost-evaluation. The heuristic is that if a state from the diversity-set becomes qualified it would “jump” to the cost-evaluation set. A disadvantage of the “simple” approach is that the states in the diversity-set are not selected for cost-evalua- tion and so may stray towards extremely diverse but high- cost solutions. Thus a more sophisticated algorithm was developed which maintains multiple “bands” of diversity sets, each containing states within a given range of diver- sities. Within each band, the lowest-cost states are retained. Since states only compete with other states within the same band, high-diversity but higher cost states won’t replace medium-diversity but lower cost states. Note that diversity is always computed by compar- ing to all states, not just the ones sharing the same band. The idea is that some of the high-diversity states will turn into medium-diversity states which in turn may eventu- ally jump into the cost-evaluation set. The parameters to the band searcher are the number and size of the bands and the minimum diversity. For exam- ple, if the minimum diversity were 2, the number of bands were 3 and the band-size were 2 then the first band would contain states with diversity 2 and 3, the second would contain states with diversity 4 and 5, and so on. The next section measures the effect of these diversity techniques on the global searcher. Empirical Results The standard CRESUS beam-searcher and 3 variations of the diversity searcher were run on 4 separate weeks of 1993 company treasury data. The total cost for each weekly solution is computed by summing the costs of credit-line dispositions, funds-movement and payment and collection commissions, and overdrawn-account fees. For the standard beam-searcher, the beam-width K of 10 was used; for the diversity searchers, the cost-eval beam- width li was 5 and the diversity-eval K’ was 5. In this way we can determine if the 5 additional states are most effec- tively used as cost-eval states or diversity-eval states. The Y axis in Figure 1 plots the cumulative total cost of solutions found by each search strategy. The simple diver- sity searcher, simple, and two variants of band-searching are shown. In the first variant, band(4,1), there were 4 bands and the band-size was 1; in band(3,2), the number of bands was 3 and the band-size was 2. The minimum diversity in both band searchers was 2. All three diversity algorithms did better than standard beam-searching. Week 1 saw the largest improvement. It contained many local maxima because it contained a holi- day and there were more constraints on funds-move- ments. In the standard search all of the states converged to a situation where idle funds were stuck in unusable accounts. In simple and band(3,2), some funds had still been allocated to accounts which were affected by the holiday; in band(4,1), all money had been correctly allo- cated. Simple also did surprisingly well on week 2 but worse than standard search on week 4. Band(4,I) did the best overall because of consistently good performance (see Table 2). Band(4,I) did better than band(3,2) because the latter suffers from the same problem as simple: within each band of size 2, slightly lower-cost states will be selected over more diverse states. Thus bands should probably always be of size 1. The reason that band(4,l) did slightly worse than simple on week 4 may be that that week didn’t contain many local maxima which fooled simple; or that the local maxima fooled the diversity approaches as well as simple. In this case the benefits of using diversity weren’t used and the space devoted to diversity states was wasted. Stundafd Beam-searcher C--- Simple Diversify Q - - - . - Band Diversiiy(4,l) A..--- Band Diversiiy(3,Z) A _ 1600 ..................................................................................... 1400 ..................................................................................... 1200 G 8 800 u fj 600 3 E 400 2 2 200 ......................................... .............................. ............................................................ Week: 7 2 3 4 Figure 1: Total cost of the standard beam-search and diversity searchers in the CRESUS expert system. Genetic Algorithms 1327 References Table 2: Percentage cost of diversity searchers compared to standard beam searcher Conclusions Diversity searching is a step towards extending knowl- edge-based searchers to obtain the benefits of genetic search while retaining the advantages of the symbolic approach. Although the idea of diversity has been investi- gated in genetic algorithms and simulated annealing, this is the first time that maintaining diversity during a symbolic search has been attempted. This paper addressed the issues involved and presented a framework for diversity search. A domain-independent algorithm was shown and empirical results from a working expert- system show that diversity search can substantially improve knowledge-based searchers. Diversity search will be most useful in complex domains that are not amenable to genetic algorithms or simulated annealing. These include problems which require a fast response and those which exhibit a high degree of epistasis. It may be that symbolic diversity search will occupy a useful middle-ground between knowledge-rich systems that need to do much search and genetic algorithms and simulated annealing which are not feasible in complex, knowledge-rich domains. Diversity search shows promise; it warrants more exploration. It should be evaluated with different parame- ters and combination functions. A simulated-annealing technique of decreasing the diversity as the search progresses according to a schedule may further enhance the search results. It would also be interesting to try applying it to different problems and with different searchers in order to determine how broadly applicable it is. Acknowledgments I would like to thank Jaime Carbonell, Michael Mauldin, Ben MacLaren, Rick Chimera and Alex Franz for helpful comments on earlier drafts of this paper, and the rest of the CRESUS team: Javier Berbiela, Maria Jose Moro Martin, Paloma Bilbao and Lorenzo Tello. Ackley, D.H., Hinton, G.E. and Sejnowski, T.J. 1985. A Learning Algorithm for Boltzmann Machines. Cognitive Science. 9(l): 147-169. Beal, Don F. 1990. A Generalized Quiescence Search Algo- rithm. Artificial Intelligence. 43( 1):85-98, April. Booker, L. 1987. Improving Search in Genetic Algorithms. Genetic Algorithms and Simulated Annealing, In Davis, L., Morgan Kaufmann Publishers, Los Altos, California, pages 61-73. Davis, L. and Steenstrup, M. 1987. Genetic Algorithm and Simulated Annealing. Genetic Algorithms and Simulated Annealing. In Davis, L., Morgan Kaufmann Publishers, Los Altos, California, pages 1- 11. DeJong, K.A. 1975. Analysis of the Behavior of a Class of Genetic Adaptive Systems. Ph.D. thesis, University of Mich- igan, Ann Arbor. DeJong, K.A. 1990 Special Issue on Genetic Algorithms. Machine Learning. 5(4). Holland, J. 1975. Adaptation in Natural and Artificial Sys- tems. University of Michigan Press. Jerrum, M., and Sorkin, G.B. 1993. Simulated Annealing for Graph Bisection. Technical Report, University of Edin- burgh, Dept. of Computer Science. Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P. 1983. Optimi- zation by Simulated Annealing. Science. (220):67 l-680. Mauldin, M.L. 1984. Maintaining Diversity in Genetic Search. Proceedings of the National Conference on Artiji- cial Intelligence, pages 247-250. Newell, Allen. 1978. Harpy, Production Systems and Human Cognition. Pittsburgh, PA: Carnegie Mellon Univer- sity. Shell, P. and Carbonell, J. G. 1988. The Parmenides Refer- ence Manual. CMU Computer Science Department internal Paper Shell, I? and Carbonell, J. 6. 1986. The FRuleKit Reference Manual. CMU Computer Science Department internal Paper Shell, P., et al. 1992. CRESUS: An Integrated Expert System for Cash Management. Scott, A. and Klahr, P. (editor), Inno- vative Applications of Artificial Intelligence 4. 1328 Genetic Algorithms | 1994 | 272 |
1,622 | Genetic Programming and AI Planning Syste Lee Spector School of Communications and Cognitive Science Hampshire College, Amherst, MA 01002 lspector@ hamp.hampshire.edu Abstract Genetic programming (GP) is an automatic programming technique that has recently been applied to a wide range of problems including blocks-world planning. This paper describes a series of illustrative experiments in which GP techniques are applied to traditional blocks-world planning problems. We discuss genetic planning in the context of tra- ditional AI planning systems, and comment on the costs and benefits to be expected from further work. Introduction Genetic programming (GP) is an automatic programming technique developed by Koza that extends the genetic al- gorithm framework of Holland (Holland 1992). Whereas the conventional genetic algorithm uses evolution-inspired techniques to manipulate and produce fixed-length chro- mosome strings that encode solutions to problems, GP ma- nipulates and produces computer programs. Koza shows how programs can be “evolved” to solve a wide range of otherwise unrelated problems (Koza 1992). Several of the problems that Koza describes are of inter- est to AI planning research. These include control programs for artificial ants, box-moving robots, wall-following robots, and block-stacking systems. The block-stacking problems are closest to the classic problems in the litera- ture of AI planning systems, but Koza uses an unusual variant of blocks-world, making it difficult to relate his re- sults to those of mainstream AI planning research (Tate et al. 1990). In this paper we apply GP to the block-stacking prob- lems that have been central in the literature of AI planning. In particular, we describe experiments in using GP tech- niques to 1) find a plan to achieve a single goal from a sin- gle initial state, 2) find a “universal plan” for achieving a single goal from a range of initial states, 3) find a domain- dependent planning program, capable of producing action sequences to achieve different sets of goals from a variety *The author acknowledges the support of the Dorothy and Jerome Lemelson National Program in Invention, Innovation, and Creativity. *The description of genetic programming that follows covers only the simplest variant of the technique. See (Koza 1992) for more sophisticated variants. of initial states. We conclude that while GP has much to offer to AI planning research, more work must be done to determine exactly how it can be best applied. Genetic Programming GP works with a large population of candidate programs and uses the Darwinian principle of “survival of the fittest” to produce successively better programs for a given prob- lem. To use GP one must choose the primitive elements (functions and terminals) out of which the programs will be constructed.* Every terminal in the terminal set and ev- ery value that may be returned by any function in the func- tion set must be acceptable as an input for every argument position of every function in the function set; this is called the closure property. The programmer wishing to employ GP must also pro- duce a problem-specific fitness function. This function must take a program as input, producing a number that in- dicates the “fitness” of the program as output. This de- scribes “how good” the program is at solving the problem under consideration, and determines the likelihood that the program and its offspring will survive to subsequent gener- ations. In this paper all fitness values are “standardized fitness” values, for which lower fitness values indicate bet- ter programs (Koza 1992, p. 96). Fitness is normally assessed by running the program on some number offitness cases, each of which establishes in- puts to the program and describes the corresponding output that the individual program should produce. One is often interested in producing a program that works over a very large, perhaps infinite, set of inputs; but the fitness of indi- vidual programs is assessed only with reference to a usual- ly small, finite set of fitness cases. A program is said to be robust if it produces proper results for inputs that were not used in assessing fitness during the GP process. The GP process starts by creating a random initial popula- tion of programs. The closure property ensures that each of these programs, unfit though it may be, will execute without signalling errors. Each of the programs is assessed for fitness, and fitness-sensitive genetic operations are then used to produce the subsequent generation. These may include re- production, crossover, mutation, permutation, and others (Koza 1992); we use only reproduction and crossover here. The reproduction operator selects a highly fit individual and simply copies it into the next generation. Selection for re- Genetic Algorithms 1329 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. production is random but biased toward highly fit programs. The crossover operation introduces variation by selecting two highly fit parents and by producing from them two ofs- spring. The crossover operation selects random fragments of each of the two parents and swaps them; the resulting pro- grams are copied to the next generation. If GP is “working” on a given run then the average fitness of the population will tend to improve over subsequent gen- erations, as will the fitness of the best-of-generation individ- ual from each generation. After a preestablished number of generations, or after the fitness improves to some preestab- lished level, the best-of-run individual is designated as the result and is produced as the output from the GP system. GP appears to be a powerful technique with wide appli- cability. It is CPU intensive, but there are ample opportuni- ties for parallelism (e.g., in the assessment of fitness across a large population). We believe that it has great promise, but as Dewdney wrote of genetic algorithms more general- ly, “The jury is still out on a method that (a) claims to solve difficult problems and (b) is suspiciously painless.” (Dewdney 1993, p. xiii) In order to understand the strengths and weaknesses of the technique we must apply it to areas in which prior research has mapped the compu- tational territory. This strategy is being pursued by many, and is evident in (Koza 1992); in the remainder of this pa- per we endeavor to lay the foundations for such work in the mainstream of AI planning. Genetic Planning One can apply the techniques of GP to AI planning prob- lems in a variety of ways.3 GP systems produce programs; AI planning systems produce plans. Insofar as a plan is a program for an execution module, one can use a GP sys- tem as a planning system-one can use a GP system to evolve a plan which, when executed in the context of a given initial state, achieves a given set of goals. A traditional AI planning system takes as input an initial state, a goal description, and a set of operator schemata, and produces as output a sequence of operator schemata, along with any necessary variable bindings. One can use a GP system in a similar way; given an initial state, a goal description, and a description of the actions that the execu- tion module can perform, one can produce a program for the execution module that will achieve the goals from the initial state. The first of the experiments described below uses GP in this way. The parallel between the traditional planning system and the genetic planning system need not be exact; whereas most planning systems require that the available actions be described declaratively (using, e.g., STRIPS operators 3Note, however, that although Holland’s seminal work on ge- netic algorithms (Holland 1992) contains much of interest to plan- ning researchers, its use of the phrase “genetic plan” has no rela- tion to “planning” as used in the literature of AI planning systems. 4Some “traditional” planners use operators that include proce- dural components as well, e.g. NOAH (Sacerdoti 1975). (Pikes & Nilsson 197 l)), purely procedural “operators” will suffice for the genetic planning system.4 This is be- cause the genetic planning system can assess the utility of action sequences by running them in simulation, rather than by analyzing declarative structures that describe oper- ator effects. The cost of simulation can be high, both in runtime and in simulation development time, but the simu- lation approach obviates the need for declarative action representation. Since declarative action representation is an active research area with many outstanding problems (Ginsberg 1990), the availability of a planning methodolo- gy that does not require such representations is interesting for this reason alone. In addition, the way that simulation is used in GP is clearly parallelizable; the fitness of each program can be assessed in an independent simulation. A more ambitious approach to genetic planning is to evolve control programs that can achieve some given set of goals from a variety of initial conditions. If one augments the function set to allow for decision-making and iteration in the evolved plans, one can actually evolve such “univer- sal plans” (in the sense of (Schoppers 1987)). Koza’s work on blocks-world planning takes this approach, as does the second of the experiments described below. A third approach to genetic planning is to evolve com- plete domain-dependent planners. The function set must in this case include functions that access the system’s current goals; given such a function set one can evolve programs that can achieve a range of goal conditions from a range of initial states. The third of the experiments described below uses GP in this way. A fourth approach to genetic planning is to evolve com- plete domain-independent planners. The function set would in this case presumably include functions that have proven to be useful in existing domain independent plan- ners; e.g., functions for constructing partial orders of plan steps. We have not yet conducted any experiments using this ambitious approach. Koza’s Genetic Blocks-World Planner Koza has described the use of GP for a set of planning problems in a variant of blocks-world (Koza 1992, sec. 18.1). In this domain the goal is always to produce a single stack of blocks. The domain never contains more than one stack; every block is always either part of the stack or on the table (and clear). He considers the example of produc- ing the 9-block stack that spells “UNIVERSAL” from a vari- ety of initial configurations. Note that this is an instance of the second approach to genetic planning outlined above; we seek a single program that transforms a range of initial states to satisfy a single, prespecified goal condition. Koza’s blocks-world is unusual both because it is limit- ed to a single stack of blocks and because it uses an unusu- ally powerful set of functions and terminals (defined by (Nilsson 1989)). The terminal set consists of the following “sensors”: CS, which dynamically specifies the top block of the stack; TB (“Top Correct Block”), which specifies the highest block on the stack such that it and all blocks below it are in the correct order; and NN (“Next Needed”), which 1330 Genetic Algorithms specifies the block that should be on top of TB in the final stack. The functions are: MS (“Move to the Stack”), which takes a block as its argument and, if it is on the table, moves it to the stack and returns T (otherwise it returns NIL); MT (“Move to the Table”), which takes a block as its argument and, if it is anywhere in the stack, moves the top block of the stack to the table and returns T (otherwise it returns NIL); DU (“Do Until”), which is actually a macro that implements a control structure-it takes two bodies of code, both of which are evaluated repeatedly until the sec- ond returns non-NIL; NOT, which is the normal LISP boolean negation function; and EQ, which is the normal LISP equality predicate. Note that the function and terminal sets are carefully tai- lored to the specialized nature of the domain (O’Reilly & Oppacher 1992). CS would not generalize in any obvious way to a domain with multiple stacks. TB, though de- scribed as a “sensor,” depends on the goal and must per- form computation to match several elements in the world to components of the goal. Goal-sensitivity in the function and terminal sets is not necessarily to be avoided; indeed, in some cases it is necessary, and we use goal-sensitive functions below. But it is important to note that TB is goal- sensitive in a highly specialized, domain-dependent way. TB also depends on the fact that the domain can contain only one stack. NN is domain-specific in much the way that TB is. MS and MT make sense only in a single-stack world. Koza ran his GP system on the “UNIVERSAL” problem for 51 generations with a population size of 500 individuals. He assessed fitness with respect to 166 of the millions of possi- ble initial configurations. Fitness for an individual program was calculated as 166 minus the number of fitness cases for which the stack spelled “UNIVERSAL” after the program was run. A 100% correct program emerged in generation 10. It was: (EQ (DU (MT CS) (NOT CS)) (DU (MS NN) (NOT NN))) Although this program is correct, it is not particularly efficient. It used 2,3 19 block movements to handle the 166 fitness cases, whereas it is possible to use only 1,641. By factoring the number of block movements into the fitness function Koza was able to produce a correct and maximal- ly efficient program. That program, however, was longer than it needed to be. By factoring the number of symbols in the program into the fitness function (a “parsimony” measure) he was able to produce a correct, maximally efficient, and maximally parsimonious program. Blocks-World Experiment #I We have performed several experiments to assess the appli- cability of GP techniques to more traditional AI planning domains. The three that we describe here are all blocks- world experiments. Koza’s GP code was used in all cases.5 Our first experiment was to use GP to produce a single correct plan that achieves a particular (conjunctive) goal condition from a particular initial state. We chose the prob- lem known as the Sussman Anomaly as a representative 5Koza’s code can be found in the appendix and can also be obtained by anonymous Fll? to (Koza 1992), problem from the blocks-world domain. The goal in this problem is to start with a world in which C is on A, and in which A and B are both on the table, and to produce a state in which A is on B, B is on C, and C is on the table. We will refer to the resulting state as an {ABC} tower. We built a simple blocks-world simulation environment and wrote NEWTOWER and PUTON functions that are proce- dural versions of the following STRIPS-style operators. In these operators distinctly named variables must bind to dis- tinct blocks: Operator: (NEWTOWER ?X) ;; move X to the table if clear Preconditions: (ON ?X ?Y) (CLEAR ?X) Add List: ((ON ?X TABLE) (CLEAR ?Y)) Delete List: ((ON ?X ?Y)) Operator: (PUTON ?X ?Y) ;; put X on Y if both are clear Preconditions: (ON ?X ?Z) (CLEAR ?X) (CLEAR ?Y) Add List: ((ON ?X ?Y) (CLEAR ?Z)) Delete List: ((ON ?X ?Z) (CLEAR ?Y)) Our functions check that the required preconditions hold and change the world according to the add and delete lists if they do. Each function returns its first argument (the top of the resulting stack) upon success, or NIL if passed NIL or if the preconditions do not hold. We used a function set consisting of NEWTOWER, PUTON, and two sequence- building functions, PROGNP and PROGNB, which are ver- sions of LISP’s PROGN that take 2 and 3 arguments respec- tively. The resulting programs may have a hierarchical structure since the functions in the function set can be nest- ed in many ways. The terminals used for this experiment were the names of the blocks: A, B and C. We calculated fitness with respect to a single fitness case: INITIAL: ((ON C A) (ON A TABLE) (ON B TABLE) (CLEAR C) (CLEAR B)) GOALS: ((ON A B) (ON B C) (ON C TABLE)) Our fitness function had three components: a correctness component, an efficiency component, and a parsimony component. The correctness component was calculated as 70 times the number of achieved goals divided by the total number of goals (in this case 3). This produces a number between 0 and 70, with higher numbers indicating better programs. The efficiency component was calculated from the number of NEWTOWER and PUTON actions actually exe- cuted in running the program. All executions were counted, even if the action was not successful. The number of ac- tions was scaled to produce a number between 0 and 15, with higher numbers indicating more efficient programs. The parsimony component was calculated from the number of symbols in the program, scaled to produce a number be- tween 0 and 15, with higher numbers indicating more parsi- monious programs. The values of the correctness, efficien- cy, and parsimony clauses were summed and subtracted from 100, producing an overall fitness value between 0 and 100, with lower numbers indicating better programs. Following a suggestion of Koza, we staged the introduc- tion of the efficiency and parsimony components into the Genetic Algorithms 1331 80 ,A 60 8 Best of Gen -e Average 0 10 20 30 Generation 40 50 Figure 1. Best-of-generation and average fitnesses for exp. #l. fitness function. In generations O-14 only the correctness component of the fitness function was used. The efficiency component was introduced at generation 15 and was used thereafter. The parsimony component was introduced at generation 25 and was used thereafter. We ran the GP system for 50 generations with a popula- tion size of 200. The overall performance of the GP system on this problem is summarized in Figure 1. In the initial generation of random programs the average fitness was 92.88. The best individual program of the population had a fitness measure of 53.33. It was: (PUTON (PROGNS C B) (NEWTOWER C)). This gets C on the table and B on C, achieving 2 of the 3 goals. The average fitness of the popu- lation improved over the subsequent generations, but there was no improvement in the best-of-generation program un- til generation 5, when the following program was produced with a fitness measure of 30.0: (PROGN3 (PROGNP (NEWTOWER C) (NEWTOWER (NEWTOWER A))) (NEWTOWER (PROGN2 B B)) (PROGN3 (PUTON B C) (PUTON B C) (PUTON A B))) This program solves the Sussman Anomaly, but it is nei- ther efficient nor elegant. The average fitness of the popula- tion continued to increase through the subsequent genera- tions, although no improvement of best-of-generation individual was possible until generation 15, when the efficiency component of the fitness function became effec- tive and allowed for differentiation among the correct plans. At generation 25 the parsimony clause became effective as well, and by generation 32 a maximally efficient, parsimo- nious, and correct plan had evolved with a fitness measure of 3.15: (PROGN3 (NEWTOWER C) (PUTON B C) (PUTON A B)). locks-World Experiment #2 The best-of-run plan from experiment #l solves the Suss- man Anomaly, but it is not useful in many other cases. In our second experiment we wanted to evolve a “universal plan” for achieving a single goal condition from a range of initial states. To achieve greater generality we changed the terminal and function sets: FUNCTION SET: (NEWTOWER PUTON PROGNS PROGN3 TOP- OVER DO-ON-GOALS) TERMINAL SET: (TOP BOTTOM) The TOPOVER function takes one argument, a block, and returns the top of the stack of which that block is a part. It returns its argument if it is something that is currently clear, or NIL if it is NIL. DO-ON-GOALS is actually a macro that im- plements a limited iteration control structure. It takes one argument, a body of code, that it evaluates once for each of the system’s unachieved “ON” goals. During each iteration the variables TOP and BOTTOM are set to the appropriate components of the current goal. Note that we have removed A, B and C from the terminal set; programs can refer to blocks only via TOP and BOTTOM. TOP and BOTTOM are both NIL outside of any calls to DO-ON-GOALS, and calls to DO-ON-GOALS can be nested. The DO-ON-GOALS macro was developed for experiment #3, below, in which the need for access to the system’s goals is more obvious. We used 20 fitness cases and averaged their results; they were constructed from the following lists by pairing each initial state with each goal list: INITIAL: 1. ((ON A TABLE)(ON B TABLE)(ON C TABLE) (CLEAR A)(CLEAR B)(CLEAR C)) 2. ((ON A B)(ON B C)(ON C TABLE)(CLEAR A)) 3. ((ON B C)(ON C A)(ON A TABLE)(CLEAR B)) 4. ((ON C A)(ON A B)(ON B TABLE)(CLEAR C)) 5. ((ON C A)(ON A TABLE)(ON B TABLE)(CLEAR C)(CLEAR B)) 6. ((ON A C)(ON C TABLE)(ON B TABLE)(CLEAR A)(CLEAR B)) 7. ((ON B C)(ON C TABLE)(ON A TABLE)(CLEAR B)(CLEAR A)) 8. ((ON C B)(ON B TABLE)(ON A TABLE)(CLEAR C)(CLEAR A)) 9. ((ON A B)(ON B TABLE)(ON C TABLE)(CLEAR A)(CLEAR C)) 10. ((ON B A)(ON A TABLE)(ON C TABLE)(CLEAR B)(CLEAR C)) GOALS: 1. ((ON A B)(ON B C)(ON C TABLE)) 2. ((ON B C)(ON A B)(ON C TABLE)) e- Best of Gen c Average 0 10 20 30 Generation 40 50 Figure 2. Best-of-generation and average fitnesses for exp. #2. 1332 Genetic Algorithms Note that the 10 fitness cases using goal list 2 are dupli- cates of the those using goal list 1 but with the order of the goal clauses changed; since DO-ON-GOALS loops through the goals in the order that they are presented, this helps to ensure that the resulting program is not overly dependent on goal ordering. All other GP parameters were set to the values used in experiment #l. The overall performance of the GP system in this experiment is summarized in Figure 2. In the initial generation of random programs the average fitness was 7 1.20. The best individual program of the popu- lation had a fitness measure of 53.33 and correctly handled 6 of the 20 fitness cases. It was: (NEWTOWER (DO-ON-GOALS (PROGNS (PUTON TOP BOTTOM) (PUTON BOTTOM BOTTOM) (DO-ON-GOALS TOP)))) The best-of-run individual program for this run was found on generation 48. It had a fitness measure of 5.91 and correctly handled all 20 fitness cases. It was: (PROGN2 (DO-ON-GOALS (DO-ON-GOALS (PROGN3 (NEWTOWER (DO-ON-GOALS (TOP-OVER TOP))) (PROGN2 (TOP-OVER TOP) TOP) (PUTON TOP BOTTOM)))) (DO-ON-GOALS (PUTON TOP BOTTOM))) Note that the program is robust over initial states that were not in the set of fitness cases. The program correctly builds an {ABC} tower from all three of the possible configurations that were not used as fitness cases: the tow- ers {CBA}, { BAC}, and {ACB}. Because many problems are isomorphic, the use of function and terminal sets that refer to blocks only by their positions in goals, and not by their names, is helpful in achieving this robustness. The robustness of the solution program does not extend to changes in goal sets. For example, the program will not achieve the unary goal list ((ON B A)) from an initial state consisting of a { BCA} tower. Blocks-World Experiment #3 Our third experiment was an attempt to evolve a blocks- world planner capable of achieving a range of goal condi- tions from a range of initial conditions. We used the same terminal and function sets as in experiment #2. We in- creased the population size to 500 and the number of gen- erations to 201, with efficiency introduced into the fitness function at generation 33 and parsimony introduced at gen- eration 66. We used 40 fitness cases, constructed by pair- ing each of the initial states from experiment #2 with each of the following goal lists: 1. ((ON A B) (ON B C) (ON C TABLE)) 2. ((ON B C) (ON A B) (ON C TABLE)) 3. ((ON C B) (ON B TABLE)) 4. ((ON B A)) All other GP parameters were set to the values used in ex- periment #l. The performance of the GP system in this ex- periment is summarized in Figure 3. In the initial generation of random programs the average fitness was 77.02. The best individual program of the population had a fitness of 59.17 and correctly handled 14 of the 40 fitness cases. It was: (TOP-OVER (PROGN3 (PUTON (NEWTOWER (DO-ON-GOALS BOTTOM)) (DO-ON-GOALS (PUTON TOP BOTTOM))) (DO-ON-GOALS (TOP-OVER (DO-ON-GOALS BOTTOM))) (DO-ON-GOALS (NEWTOWER (PROGNP BOTTOM BOTTOM))))) The first 100% correct solution emerged at generation 25. It had a fitness of 30.0, contained 49 symbols, and was messy; we do not show it here. The efficiency and parsimo- ny components of the fitness function, introduced at genera- tions 33 and 66 respectively, helped to improve the pro- grams considerably. The best-of-run individual program was found on generation 168 and had a fitness of 6.54. It was: (PROGN3 (TOP-OVER (DO-ON-GOALS (NEWTOWER (DO-ON-GOALS (TOP-OVER TOP))))) (DO-ON-GOALS (NEWTOWER (TOP-OVER BOTTOM))) (DO-ON-GOALS (DO-ON-GOALS (PROGN2 (NEWTOWER (TOP-OVER TOP)) (PUTON TOP BOTTOM))))) The planner evolved in experiment #3 is considerably more robust than that evolved in experiment #2. In fact, al- though it was evolved with only 40 fitness cases, it correctly solves all 13x13=169 possible 3-block problems. It even solves some 4-block problems: for example, it will correctly produce both an { ABCD} tower and a { DCBA} tower from an initial state containing an {ABC} tower and the additional block D on the table. We have not yet fully analyzed the pro- gram’s robustness for 4-block and larger problems. 80 60 8 Best of Gen + Average 0 100 200 Generation Figure 3. Best-of-generation and average fitnesses for exp. #3. Genetic Algorithms 1333 Discussion Conclusions In experiment #l we wanted to see how well a GP engine could function in place of a traditional planner, which is generally invoked to produce a single plan that achieves a particular set of goals from a particular initial state. While we were able to evolve a correct, efficient, and parsimo- nious plan, one is lead to ask why a genetic technique should used in this case; traditional AI planning algorithms can solve such problems more reliably and more efficient- ly. Further, we should note that single blocks-world prob- lems, at least with our fitness function (based on number of goals achieved), are not well suited to solution by genetic programming. This is because the coarseness of the fitness function provides little guidance to the evolutionary pro- cess. This can be seen in the first 10 generations of Figure 1, in which the coarseness of the fitness metric leads to large jumps in the best-of-generation fitness. We succeeded because the combinatorics of a 3-block world are manage- able even with minimal guidance, especially with a pro- gram population size of 200. A more complex domain would demand a more informative fitness function. But GP may nonetheless be a good choice for solving some single- initial-state/single-goal planning problems. In particular, it can be appropriate when we have trouble representing the system’s actions declaratively, or when the dynamics of the domain are best represented via simulation. GP seems better suited, overall, to the construction of uni- versal planners of the sort produced in our experiment #2, or complete domain-dependent planners of the sort produced in our experiment #3. There will always be problems in achieving robustness, however, and the genetic program- ming of universal planners is necessarily an iterative, experi- mental process. The success of a particular run of GP is highly sensitive to seemingly minor changes of parameters. Population size, crossover parameters, details of the terminal and function sets, choice of fitness cases, and variations in fitness metrics may all have large, difficult to predict effects. For example, we tried variations of blocks-world experiment #3 with identical parameters except for minor variations in the function and terminal sets (e.g., substituting a DO-UNTIL for DO-ON-BLOCKS, and providing other functions to access the goals). Many of these variations failed to produce fit pro- grams. O’Reilly and Oppacher discuss the sensitivity of GP to this kind of variation and suggest modifications to the technique that they believe will lessen this sensitivity (O’Reilly & Oppacher 1992). But GP is an inherently exper- imental technique, and the resulting orientation may actually be quite welcome in some segments of the AI planning community; several planning researchers have recently called for just the sort of experimental framework that GP allows, and indeed requires (Hanks et al. 1993). Genetic methods may also provide so-called “anytime” behavior (Dean & Body 1988), another feature of interest to the planning community: As can be seen in the fitness graphs in this paper, genetic programming starts by pro- ducing poor programs, and gradually improves the quality of its programs over time. The process can be stopped at any point to provide the current best-of-run program. We conclude that GP has much to offer as an AI plan- ning technology: freedom from declarative representation constraints, a methodology for building fast, domain- specific systems, a welcome experimental orientation, and anytime behavior during evolution. 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1,623 | Hierarchical Chunking in Classifier Systems Gerhard We% Institut fiir Informatik, Technische Universitat Miinchen D-80290 Miinchen, Germany weissg@informatik.tu-muenchen.de Abstract Two standard schemes for learning in classifier systems have been proposed in the literature: the bucket brigade algorithm (BBA) and the profit sharing plan (PSP). The BBA is a lo- cal learning scheme which requires less mem- ory and lower peak computation than the PSP, whereas the PSP is a global learning scheme which typically achieves a clearly better perfor- mance than the BBA. This “requirement ver- sus achievement” difference, known as the local- ity/globality dilemma, is addressed in this pa- per. A new algorithm called hierarchical chunk- ing algorithm (HCA) is presented which aims at synthesizing the local and the global learn- ing schemes. This algorithm offers a solution to the locality/globality dilemma for the important class of reactive classifier systems. The contents is as follows. Section 1 describes the locality/globality dilemma and motivates the ne- cessity of its solution. Section 2 briefly introduces basic aspects of (reactive) classifier systems that are relevant to this paper. Section 3 presents the HCA. Section 4 gives an experimental compari- son of the HCA, the BBA and the PSP. Section 5 concludes the paper with a discussion and an outlook on future work. Motivation The foundations for classifier systems (CSs for short) were laid by Holland i 1975) and Holland and Reitman (1978). CSs are para lel, message-passing, rule-based systems that are capable of environmental interaction and of reinforcement learning through credit assign- ment and rule modification. Up to now two differ- ent learning schemes for credit assignment in CSs have been proposed: the bucket brigade algorithm (BBA for short, e.g. Booker, 1982; Holland, 1985, 1986; Riolo, 1988) and the profit sharing plan (PSP for short, e.g. Grefenstette, 1988; Holland & Reitman, 1978). These two schemes significantly differ from each other in that the BBA is a local learning scheme which incremen- tally assigns credit whenever the CS interacts with its environment, whereas the PSP is a global learn- ing scheme which episodically assigns credit only when the CS receives a reinforcement signal from its envi- ronment. A consequence of this difference, known as the locality/globality dilemma, is that the BBA requires less memory and less peak computation than the PSP, but the PSP typically achieves a better performance level than the BBA. Roughly, this is because the PSP needs to maintain detailed information about the past activities carried out by the CS, whereas the BBA has difficulties in generating long activity sequences that are both useful and stable. There is a lot of work centered around the local- ity/globality dilemma in the context of the BBA and the PSP; for instance, see the performance comparisons of the BBA and the PSP described in (Grefenstette, 1988; Weif3, 1992) and the investigations and consid- erations on the formation and maintenance of activity sequences presented e.g. in (Holland, 1985; Riolo, 1987, 1989; Robertson & Riolo, 1988; Wilson, 1987 . How- h ever, despite this work it is still an open and c alleng- ing research issue to develop a local algorithm like the BBA that possesses the learning abilities of a global algorithm like the PSP. This issue has been addressed by the work reported in this paper. A new learning al- gorithm called hierarchical chunking algorithm is pre- sented which offers a solution to the locality/globality dilemma for the important class of reactive CSs, that is, CSs whose activity is, at each time, exclusively trig- gered by the information they have about the actual environmental state. An Introduction to Classifier Systems This section gives a brief introduction to basic aspects of CSs. For a more comprehensive introduction the reader is referred to (Booker, Goldberg, & Holland, 1989; Goldberg, 1989; Wilson & Goldberg, 1989). The prototypical organization of a CS can be de- scribed as follows. Structurally, a CS is composed of four major components: e An input interface which consists of at least one de- tector providing information about the environment in the form of messages. o An output interface which consists of at least one effector enabling the system to interact with the en- vironment . o A classifier list which consists of condition/action rules called classifiers. The condition part specifies Genetic Algorithms 1335 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. 0 the messages that satisfy the classifier, and the ac- tion part specifies the messages to be sent when the classifier is activated. Associated with each classifier is a quantity called its strength. A message list which contains the messages sent by the detectors and the classifiers. Functionally, the overall activity of a CS results from -_ --- the repeated execution of the following major cycle: 1. 2. 3. 4. 5. Activation of the input interface: The actual detec- tor messages are added to the message list. Activation of the classifier list: The system decides which classifiers are allowed to produce new mes- sages. This is done by running a strength-based competition between all satisfied classifiers. Activation of the output interface: The system in- teracts with its environment in dependence on the contents of the message list. Credit assignment: Strength-update rules are ap- plied to adjust the classifier strengths such that they reflect the classifiers’ relevance to goal attainment. Rule modification: Some classifiers are modified by a genetic algorithm. An important class of restricted CSs is that of re- active CSs. In these systems only a single classifier is selected during each major cycle, and this selection is guided only by the actual detector messa es (and not by internal messages). Reactive CSs have % een ex- tensively used for theoretical and experimental studies (e.g., see Wilson, 1985; Grefenstette, 1988), and they are also taken as a basis for the work described in this paper. As mentioned in section 1, the BBA and the PSP have been proposed as credit assignment schemes. In its elementary form, the BBA locally updates the clas- sifier strengths as follows. Whenever a competition runs, each satisfied classifier Cj makes a bid S;dj, Bidj = b * Strj * Specj (1) where b is a small constant called risk factor, Strj is Cj’s strength (initialized with a constant Strinit for all classifiers) and Specj is Cj’s specificity (a quantity expressing the classifier’s relevance to particular envi- ronmental situations). The probability that a bidding classifier Ci wins the competition is given by Bidj c Cl Et3 Bidl (2) where B is the set of all bidding classifiers. A winning classifier reduces its strength by the amount of its bid, and hands this amount back to its predecessors, that is, to those classifiers whose preceding activities en- abled it to become active. (The winning classifiers pay for the privilege of being active, and the predecessors are rewarded for appropriately setting up the environ- ment.) Formally, if Cj is a winning classifier and Pj is the set of its predecessors, then the strengths are modified according to the following rules: Strj = Strj - Bidj and (3) Stri = stri + ,pj, siclj y(J E pj . Additionally, if an external reward is received from the environment, then it is equally distributed among the classifiers that sent the effector-activating messages. The idea underlying the BBA is to internally reward classifiers that are useful in achieving specific goals but that are not active when the external reward is ob- tained. The PSP in its elementary form updates the classi- fier strengths as follows. Bidding and selection of the winning classifiers is done according to (1 and 2 re- spectively. In contrast to the BBA, the ii ik SP g o ally rewards sequences of active classifiers. At the end of each episode (i.e., whenever an external reward Ext is received) the strength Str * of each classifier Cj that was active at least one time d ified according to rule uring this episode is mod- Strj z-2 Strj - Bidj + b * Ext (5) where b is the risk factor used in bid calculation. There are many variants of the BBA - e.g., see (Dorigo, 1991; Huang, 1989; Riolo, 1990; Wei& 1991; Wilson, 1985, 1987) - as well as of the PSP - e.g., see (Grefenstette, 1988; Holland & Reitman, 1978; Wei& 1992). However, none of these variants solves the lo- cality/globality dilemma. The Hierarchical Chunking Algorithm Chunking is an experience-based learning mechanism which was originally proposed within the frame of a psychological model of memory organization (Miller, 1956). According to this model, chunking refers to the process of correlating pieces of knowledge or sensory input in such a way that they can be treated and used as a single memory unit or “chunk” on its own. If it is explicitly assumed that already existing chunks can be used for building new ones, then this process is referred to as hierarchical chunking. Hierarchical chunking has received much attention in psychology as well as in ar- tificial intelligence; for instance, see (Chase & Simon, 1973; Chi, 1978; Newell & Rosenbloom, 1981; Rosen- bloom., 1983; Rosenbloom & Newell, 1986). In the followmg, a new algorithm called hierarchical chunk- ing algorithm (HCA for short) is described which was designed to solve the locality/globality dilemma for re- active CSs; this algorithm synthesizes the local (BBA- type) and the global (PSP-type) learning paradigms by applying the mechanism of hierarchical chunking to successful sequences of active classifiers. Under the HCA each classifier Cj is assumed to be of the generalized form CondjlActj 7 where Condj = (cjl, . . . 7 cj,j) (6) specifies the tuples (ml, . . . , mrj) of messages ??Zk that satisfy Cj and Actj = (ajl, . . . , ajsj) (7) specifies the sequence (ml, . . . , m, j) of messages mk to be sent when Cj wins the competition (rj, sj E N for all j). Each message sent within a sequence of mes- sages is immediately processed by the effecters; with 1336 Genetic Algorithms that, a CS is able to carry out several environmental interactions (instead of just a single interaction) within one major cycle .l In the following, the length.of Act. of a classifier Cj is called the level of Cj , and is denote A by Lj ; furthermore, if Lj = 1, then C’s is said to be an elementary classifier, and if Lj > 1, then Cj is said to be an extended classifier or macro-classifier or a chunk. As an illustration of this generalized view of classifiers, consider a CS which has to navigate from the start state S to the goal state G in the maze shown in figure 1. Assuming that the CS is able to interact with its environment by moving, in each location, to one of the neighbouring locations, an elementary classifier might represent the behavioral rule “If the current location is in the upper-left area, then move one step to the right”, and an extended classifier might represent the rule “If the current location is in the middle area, then first move one step to the left and then one step down”. The HCA arranges a hierarchical competition be- tween the classifiers for the right to produce new mes- sages. Among all satisfied classifiers, only the highest- level classifiers are allowed to make bids and to com- pete against each other. More exactly, if S is the set of all satisfied classifiers (in the actual cycle , then only the classifiers being contained in the set d , B = {Cj : Cj E S and Lj 2 Ll V Cl E S) , (8) are allowed to participate in the competition. Each classifier Cj E B calculates a bid according to (l), and the probability that Ci wins the competition is given bY (2). The HCA modifies the classifier strengths similar to the implicit BBA proposed by Wilson (1985). Com- pared to the general BBA described in section 2, the HCA takes a simplified point of view of a classifier’s predecessor which bases on the assumption that the temporal order of active classifiers is imposed by the environment. If the classifiers Ci and C. won the com- petition in the previous and the actua i cycle, respec- tively, then Ci is considered to be the only predecessor of Ci (i.e., Pi = (Ci)), and their strengths are ad- justeh accordmg td(3) -and (4). In this wiy a linkage is established between time-adjacent classifiers. At the beginning (i.e., before learning takes place), the classifier list is assumed to contain only elementary classifiers. The extended classifiers are dynamically formed and dissolved under the HCA in the course of environmental interaction. The formation and dissolu- tion of extended classifiers correspond to the formation and dissolution of chunks, respectively, and make up the core of the HCA. The criteria used for trigger- ing formation and dissolution are conceptually similar to (and, in fact, have been inspired by) the group- development criteria proposed by Weif (1993a, 1993b) in the context of BBA-based multi-agent learning. For- mally, the formation and dissolution criteria are as fol- lows. Let Ci be the preceding winning classifier, Cj the actual winning classifier, 13 the set of all actual bidding classifiers, and p = & CCIEB Strl the aver- age stren th of all classifiers contained in B. A new (extended$ classifier ConclJActi o Actj with ActioActj =(~il,...,ai,i,ajl,...,aj,j) (9) is formed out of Ci and Cj , if and only if where Q is a constant called formation factor. The strength of the new classifier is initialized with Strj. Conversely, an (extended) classifier Ck E B is dissolved and removed from the classifier list, if and only if Strk 5 P - P * -$!$ cTB (St?? - p)2 (11) I where p is a constant called dissolution factor. With equations (10) and (ll), formation as well as disso- lution take place if the strength of a classifier is not within the “standard range” that can be expected given the average strength and the strength deviation of the bidding classifiers. Because both criteria are defined over the strength are formed and dissolved values, extended classifiers in an exnerience-based and goal-directed manner. Furthermori. because strength adjustment, formation and dissolution are strongly&- terrelated and mutually influence each other, the HCA endows a reactive CS with highly dynamic adaptation and learning abilities. (It should be noted that the HCA does not require more information for realizing learning than the BBA; in particular, the HCA forms and dissolves classifiers on the basis of local informa- tion and, in contrast to the PSP, without the need of an episodical trace of all - useless and useful - winning classifiers.) Experimental Analysis As an initial learning domain a navigation task first introduced by Sutton 1990) has been chosen. This type of task captures 6 t e essential features of the lo- cality/globality dilemma, and it is well suited for ex- perimentally comparing the HCA, the BBA and the PSP. Subsequently experiments on the task of learn- ing to navigate through the maze shown in figure 1 are described.2 The maze is a 10 by 7 grid of locations, where the shaded locations are obstacles that cannot be entered. In each location the CS can move to each of the neighbouring locations, except where such a move- ment would take the system into an obstacle or outside the maze. The CS has to learn to move from each pos- sible location of the maze to a fixed location called goal ‘The definition of Condi corresponds to the traditional notion of a classifier’s condition part. Against that, the def- inition and interpretation of Act; establishes a rather un- conventional notion of a classifier’s action part which opens up new possibilities in the coupling between a CS and its environment. 2A number of experiments with other mazes has been performed, varying the grid size, the directions in which the system can move, and the number of possible starting - states, the position of the goal state, and the number an: positions of the obstacles. The results of these experiments are qualitatively similar to those presented below. Genetic Algorithms 1337 Figure 1: Maze. state (G). If and only if the goal state is reached, then a non-zero external reward is provided, a new location called-start state (S) is randomly chosen and the next episode starts. Some imnlementational details. A problem of ev- ery system ihat works with an internal-representation of its environment is the mapping problem., that is, the problem that the system can produce dlscontinu- ous mappings from input to output even if the envi- ronment is continuous (and vice versa). This problem also exists for CSs Wilson & Goldberg, 1989), and in order to avoid or at \ east strongly reduce it, the follow- ing domain-specific decimal coding is used. If the CS is in the location (z, y), then the actual detector message simply is of the form 2, y). Furthermore, each classi- fier is of the form (~6, v /(WI,. . . , 205), with (11, v) being its condition part and i u11, . . . , wj) being its action part (U E (1,. . ., 101, v E (1,. . .,7} and Uli E (0,. . .,7}). Associated with each classifier Cj is an integer Mj called its matching radius. Mj is randomly chosen from the integer interval [0, . . . , JVmaZ], and is used to de- fine Cj ‘S specificity as S$WCj = &. (The smaller a classifier’s matching radius, the higher is its specificity, and reversely.) A classifier Cj having (u, v) as its con- dition part matches each detector message (z, y) with XE [U-Mj,..., u+Mj] and y E [v-Mj,. . .,v+Mj]. A classifier having (tur , . . . , ufs) as its action part codes the activity sequence “First go to direction ~11, then to direction 202, . . ., and finally to direction 20~“) where direction “0” is interpreted as “north”, “1” as “north- east”, “2” as “east”, and so on. (As an illustration, consider the classifier C* - that Mj = i - (9,6)/(5,6,4), and assume 1. This c assifier matches the detector (W9, (W9, (W’), (10,5), for the activity sequence finally one step south” .)3 then one step west, and In order to guarantee the system’s capacity to act, a variant of Wilson’s (1985) create operation has been implemented as follows. Whenever the system enters a location (2, y) whose associated detector message is 3Traditiona.lly, a tertiary coding over the alphabet (0, 1, #} is used, where # acts as a don’t-care symbol. Ob- viously, this is a very problematic, discontinuous coding for the task domain under consideration, because in this case the condition part of a classifier can match detector messages that locations. represent completely different, non-adjacent not matched by any classifier, then a new elementary classifier Cj = (‘u,v)/(w~) is created, where u is ran- domly chosen from the interval [Z - Mj , . . . , x + Mj 1, v is randomly chosen from [y - Mj , . . . , y + Mj], and u)l is randomly chosen from (0,. . . ,7}. With that, the system never stops moving around and searching for the goal state. In the experiments a slightly modified, more “re- active” PSP has been used: instead of adjusting the strengths of all classifiers that won during an episode, only the strengths of the last 4 winning classifiers are adjusted according to (5). This modification is consis- tent with the general notion of a reactive system; in particular, it is realistic to assume that a purely re- active CS is only “aware” of the last few actions, no matter when the last external reward was received. Finally, some details on the implemented genetic al- gorithm. The genetic algorithm is applied with prob- ability 0.04 at the end of each episode. If applied, 5 percent of the classifiers, which are selected with proba- bility proportional to the inverse of their strengths, are replaced by new classifiers. The new classifiers are cre- ated as follows. Until no further classifier is required, a classifier Cj is selected with probability proportional to its strength and mutated, resulting in a new classi- fier Cj. If Cj is of the form (u,v)/(201,. . .,w$) and 1Mj is its matching radius, then Cj is of the form (u’, v’)/(wi, . . . , w:) with u’ = u + a, 21’ = v + b and 4 = (wk + ck)mod8 for all k E (1,. . . , s}, where Q and b are randomly chosen from the integer inter- val [-Mj, . . . , +Mj] and ck is randomly chosen from [-1, 0, +l]. The matching radius of Cj is randomly chosen from [0, . . . , jV’,‘=]. No crossover operator is applied. paper we i In other experiments not described in this ound that the standard crossover operators are rather inefficient for the learning domain under consideration, since they typically produce classifiers which represent illegal moves.) Figure 2 shows the performance profiles of the PSP, the HCA, the BBA and a random-walk algorithm (i.e., an algorithm which randomly and with uniform prob- ability selects, in each location, a legal direction and moves one step in this direction). The parameter set- ting was as follows: b = 0.1, Strinit = Ext = 1000, 0= P = 2, and Mm’” = 3. (The classifier system turned out to robust over a broad range of the pa- rameters, and the learning effects reported here are not restricted to exactly this setting.) Each curve shows, averaged over 100 runs, for each of the episodes 1 to 1000 the number of decisions (cycles) required to reach the goal state. In each run the CS was ini- tialized with a set of 100 randomly generated classi- fiers. At the beginning of learning, each learning algo- rithm started at the random performance level. Each of the three learning curves rapidly falls within the first 30 episodes. HCA and the BB 6 Interestingly, with that the PSP, the led to an early behavioral improve- ment much like the dynamic-programming approaches investigated by Sutton (1990 did for the same type of task.) After about episo d! e 40, the curves of the PSP and the HCA continuously decrease; the curve of the BBA requires a longer period to become smooth, 1338 Genetic Algorithms FIANDOM BBA CHUNKING PSP 400 500 600 700 600 900 1000 episodes Figure 2: Performance Profiles. namely about 230 episodes. Averaged over the last 100 episodes, the mean episode length achieved by the PSP, the HCA, the BBA and the random-walk algo- rithm is 6.2, 15.4., 27.3 and 142.8, respectively. The behavior of the learning algorithms was observe 6 up to episode 5000. After episode 1000 the performance levels of the three learning algorithms did not further improve and remained almost constant .) Obviously, each of the three learning algorithms performed sig- nificantly better than the random-walk algorithm. In particular, after about 85 episodes, the curve of the HCA runs between the curves of the BBA and the PSP: the HCA clearly outperformed the BBA and, at the same time, remained below the performance level of the PSP. This illustrates that hierarchical chunking is an appropriate mechanism for synthesizing local and global learning principles, and that the HCA success- fully combines BBA-type and PSP-type learning. (It is worth to note that even the best performing algorithm, the PSP, left room for improvement, since the minimal episode length, averaged over all legal po- sitions, is 3.0. This shows that CSs, after more than 15 years of existence, still establish an open and chal- lenging area of research on machine learning.) Conclusion The HCA attacks the locality/globality dilemma in the context of reactive CSs by bringing together local and global learning principles known from the BBA and the PSP, respectively. On the one side, the HCA re- tains the local strength adjustment rules of the BBA. On the other side, by introducing the concept of ex- tended classifiers or chunks and by providing mech- anisms for their formation and dissolution, the HCA achieves global adjustment qualities much like the PSP does. As a consequence, the HCA approaches to both the lower computational requirements of the BBA and the higher performance level of the PSP. Wilson and Goldberg (1987) proposed to introduce higher organizational umts in the learning and per- formance processes of a CS in order to cope with the chaining problem (i.e., the problem of generating and maintaining long chains of active classifiers) as well as with the cooperator/competitor dilemma (i.e., the dilemma that classifiers being active in a chain are cooperative w.r.t. strength adjustment but competi- tive w.r.t. the selection mechanism of the genetic algo- rithm). The HCA is much in the spirit of this proposal: the chunks formed and dissolved under the HCA act as such organizational units, since they eliminate (or at least greatly reduce) the need for long chains of el- ementary classifiers. Like the standard PSP, the HCA in its present form is not applicable to general CSs. This is an important objection because general CSs, compared to reactive ones, allow multiple winning classifiers per cycle as well as the processing of internal messages, and, with that, achieve a higher degree of parallelism and cognitive plausibility. We think, however, that the HCA can be fully extended towards general CSs. In particular, in artificial intelligence there is a plenty of work on learn- ing by chunking in rule-based systems and production systems (e.g., see (Laird, Rosenbloom & Newell, 1986) and the references therein), and this work is likely to be very stimulating and useful for constructing such an extension. The work described in this paper shows new per- spectives of several issues of current CS research, in- cluding the locality/globality dilemma, the coopera- tor/competitor dilemma, the chaining problem, the mapping problem, and the system-environment mter- action. However, further investigations are needed in order to fully understand the merits and limitations of hierarchical chunking in CSs. Acknowledgements I want to thank Armin Wirth and Martin Eldracher for many stimulating and fruitful discussions on learning in classifier systems. Genetic Algorithms 1339 References Booker, L.B. 1982. Intelligent behavior as an adaptation to the task environment. Ph.D. diss., Dept. of Computer and Communication Sciences, Univ. of Michigan. Booker, L.B., Goldberg, D.E., and Holland, J.H. 1989. Classifier systems and genetic algorithms. Artificial In- telligence 40: 235-282. Chase, W.G., and Simon, H.A. 1973. Perception in chess. Cognitive Psychology 4: 55-81. Chi, M.T.H. 1978. 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Action selection and learning in multi- agent environments. In J.-A. Meyer, H.L. Roitblat, and S.W. Wilson eds. From Animals to Animats 2, 502-510. Cambridge, MA: MIT Press. We& G. 1993b. Learning to coordinate actions in multi- agent systems. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, 311-316. San Mateo, CA: Morgan Kaufmann. Wilson, S.W. 1985. Knowledge growth in an artificial animal. In Proceedings of the First International Con- ference on Genetic Algorithms and Their Applications, 16-23. Pittsburgh, PA: Erlbaum. Wilson, S.W. 1987. Hierarchical credit allocation in a classifier system. In L. Davis ed. Genetic a2gorithms and simulated annealing, 104-115. Los Altos, CA: Morgan Kaufmann. Wilson, S.W., and Goldberg, D.E. 1989. A critical review of classifier systems. In Proceedings of the Third In- ternational Conference on Genetic Algorithms, 244-255. Fairfax, VA: Morgan Kaufmann. 1340 Genetic Algorithms | 1994 | 274 |
1,624 | Exploiting Algebraic Structure in arallel State Space Search Jonathan Bright* Simon Kasift Lewis Stiller$ Department of Computer Science The Johns Hopkins University Baltimore, MD 21218 Abstract In this paper we present an approach for perform- ing very large state-space search on parallel machines. While the majority of searching methods in Artificial Intelligence rely on heuristics, the parallel algorithm we propose exploits the algebraic structure of prob- lems to reduce both the time and space complexity required to solve these problems on massively parallel machines. Our algorithm runs in O(N1’4/p) time us- ing O(Nl/*) space with P processors where N is the size of the state space and P is the number of proces- sors. The technique we present is applicable to several classes of exhaustive searches. Applications include the knapsack problem and the shortest word problem in permutation groups which is a natural generaliza- tion of several common planning benchmarks such as Rubik’s Cube and the n-puzzle. Introduction The best-known algorithm for finding optimal solu- tions for general planning problems on sequential com- puters is IDA* developed by R. Korf (Korf 1985a; 198513). IDA* has an exponential worst-case complex- ity and its efficiency heavily depends on the ability to synthesize good heuristics. There are many attempts to parallelize state space search (Evett et al. 1990; Powley & Korf 1991; Powley, Ferguson, & Korf 1991; Powley & Korf 1988; Rao & Kumar 1987). In this paper we examine several problems for which the com- putational cost of exploring the entire space of possi- ble states may be prohibitive and derivation of good heuristics is difficult. Exploitation of the algebraic structure of the problems we are considering substan- tially reduces the time and space complexity of the algorithm. For example, we consider problems that have brute-force O(V) solutions (where n is the size of the input to the algorithm) and suggest parallel solu- tions whose time complexity is O(rC”i2/P) (where P is *Supported by the 1993 CESDIS Cray Research Earth and Space Science Fellowship +Supported in part by NSF/DARPA Grant CCR- 8908092 SSupported by U.S. Army Grant DAAL03-92-G-0345 the number of processors) and whose space complexity is O(lc”j4). While the time-space complexity remains exponential, these algorithms are capable of solving problems that were not tractable for conventional ar- chitectures, There are several examples where reduc- ing the time complexity of an algorithm from O(kn) to O(lcni2) has resulted in significant progress. Chess is one such example since it is known that alpha-beta at best accomplishes this type of complexity reduc- tion. Thus our main goal is to double the depth of the search current technology can perform. We feel that this class of problems seem to be particularly well matched with massively parallel machines such as the CM-2 or CM-5 (Thinking Machines Corporation 1992; Hillis 1985) . Our approach is influenced by the elegant sequential algorithm proposed by Schroeppel and Shamir and the later generalization by Fiat, Moses, Shamir, Shimshoni and Taros, which we will review in the next section (Schroeppel & Shamir 1981; Fiat et al. 1989). We view our work as a direct parallel implementation of this algorithm. In this paper we describe parallel algorithms using the shared memory (CREW PRAM) model of paral- lel computation. This model allows multiple proces- sors to read from the same location and therefore hides the cost of communication. While this assumption is unrealistic in practice it allows us to simplify the de- scription of a relatively complex algorithm. Detailed analysis of our algorithms suggests that they can be expressed by efficient composition of computationally efficient primitives such as sorting, merging, parallel prefix and others (Stiller 1992). eview of the Schroeppel and Shamir Algorithm In this section we consider the knapsack (decision) problem to illustrate this approach. This is a canonical NP-complete problem of the “monotonic and decom- posable” genus proposed by Schroeppel and Shamir. The knapsack problem has also been used as the basis for certain cryptographic schemes and other applica- tions (Merkle & Hellman 1978; Diffie & Hellman 1976; Search 1341 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Tarjan & Trojanowski 1977). The input to the algo- rithm is a list of integers S and a number Z. The output is a sublist of S, call it S’, such that the sum of the elements in S’ is equal to x. This problem has ap- plications in scheduling, cryptography, bin packing and other combinatorial optimization problems. For exam- ple, we can use solutions to this problem to minimize the total completion time of tasks of fixed duration executing on two processors. Let n the size of S. We will introduce some helpful notation. Let A and B to be sets of integers. Define A + B to be the set of integers c such that c = a + b where a E A and b E B. Define A - B to be the set of integers c such that c = a - b where a E A and b E B. Observation 1: The knapsack problem can be solved in O(n2”j2) time and O(2”i2) space. Proof: We partition S into disjoint lists Sr and S2 such that the size of Sr is n/2. Let Gr and G2 be the lists of all sums of sublists of elements in Sr and S2 re- spectively. Clearly, our problem has a solution iff the list Gr has a non-empty intersection with {x} - G2. However, note that we can sort both lists and find the intersection by merging. Thus, the time complexity of this algorithm can be seen to be O(n2”i2) using any optimal sorting algorithm and noting the trivial iden- tity 2 log(2”i2) = n. Unfortunately, the space com- plexity is also O(2”i2) which makes it prohibitive on currently available machines for many interesting prob- lems. This approach was first suggested by Horowitz and Sahni (Horowitz & Sahni 1974). However, in the AI literature the algorithm has a strong similarity to bi-directional search studied by Pohl (Pohl 1971). The next observation allows us to reduce the space com- plexity to make the algorithm practical. Observation 2: (Schroeppel and Shamir 1981) The knapsack problem can be solved in O(n2”i2) time and O(2”i4) space. Proof: We partition S into four lists, Si, 1 5 i 5 4. Each set is of size n/4. Let Gi, 1 5 i 5 4 be the lists of all possible sublist sums in Si respectively. Clearly, the partition problem has a solution iff Gi+G:! has a non-empty intersection with the list ({x} - G4) - Gs. This observation essentially reduces our problem to computing intersections of A + B with C + D (where A, B, C and D are lists of integers each of size n/4). To accomplish this we utilize a data structure that al- lows us to compute such intersections in O(n2”i2) time without an increase in space. The main idea is to create an algorithm that generates the elements in A + B and C + D in increasing order, which allows us to compute the intersection by merging. Since we will use a very similar data structure to the one proposed in (Fiat et al. 1989) we review their implementation in the next section. 1342 Search A Parallel Solution to Intersecting A+B withC+D We will first review how to generate elements in A + B in ascending order sequentially. First, assume without loss of generality that A and B are given in ascending sorted order. During each phase of the algorithm, for each element a,& in A we keep a pointer to an element bj such that all the sums of the form ak + bi (i < j) have been generated. We denote such pointers by ak --+ bj. For example, part of our data structure may look similar to the figure below: a1 + ho a2 -+ b7 a3 + b6 a4 + b4 Additionally, we will maintain a priority queue of all such sums. To generate A + B in ascending order we repeatedly output the smallest al, + bj in the priority queue, and insert the pointer al, -+ bj+l into the data structure and also insert ok + bj+l into the priority queue. It is easy to see that, if A and B are of size 2”i4 we can generate all elements in A + B in ascending order in O(n2”i2) time. However, this algorithm is strictly sequential as it generates elements in A + B one at a time. Our algorithm is based on the idea that instead of generating the elements of A + B one at a time we will in parallel generate 2 n/4 elements at a time. To sim- plify our presentation, we describe the algorithm as- suming that we have 2”i4 processors (which is of course unfeasible). By applying Brent’s theorem (Brent 1974) we obtain speed-up results for any number of proces- sors less than or equal to 2”j4. This is important since 2”14 in practice will be far larger than the number of processors in the system. The main idea of the algorithm is as follows. Each element ak in A points to the smallest element of the form al, + bj that has not been generated yet. Our algorithm works as follows. We first insert these 2”i4 elements in an array Z’EMP of size 2 * 2”i4 which will keep track of the elements that are candidates to be generated. The reader should note that we cannot just output these elements. We call those ok such that ak + bj is in TEMp alive (this notion will be clarified in step 5 below). We execute the following procedure: 1. 2. 3. 4. 5. offset=l. Repeat 3-6 until oflset equals 2 * 2”i4. Each ak that is alive and points to bj (ak -+ bj ) inserts all elements of the form ak + bj+,, where m 5 ovffset in the array TEMP. Find the 2”i4th smallest element in TEMP and delete all elements larger than it. If the element of the form a,+ + bj+,gset remains in TEMP we will call ak alive. Otherwise, ai is called dead, and will not participate in further computa- tions. 6. Double the offset (i.e., ofSset := 2*oflset). Note that the number of elements in TEMP never exceeds 2 * 2”i4. This is true for the following reason. Assume that at phase t the number of live elements ak is L. Each of these L elements contributes exactly ofSset pairs ai + bj to TEMP. In the next phase, each such ok will contribute 2 x offset pairs, doubling its previous contribution. Thus, we will add oflsetxl new pairs to TEMP. Since o#set x L < 2n/4, the number of pairs in TEMP never exceeds 2 x 2”i4. It is easy to see that the procedure above terminates in O(log(2”/“)) ‘t 1 erations since we are doubling the offset at each iteration. Therefore, the entire process of generating the next 2 n/4 elements can be accomplished in O(log2(2n/4)) = O(n2) time using O(2”i4) storage. We use the procedure above repeatedly to generate the entire set A + B in ascending order. Parallel Solution to KNAPSACK Using our idea above we can obtain significant speed- ups in the implementation of each phase of the knap- sack algorithm. We provide informal analysis of each phase indicating the speed-up that is possible in each phase. We partition S into four lists, Si, 1 5 i I: 4. Each list is of size n/4. We generate the lists G;, 1 5 i 5 4, i.e., the lists of all possible subset sums Si7 1 5 i 5 4. Each set is of size 2”i4 = n/l. It is trivial to obtain M/P time complexity for this problem for any number of pro- cessors P 5 M. We sort Gi , G2, Gs and G4. Parallel sorting is a well studied problem and is amenable to speedup. We invoke our algorithm for computing the next M elements in the set A + B as described in the previous section to generate Gi +G, and G3 +G4 in ascending order. This phase take M/P time. We intersect (by merging) the generated sets in M phases, generating and merging h/ir elements at a time. Merging can be accomplished in M/P + O(log log P) time by a known parallel merge algo- rithm. Since at least iV elements are eliminated at each phase, and the number of possible sums is iV2, the total time to compute the desired intersection is O(M2/P) time. The algorithm we sketched above provides a frame- work to achieve speed-up without sacrificing the good space complexity of the best known sequential algo- rithm. The novel aspect of the algorithm is step 3 where we suggest an original procedure. There are many details missing from the description of the algo- rithm above. There have been a variety of approaches to paralleliz- ing this problem (Chen & Jang 1992; Chen, Chern, & Jang 1990; Teng 1990; Lee, Shragowitz, & Sahni 1988; Lin & Storer 1991). Dynamic programming is efficient in certain cases. Karnin (Karnin 1984) proposes a par- allel PRAM algorithm that takes O(2n/2) time and uses space O(2n/6) but it requires O(2”i6) processors. Ferreira (Ferreira 1991) gives an 0( 2n/4) time algo- rithm with 0(2n/4) processors but which uses O(2”i2) space. Since the space requirements are quadratic in the time and in the number of processors, space be- comes a bottleneck on most machines. An open ques- tion he posed, therefore, was to find an algorithm with 0(2”14) space complexity(Ferreira 1991). This paper provides such an algorithm. Furthermore, our method- ology can be applied to the taxonomy of problems presented in (Schroeppel & Shamir 1981) to paral- lelize of monotonically decomposable problems along a range of time-space tradeoffs, although we feel that the S = O(2n/4), T = O(2”i4), P = O(2n/4) is the simplest and most useful. Parallel Planning It turns out that the algorithm sketched above has ap- plications to a variety of problems which on the surface appear different from the knapsack problem. In partic- ular, it is possible to adapt the approach to versions of planning problems. The idea was first outlined in a pa- per by Fiat, Moses, Shamir, Shimshoni and Tardos on planning in permutation groups (Fiat et al. 1989). We give a very informal description of their idea and then show how to use the parallel algorithm we discussed in the previous section, with some modifications, to im- plement the approach on massively parallel machines. A planning problem we consider may be stated as fol- lows. Let S be a space of states. Typically, this space is exponential in size. Let G be a set of operators map- ping elements of S into S. We denote composition of gi and gj by gi o gj. AS before, by G, o Gj we denote the set of operators formed by composing operators in Gi and Gj respectively. We assume that each operator g in G has an inverse denoted by 9-l. The planning problem is to determine the shortest sequence of operators of the form gi,g2, . . . that maps some initial state Xc to a final state Y. Without loss of generality assume the initial and final states are al- ways some state 0 and E respectively. In this paper we make the planning problem slightly simpler by asking whether there exists a sequence of operators of length n that maps the initial state into the final state. Assume k is the size of G. Clearly, the problem can be solved by a brute force algorithm of time complexity O(lc”). We can also solve it with O(n) space by iterative-deepening depth-first search. We are interested in problems for which k” time is prohibitive but fi as the total num- ber of computations is feasible. Let us spell out some assumptions that make the ap- proach work. We assume that all the operators have inverses. We refer to G-l as the set of all inverses Search 1343 of operators in G. We also assume that it is possi- ble to induce a total order < on the states of g. For example, in the example above the states are sums of subsets ordered by the < relation on the set of inte- gers. In the case of permutation groups considered in (Fiat et al. 1989), permutations can be ordered lexico- graphically. There are several additional mathematical assumptions that must be satisfied, some of which are outlined in the full version of our paper. LetG1=Gz=Ga=G~=GoGo+++oG,(Gcom- posed with itself Z/4 times). To determine whether there exists a sequence gi , , . . . . gl that maps 0 into E (i.e., gi...gl(O) = E), we instead ask the question whether E is contained in Gi o G:! o Gs o GJ(0). But since the operators have inverses we can ask the question of whether CT1 o G;‘(E) has a non-empty intersection with Gs o Gd(0). However, this naturally suggests the very similar scenario that we considered in the discussion on the knapsack problem. If the sizes of Gi, Gz, Gs and Ga are M, we can solve this intersection problem in time O( M2 /P) and space O(M). This assumes that we can generate the states in A o B (where o is now a compo- sition on operators) in increasing order. To illustrate this approach let us consider a very simple problem. Let fi (2) = x + 5 and f2 (2) = 3 *x be two functions (operators). Given integers cl and c2 we want to find whether there is a sequence of applications of either fi or f2 to cl that yield ~2. E.g., (10+5)*3)+5 = 50, that is 50 is reachable from 10 by fi (f2 (fi (10) = 50. To find out whether c2 is reachable from cl in 40 applications of our operators we first create a set F of all possible functions of the form f(x) = a * x + b that can be created by composing fi and f2 with each other ten times. This set is of size 21°. Now consider the two inverses of fi and f2, namely hi(y) = y - 5 and hz(z~) = y/3. We create a set H of all possible functions of the form h(y) = y/c - d that can be generated by composing hi and h2 ten times. This set is also of size 2 lo. Now we need to find out whether F o F(cl) has a non empty intersection with H o H(c2). The reader can verify that we can produce a monotone order on the operators in F and H that allows us to apply the approach we sketched above. Therefore, we can solve this problem sequentially in time proportional to roughly 20 * 220 with 21° storage. The brute force bidirectional search requires 220 stor- age. Using the algorithms we developed in this paper we can parallelize this approach without increase in storage. As another application of this approach, we can ob- tain a parallel algorithm for problems such as Rubik’s Cube and other similar problems. The implementa- tion of the algorithm sketched above becomes some- what more involved because composition of operators is not necessarily monotonic, as defined later. We, nev- ertheless, can modify the algorithms sketched above to obtain efficient parallel implementations with reduced space. To describe the algorithm, we assume that our oper- ators are members of a permutation group II. The de- gree of II is defined to be the number of points on which II acts. We set this to be q. We can suppose without loss of generality that each permutation P is a bijection from the set of integers [l, 2, . . . . q] to itself. The nota- tion for P will be the vector (P(l), P(2), . . . , P(q)). For example, (4,3,2,1) is the reversal permutation of degree 4 that sends 1 into 4, 2 into 3, 3 into 2, and 4 into 1. If P and Q are permutations then we define their product P o Q by (P o Q)(i) = Q(P(i)). This or- der of multiplying permutations is customary in much contemporary group-theoretic literature, so we will re- tain it. Let G be a subset (not a necessarily a sub- group) of k permutations in II. The elements of G are our basic operators. Given an integer n and a group element y we ask if y can be written as the product of n elements from G. We have seen that this prob- lem is reducible to the following: Given 4 sorted lists of permutations A, B, C, D, each of size O(kn/*), does A o B intersect C 0 D? This problem in turn reduces to the problem of generating the elements of A o B in sorted order. We order permutations lexicographically. (Remark: the number of elements in A, B, C, D may be smaller, in certain cases, than O(lc”i4) because the same group element may be written in many differ- ent ways as words in G of length k/4.) We apply our earlier parallel algorithm for the knapsack problem to generate the elements of A o B in batches of kni4 at a time. A problem arises becauses our algorithm requires, given an ai E A and a bj E B, the generation of the next oflset elements of the form ai o b, b E B. When o was the + operator, we could simply let these elements be ai+bj+i, ai+bj+s,. . . , ~i+b~+~t~~t. This works be- cause sum is a monotonic operator: b < b’ e a + b < a + b’. This monotonicity fails in the case of permu- tations, however. For example, (1,3,2,4) < (1,3,4,2), but (4,3,2,1)0(1,3,2,4) = (4A371) > (WA 1) = WG’,1)o(LW,2) Thus, each a will induce a new ordering of B, and B will have to be traversed in this ordering, in parallel, for all f-2. As in the sequential case, a list of permutations will be stored in a trie, a depth q tree whose leaves cor- respond to permutations in the list and whose unused branches are pruned. Each edge is labeled and the la- bels encountered when traversing the tree from root to leaf are the images of [l, 2,. . . , q] of the permutation that is represented by that leaf (see Figure 1). If the edges emanating from any node in the tree are arranged in increasing order, then the leaves of the tree will be in lexicographically increasing order from 1344 Search Figure 1: Tree representing the list of 6 permutations (1,2,3,4), (L3,2,4), (L3,4,2), (2,4,1,3), (2,4,3,1); (4,3,2,1). Each leaf represents a permutation and the leaves are in lexicographically increasing order from left to right. The leftmost leaf is the identity permu- tation (1,2,3,4) and the rightmost leaf is the reversal permutation (4,3,2,1). left to right. Given a permutation a, we can rearrange the order of edges emanating from each node to reflect their order in a. The leaves of the new tree, reading from left to right, are increasing with respect to the order induced by a. If the leaf b is to the left of the leaf b’ in the new order, then a o b < a o b’ (see Figure 2). In order for-the earlier algorithm to go through, it is necessary, given ai and bi to find the b such-that there are precisely m leavesa between bj and b in the order induced by ai. This is done by initially storing the number of leaves in the rooted tree at each node of B with that node. In addition to the pointer from ai to bi, ai also stores the index of bi in the ordering it introduces. A top down search starting at the root can then find b by performing a prefix sum on the number of leaves in the subtrees of the children of each node in the ai ordering. This requires only time linear in q, and from this information the child of the node in whose subtree b resides can be inferred. This requires O(q2) work, as in the sequential algorithm. Note that the step at each node can be performed in parallel with only q extra processors because in the algorithm we use we only needa subinterval of B so that nodes to the left of b are all generated. However, because q is usually fairly small it would almost certainly be a waste of time in practice to perform the prefix sum of the q values in parallel due-to communication and synchronization overheads. This method gives a complexity of T = O(V/P), S = O(n), for P 5 fi up to logarithmic factors and multiplicative factors in q for finding a length n shortest word on k generators, where V = Cn/2T and Figure 2: Reordered tree of Figure 1. Each interior node has been reordered according to the permutation (4,3,2,1). If leaf b is to the left of leaf b’ then the permutation (4,3,2,1) o b is lexicographically less than the permutation (4,3,2,1) 0 b’. the time complexity of the best sequential algorithm is O(V). This parallelizes the method of Fiat et al. efficiently with respect to work on a CREW PRAM when P 5 sqrtV without asymptotic space utilization greater than the sequential method. Other time space tradeoffs, though possible, are not as useful. Although this technically only applies to a group of operators it is easy to modify the algorithm to apply to a groupoid of operators such as arises in the 15-puzzle. The CREW PRAM model is unrealistic for current parallel architectures and was used here only for sim- plicity of exposition. A direct implementation of the algorithm we described would be slow on real machines because of its extensive reliance on complex communi- cation and synchronization patterns. We have devel- oped a slightly more complex algorithm with the same asymptotic time/space complexity (up to logarithmic factors) which is better suited to implementation be- cause of its greater reliance on local memory accesses and should also perform better when P < @. In general there are many implementation-dependent pa- rameters that can affect the performance of parallel permutation group manipulation algorithms such as whether to perform permutation composition itself lo- cally (York 1991). Although fundamental permutation group operations are theoretically parallelizable, their practical implementation remains challenging (Babai, Luks, & Seress 1987; Cai 1992; Stiller 1991). Discussion We presented an approach for massively parallel state- space search. This approach is a parallel implementa- tion of the sequential algorithm proposed in (Fiat et al. 1989) for finding shortest word representations in permutation groups. Our implementation relies on a Search 1345 new idea for computing the Ic-smallest elements in the set A + B. This idea is used to parallelize a key part of the algorithm. As future work we would like to apply compres- sion techniques such as binary decision diagrams to this state space (Clarke, Filkorn, & Jha 1993; Burch, Clarke, & McMillan 1992). References Babai, L.; Luks, E.; and Seress, A. 1987. Permutation groups in NC. In STOC 87, volume 19, 409-420. Brent, R. P. 1974. The parallel evaluation of gen- eral arithmetic expressions. Journal of the ACM 21(2):201-206. Burch, J. R.; Clarke, E. M.; and McMillan, K. L. 1992. Symbolic model checking: 102’ states and be- yond. Information and Computation 98(2):142-170. Cai, J.-Y. 1992. Parallel computation over hyperbolic groups. In %$‘th Annual STOC, 106-115. ACM. Chen, G.-H., and Jang, J.-H. 1992. An improved parallel algorithm for O/l knapsack problem. Parallel Computing 18(7):811-821. Chen, G.-H.; Chern, M.-S.; and Jang, J.-H. 1990. Pipeline architectures for dynamic programming al- gorithms. Parallel Computing 13(1):111-117. Clarke, E. M.; Filkorn, T.; and Jha, S. 1993. Exploit- ing symmetry in temporal logical model checking. In Proceedings of the Fifth Workshop on Computer- Aided Verification, 450-462. Diffie, W., and Hellman, M. 1976. New directions in cryptography. IEEE Trans. Information Theory IT-22:644-654. Evett, M.; Hendler, J.; Mahanti, A.; and Nau, D. 1990. PRA*: A memory-limited heuristic search pro- cedure for the Connection Machine. In Third Sympo- sium on the Fontiers of Massively Parallel Computa- tions, 145-149. Ferreira, A. G. 1991. A parallel time/hardware trade- off T . H = O(2”j2) for the knapsack problem. IEEE Transactions on Computers 40(2):221-225. Fiat, A.; Moses, S.; Shamir, A.; Shimshoni, I.; and Tardos, G. 1989. Planning and learning in permuta- tion groups. In 30th Annual Symposium on Founda- tions of Computer Science, 274-279. IEEE Computer Society Press. Los Alamitos, CA, USA. 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Group graphs and computational symmetry on massively parallel architecture. Journal of Supercomputing 5(2/3):99-117. Stiller, L. 1992. An algebraic paradigm for the de- sign of efficient parallel programs. Technical Report JHU-92/26, Dept. of Computer Science, Johns Hop- kins University, Baltimore, MD 21218. Tarjan, R., and Trojanowski, A. 1977. Finding a max- imum independent set. SIAM Journal on Computing 6:537-546. Teng, S.-H. 1990. Adaptive parallel algorithms for in- tegral knapsack problems. J. Parallel and Distributed Computing 8(4):400-406. Thinking Machines Corporation. 1992. Connec- tion Machine CM-5 Technical Summary. 245 First St., Cambridge, MA 02142-1264: Thinking Machines Corporation. York, B. W. 1991. Implications of parallel ar- chitectures for permutation group computation. In Finkelstein, L., and Kantor, W., eds., Proceedings of the Workshop on Groups and Computation, 293-313. Rutgers, NJ: DIMACS. 1346 Search | 1994 | 275 |
1,625 | The Trailblazer Search: A New Method for.Searching and Capturing Moving rgets Fumihiko Chimura and Mario Tokoro* Department of Computer Science, Faculty of Science and Technology, Keio University 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223, Japan {chimura, mario}@mt.cs.keio.ac.jp Abstract This paper proposes a new search algorithm for targets that move. Ishida and Korf presented an algorithm, called the moving target search, that captures a tar- get while deciding each search step in constant time (Ishida 8-r Korf 1991). H owever, this algorithm re- quires many search steps to solve problems, if it uses a heuristic function that initially returns inaccurate values. The trailblazer search stores path information of the region it has searched and exploits this informa- tion when making decisions. The algorithm maintains a map of the searched region, and chases the target once it falls on a path found on the map. We em- pirically show that the algorithm’s map function can significantly reduce the number of search steps, com- pared with the moving target search. We also dis- cuss the efficiency of the trailblazer search, taking the maintenance cost of the map into consideration. Introduction Heuristic search for moving targets models the case where the location of the goal changes dynamically. This assumption is realistic because there are many applications in which the goal moves before the search reaches the original location. Search for moving tar- gets is a real-time task that interleaves decision and execution of search steps (Korf 1990). The search is illustrated intuitively when you try to meet someone in a crowd. You have to be careful in performing the search: there is a possibility that you and the person will cover the same ground many times before you ac- tually meet. We study the search in an abstract search space as multiple paths finding to every possible loca- tion of the goal. Ishida and Korf proposed the moving target search (MTS) algorithm (Ishida Sr: Korf 1991). MTS tries to learn the exact distance to the target, while exploring the search space. It starts with an initial heuristic estimate of the distance. After the exact distance to the target is known, the search is just the process of catching the target up. The distinctive characteristic *Also with Sony Computer Science Laboratory Inc., 3-14-13 Higashigotanda, Shinagawa-ku, Tokyo 141, Japan. of MTS is that it makes decisions in constant time. The major concern in MTS is that it requires many search steps to solve a problem, if the initial heuristic estimate of the distance to the target greatly differs from the exact value. This paper investigates an underlying intelligence that reduces the number of search steps, in the search for moving targets. We propose the trailblazer search: a method that stores path information of the region it has searched, and exploits this information when mak- ing decisions. ’ Information of the searched region is organized into a map that contains paths and associ- ated costs to every site in the region from the current location of the algorithm. The trailblazer search uses a heuristic function, in an algorithm that conducts a systematic search and avoids exploring the same region twice. Once the target crosses a path on the map, the algorithm follows the path to catch the target up. Un- der the assumption of moving faster than the target, the trailblazer search captures the target. The trailblazer search makes decisions using a map that gets larger as the algorithm steps further. We will discuss the efficiency of the trailblazer search, taking the maintenance cost of the map into consideration. Search for Moving Targets We study the search for moving targets in an abstract search space: a connected and undirected graph with a unit cost on each edge. A problem solver searches for a target representing the goal. At any point during search, both the problem solver and the target are as- signed nodes in the graph that represent their states, or simply denote their locations. They can move to any node adjacent to their current locations. We as- sume that they move on alternate turns. The problem solver and the target are assigned initial nodes at the beginning of the search; the search ends when their lo- cations coincide. We say a node is explored if it has been the location of the problem solver. We make three assumptions to assure a solution to the search. The first is that the problem solver always r We use the term “trailblazer” in the sense of a guide or pathfinder since it uses a map. Search 1347 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. knows the location of the target. The second is that the problem solver has a heuristic function that re- turns an estimated distance between any two nodes in the search space. We further assume that the heuris- tic function is initialized to return non-overestimated values, that is the function is admissible (Pearl 1984). The last assumption is that the problem solver moves faster than the target. In the particular search space defined above, we realize this by eventually skipping the turn of the target. Search for moving targets is a real-time task that in- terleaves decision and execution of search steps. This is the result of practical resource limitations that do not allow a method to first find a sequence of steps that leads to the goal, and then execute the sequence. Korf presented the learning real-time A * (LRTA*) al- gorithm that reaches the goal while making decisions in constant time (Korf 1990). Basically, LRTA* starts with an initial heuristic estimate of the distance from a node in the search space to the goal and, while explor- ing the search space, tries to find the exact distance. In the learning step, the heuristic distance h(z) be- tween node x and the goal is updated to the value of min;{c(x, xi) + h(xi)}, where xi is a node adjacent to x, c(x, x;) is the actual distance from x to xi, and h(xi) is the heuristic distance between xi and the goal. This update is done to ensure that h(x) is not smaller than the estimated length of the path from x to the goal that goes through a node adjacent to x. Ishida and Korf extended the learning method of LRTA* to tackle the search problem for moving targets (Ishida 8.~ Korf 1991). Their algorithm, the moving target search (MTS), 1 earns the exact distance between any pair of nodes in the search space. This capacity is added because both the problem solver and the target can move to any location in the search space. Once the problem solver knows the complete set of exact distance values, the search task is reduced to moving to the adjacent nodes that are closer to the target. MTS is guaranteed to reach the target if the search problem follows the above assumptions. The worst case time complexity of MTS is O(N3), and the worst case space complexity is O(N2), where N is the number of nodes in the search space. The major concern of LRTA” and MTS is that they require a significant number of search steps to reach the goal, if their heuristic functions initially return inaccurate values. In MTS, excessive search steps is typically shown using a target on a plane with ran- domly placed obstacles. When trapped in dead ends, the problem solver moves back and forth because the obstacles prevent direct movement to the target placed just beyond the obstacles. Ishida presented an exten- sion to MTS that conducts a lookahead search in order to get out of dead ends fast (Ishida 1992). His algo- rithm, the Intelligent Moving Target Search (IMTS), considers the tradeoff between the increased computa- tion cost to explore nodes with the lookahead search, and the reduced execution cost to reach the target with fewer steps. The learning method in LRTA” and that in MTS is a sort of reinforcement learning; learn- ing from positive and negative rewards of executing search steps. Whitehead, and also Koenig and Sim- mons studied the issue of excessive search steps in the context of reinforcement learning (Whitehead 1991; Koenig & Simmons 1993). The Trailblazer Search We propose a new search algorithm for targets that move. We aim at reducing the number of search steps, yet guaranteeing the accomplishment of the task. The basic idea is to store path information of the region where the algorithm has searched, and exploit this in- formation for the task. The information of the searched region is especially useful when the target is moving because, as the region expands, there is a good chance that the target will cross a path that the problem solver has already used for search. The problem solver records every search step it takes by remembering an undirected edge connecting the de- parture and arrival nodes of the step. This record is organized into a graph called the trail. The map is a table calculated from the trail and it contains the information of minimum cost paths from the current location of the problem solver to any node it has ex- plored. The map is a partial map of the whole search space, and is relative to the search steps that the prob- lem solver has taken so far. Thus we consider it as a relative search tree rooted at the current location of the problem solver. In the following, we describe how we maintain the map. Let p, be the node the problem solver reaches after n steps, where n is a non-negative integer. We assume that pn takes values from a set of integers that identify the actual nodes in the search space. Let Vpn and Ep,, be the sets of accumulated nodes and edges at location pn. Weighted and undirected edges are denoted by triplets, (P,, P,+I, c(P,,P,+~)), where c(P,,P,+~) is the actual cost to traverse the edge. Definition 1 (The Trail) Let po be the initiak node of the problem solver. The trail of the problem solver at location po is a weighted and undirected graph G,, = (I&,, EPO), where the set of nodes VP0 is {po} and the set of edges EPO is { }. Assume that the problem solver moves from pnml to p, on its nth step with actual cost c(p+l,p,), where n is a positive integer. The trail of the prob- lem solver at location p, is a weighted and undi- rected graph G,, = (VPn, EP,), where the set of nodes VP,, is VP,,+ U (pn) and the set of edges EP,, is J&,-1 u ((Pn-17 Pn7 c(Pn-l,Pn)))* We assume that the problem solver is able to record the trail of the target and to maintain the map of the target. This means that the location of the target is regarded as a sort of explored node for the problem 1348 Search solver. Using the above procedure, we define the trail of the target at location qm to be a graph Ghm = (vim, Ei,J, where qm is the node the target reaches after m steps, where m is a non-negative integer. The problem solver is able to refer to a graph G = (Vpn U Vim, Epn U EL,) at location p, as the total trail of the search. We use Dijkstra’s shortest path algorithm, a routing algorithm, to calculate the map. Dijkstra’s algorithm has a time complexity of O(N2) when the number of nodes in the search space is fixed to N (Aho, Hopcroft, St Ullman 1974). Let C(x, y) be the cost of the mini- mum cost path from the current location x of the prob- lem solver to some node y in the trail. The path goes only through nodes in the trail, and the cost of the path is the sum of the costs of the edges that constitute it. The routing algorithm calculates a routing table that holds the value for C(x, y), and the node x’ succeeding x on the path to y. 2 The value of C(x’, y) is simply C(x, y) - c(x, x’), where c(x, x’) is the cost of the edge between x and x’. The value of C(x, y) is co if there is no path between 2 and y. In other words, we know that there is a path from x to y if C(x, y) has a finite value. The map is nothing else than the routing table calculated from the trail by the routing algorithm. We use trailblazer search to refer generally to al- gorithms that maintain a map to perform a search. A trailblazer search has two distinct phases: (1) a search phase in which the map has no path to the target, and the search space is heuristically searched, and (2) a chase phase in which the map has a path to the target that is deterministically followed to catch the target up. The phases are characterized by the evalu- ation functions they use to determine which adjacent node to move to next. In the search phase, decisions are made using the heuristic estimates of the distances from the adjacent nodes to the goal. In the chase phase, decisions are made using the costs on the map that indicate the best known paths from the adjacent nodes to the goal. We describe a particular instance of the trailblazer search that uses hill-climbing in the search phase. The Trailblazer Search with Will-Climbing Let x and y be the locations of the problem solver and the target. Let h(x, y) be the heuristic estimate of the distance between x and y, and C(x,y) be the cost of the minimum cost path between x and y, To elimi- nate unnecessary re-exploration of the same node, we assume that the problem solver holds the set of ex- plored nodes. We also assume that the problem solver records, for each explored node, the parent node from which it has arrived to the node for the first time. 2We applied some minor modification to Dijkstra’s al- gorithm to avoid repeated calculation for known paths. Procedures of the problem solver when it is its own turn to move. Update the routing table according to the location x of the problem solver. For each node x’ adjacent to x, read C(x’, y) to find if there is a path from x’ to y. If there is no path on the map, enter the search phase. Otherwise, enter the chase phase. In the search phase: For each non-explored node x’ adjacent to x, cal- culate h(x’, y), move to the node x’ with minimum h(x’, y). If all of the adjacent nodes have been ex- plored, move to the node x’ that is the parent node of x. Assign the value of x’ to x as the new location. In the chase phase: Move to the adjacent node x’ with minimum C(x’,y), and assign the value of x’ to x as the new location. In both the search, phase and th,e chase phase: Record the move of the problem solver in the trail. Procedures of the problem solver when it is th,e target’s turn to move. In both the search phase and the chase phase: Record the move of the target in the trail. If a tie occurs such that two node evaluations return the same cost, the tie is broken randomly. The algorithm is complete in the sense that it never fails to capture the target if the search problem follows the assumptions in the previous section. As a short proof, consider first the search phase. Since the search space is finite. the algorithm must either find the tar- get or the trail of the problem solver and the target must overlap before all the search space is explored. If the trails overlap, the algorithm enters the chase phase because there is now a path to the target on the map, whatever steps the target may take. The cost of the path never increases when the problem solver and the target alternate turns. Hence, under the assumption that the problem solver moves faster than the target, it will eventually reach the target. We will now analyze the complexity of the algori$hm. Let N be the number of nodes in the search space, and M the number of search steps. The time complexity of the trailblazer search is the number of search steps plus the time complexity of map maintenance. The time complexity of map maintenance on the Mth step of the problem solver is 0((2 *AJ)2) = O(M2). Although we omit a formal proof, this can be seen intuitively be- cause the total number of steps of the problem solver and the target, and thus the number of nodes in the total trail, is at most 2 * M when the problem solver moves M steps. The algorithm re-calculates the map every time the problem solver moves. Thus the time complexity of map maintenance is O(~~, i2) when the problem solver moves M steps. Since this value is bounded by O(M3), the time complexity of the trail- Search 1349 blazer search is O(2M + M3) when the problem solver moves M steps. In the search phase, the steps of the problem solver are along a search tree that grows to exhaust the search space. Since this tree has at most N - 1 edges and it, takes 2 * (N - 1) steps to traverse the whole tree, in the search phase, the worst case of the number M of search steps is 2 * (N - 1). In the chase phase, the steps of the problem solver are along a path found on the map. Since the initial cost of this path is at most N- 1, in the chase phase, the worst case of M is (N - 1)/a, where Q! is the difference in speed between the problem solver and the target; it takes (N - 1)/a! steps to catch the target up. In each phase of the search, M is bounded by O(N)? if we assume Q is a constant. Consequently, the algorithm’s worst case time com- plexity is O(N + N3) that is bounded by O(N3). The worst case space complexity is O(N2) because this is the size of the complete routing table. Note that these values are the same as those for MTS. However, the factor that determines the worst case time complexity of the trailblazer search differs from that of MTS. In MTS, the determining factor is the number of search steps. In the trailblazer search, it is the time com- plexity of map maintenance, since the worst case of the number of search steps reduces from O(N3) to O(N), compared with MTS. This indicates that the trailblazer search considers the tradeoff between the computation cost to maintain the map, and the execu- tion cost of the search steps. Performance of the Trailblazer Search We empirically evaluate the performance of the trail- blazer search. We also discuss its efficiency, while con- sidering the maintenance cost of the map. The search space of our problem is a rectangular grid with ran- domly placed obstacles. The problem solver and the target move along the grid from junctions to adjacent, junctions, but not to those occupied by obstacles. Log- ically, increasing the number of obstacles changes the regularity of the search space and causes the heuristic function to return an increasing number of errors. The grid is a square of 50 junctions on each side, organized as a torus. We implemented the trailblazer search with hill- climbing (denoted by TBS), and. for comparison. the moving target search algorithm by Ishida and Korf (de- noted by MTS). The problem solver uses the Manhat- tan distance as its heuristic function. We performed four experiments, using for each, a different movement strategy of the target. (1) Aztoid: the target moves to the furthest adjacent junction from the problem solver, estimated by the Manhattan distance, (2) Stationary: the target does not move, (3) Ran.dom.: the target moves randomly, (4) Meet: the target moves to meet the problem solver, i.e., searches for the problem solver. With the Avoid strategy, the target executes the same learning method as MTS in the hope to flee from the problem solver cleverly. With the Meet strategy, the target uses the same search method as the problem solver (TBS matches TBS, MTS matches MTS). We set the speed of the target to 4/5 that of the problem solver by skipping the turn of the target once every five turns. The problem solver and the target, are initially separated diagonally on the square grid at a distance of 50 junctions in the Manhattan distance. We set the obstacle ratio between 0% and 40% at in- tervals of 5%, and randomly created 100 sample grids for each obstacle ratio. Both TBS and MTS solved the same samples, and we averaged the total num- ber of search steps of the problem solver over the 100 samples. For TBS, we also measured the actual com- plexity of map maintenance while solving the samples. The actual complexity is calculated by counting the number of references to entries on the routing table for each time the map is updated. We do this be- cause references to entries are the actual operations that decide the complexity of map maintenance. We will briefly mention some results of the actual complex- ity of map maintenance. Figure 1 shows the number of search st,eps when we change the obstacle ratio. We obtained similar results for problem sizes ranging from 20 to 50 junctions ou each side of the grid. TBS and MTS show almost the same performance when there are few obstacles. How- ever, as the obstacle ratio increases and the heuris- tic function begins to return inaccurate values, TBS significantly reduces the number of search steps. com- pared with MTS. When the obstacle ratio is 40% and when the target strategy is Avoid. Sta8tionary. Random. Meet, the proportion of the number of search steps of MTS to that of TBS is 3475/405 N 8. 1586/444 N 3. 6313/376 ZJ 16, 20981/180 N 100. respectively. The reason for the gain is that TBS can use the map to de- tour walls of obstacles. and get! out of dead ends fast. By the nature of their movements, targets with the Random. strategy do not move far from their initial lo- cations. When the obstacle ratio is high, targets with the Avoid strategy get trapped in dead ends and do not move far either. Thus, for a systematic search like TBS and a high obstacle ratio, targets with the Ra,ndom. and the Avoid strategies are as easy (takes as much search steps) to capture as targets with the Stationary strategy. Actually, with a high obstacle ratio. there is a slight tendency that moving targets will be eas- ier (takes less search steps) to capture. The fact that TBS collects more information of the search space from the movements of the target, explains the result. We predict that these results will hold, even if we change the speed ratio between the problem solver and the target because change in speed does not affect, the tar- get’s strategy. As seen in figure 1, when there are many obstacles, MTS shows a counterintuitive behavior in that, targets with the Meet strategy are far more difficult to capture than those using the Avoid strategy. even though tar- 1350 Search 0 5 IO 15 20 25 30 35 40 Obstacle Ratio (%) (a) TBS 0 5 IO 15 20 25 30 35 40 Obstacle Ratio (%) (b) MTS -Ct- Avoid =+D- Stationary +F Random -o- Meet Figure 1: Results of the number of Search Steps gets with the Meet strategy cooperate with the problem solver. Ishida and Korf pointed out this result in their paper (Ishida & Korf 1991). This doesn’t happen in TBS; in TBS, targets with the Meet strategy are the easiest to capture, regardless of the obstacle ratio. In- creasing the target’s speed increases the efficiency of TBS, reducing the number of search steps. As we de- crease the target’s speed, the number of search steps approaches that TBS needs to capture targets with the Stationary strategy. An interesting characteristic of TBS is that it does not take the optimal path even if there are no obstacles (and hence the Manhattan distance gives the correct distance to the target). When the obstacle ratio is 0%) and the target executes the Avoid strategy. TBS takes 275 steps to capture the target while MTS takes the optimal path of 239 steps. This happens because the current implementation of TBS is completely faitl~,fuZ to the map, in the sense that the problem solver always follows the map whenever a path is found, even if the distance to the target in the Manhattan distance is smaller than the cost of the path. Evaluating the Real Efficiency of the Trailblazer Search For TBS, the drastic reduction of search steps is due to the benefit of the map. Here we estimate the total cost of search, and discuss the real efficiency of TBS, while considering the maintenance cost of the map. We emphasize that, from the viewpoint of the worst case time complexity. TBS and MTS have identical ef- ficiency. Compared with IMTS (the extended form of MTS), TBS exchanges the cost to explore information with a lookahead search, for the cost to exploit infor- mation of the searched region. The total cost of search is the sum of the cost to make decisions on search steps and the cost to execute them. We simply assume that the decision cost is proportional to its time complexity. and that the execution cost is proportional to the num- ber of search steps. We further assume that the search steps are decided in a computer and are executed in the real world. That is, we weight the decision cost by l/,0. where /? is a large number. Formally. this makes the total cost for TBS, TTSS = ikl~~s +M;,,//?, and for MTS. TMTS = MMTS + MMTS/,O, where ~MTSS and MMTS are the numbers of search steps that each algorithm requires to solve a problem. The fact that, TBS maintains a map to make decisions. and that MTS makes a constant time decision, justifies the difference between TTSS and TMTS. For example, we set ,f3 to 106. This is a plausible figure because, in the real world. search steps usually take seconds of time to execute, while, in current com- puters, the unit operation of map maintenance takes on the order of microseconds. When the obstacle ra- tio is over 30%) and the target is moving, the empirical results of the actual complexity of map maintenance ranges from 4.8*103 (30% obstacles, Meet strategy tar- Search 1351 get) to 6.7 * lo4 (40% obstacles, Random strategy tar- get). These values have small impact on TTB~, when we weight them by lo- ‘. Thus, in our empirical search space, when the obstacle ratio is high and the target is moving, TTSS is smaller than TMTS because, as we observe in figure 1, MTSS is smaller than MMTS by a factor of 10 in average. This indicates the applica- bility of TBS to real domain problems that have the same size (50*50 = 2500 nodes) as our empirical search space. For large scale problems, however, the mainte- nance cost of the map increases the time TBS uses to make decisions, and this becomes an issue for TBS if we look at its ability to react to the real world. Currently, TBS maintains a full size map in the sense that it includes information concerned with all the ex- plored nodes. The aim is to utilize plenty of alternative paths to efficiently and intelligently reach the target. The idea of limiting the size of the map, while preserv- ing efficiency, is extremely important for two reasons: to improve the ability of TBS to react to the real world, and to reduce the average space complexity. Conclusion We dealt with search for moving targets, and proposed an efficient method to capture moving targets. The trailblazer search maintains a map of the searched re- gion and uses this for the search. We compared the properties of the trailblazer search with those of the moving target search (Ishida & Korf 1991). Formally, the two algorithms have the same worst case time com- plexity of O(N3) where N is the number of nodes in the search space. However, the determining factors of the values are different. For the moving target search, the number of search steps determines its worst case time complexity. For the trailblazer search, this value is determined by the maintenance of the map, since the number of search steps reduces from O(N3) to O(N) when compared with the moving target search. To examine this difference, we tested the perfor- mance of the algorithms on a grid-like search space with randomly placed obstacles. We showed that when the algorithms use inaccurate heuristic functions, the trailblazer search significantly reduces the number of search steps, when compared with the moving target search. In a square grid with 50 junctions on each side and an obstacle occupation ratio of 40%, where the problem solver and the target searched for each other, we obtained a loo-fold reduction. We also estimated the impact of map maintenance on the total cost of the trailblazer search. We made an assumption that the map is maintained in a computer and the search steps are executed in the real world, and hence weighted the cost to maintain the map by a plausible factor. In our empirical search space, the impact of map mainte- nance is small when compared with the execution cost of search steps. This indicates the applicability of the trailblazer search to real domain problems. For large scale problems, a parallel implementation of the map maintenance method decreases the cost to maintain the map (Chandy & Misra 1982). As a consequence, we showed that, for the purpose of efficient search, we can tradeoff the execution cost of search steps for the computation cost to maintain a map. When memory is limited, it is useful to consider a mixed strategy that uses the heuristic function while it returns accurate values, and maintains the map only if necessary. We plan to research this strategy further. Acknowledgements We had a fruitful discussion with Toru Ishida of Ky- ot 0 University. Members of Sony Computer Science Laboratory helped to improve initial concepts and col- leagues at Keio University supported us invaluably. Fi- nally, F. Chimura would like to express his deepest gratitude to his family for their support. References Aho, A. V.; Hopcroft, J. E.; and Ullman, J. D. 1974. The Design and Analysis of Computer Algorith,ms. Reading, Mass.: Addison- Wesley. Chandy, K. M., and Misra, 3. 1982. Distributed Com- putation on Graphs: Shortest Path Algorithms. Corn.- munications of the A CM 25( 11):833-837. Ishida, T., and Korf, R. E. 1991. Moving Target Search. In Proceedings of the Twelfth. Internatiorxal Joint Conference on Artificial Intelligence, 204-210. Ishida, T. 1992. Moving Target Search with Intelli- gence. In Proceedings of the Tenth National Conjer- ence on Artificial Intelligence, 525-532. Koenig, S., and Simmons, R. G. 1993. Complexity Analysis of Real-Time Reinforcement Learning. In Proceedings of the Eleventh National Conference on Artijicial Intelligence, 99-105. Korf, R. E. 1990. Real-Time Heuristic Search. Arti- ficial Intelligence 42:189-211. Pearl, J. 1984. Heuristics: Intelligent Search, Strate- gies for Com.puter Problem Solving. Reading, Mass.: Addison- Wesley. Whitehead, S. D. 1991. A Complexity Analysis of Cooperative Mechanisms in Reinforcement Learning. In Proceedings of the Ninth National Conferensce on Artificial Intelligence, 607-613. 1352 Search | 1994 | 276 |
1,626 | Efficient Li Subrata Ghosh Ambuj Mahanti Dana S. Nau Department of Computer Science IIM, Calcutta Dept. of Computer Science, and University of Maryland Calcutta 700 027 Institute for Systems Research College Park,MD 20742 India University of Maryland subrata@cs.umd.edu iimcal!am@veccal.ernet .in College Park, MD 20742 nau@cs.umd.edu Abstract This paper describes a new admissible tree search al- gorithm called Iterative Threshold Search (ITS). ITS can be viewed as a much-simplified version of MA* [l], and a generalized version of MREC [12]. We also present the following results: 1. Every node generated by ITS is also generated by IDA*, even if ITS is given no more memory than IDA*. In addition, there are trees on which ITS gener- ates O(N) nodes in comparison to O(N log N) nodes generated by IDA*, where N is the number of nodes eligible for generation by A*. 2. Experimental tests show that if the node-generation time is high (as in most practical problems), ITS can provide significant savings in both number of node generations and running time. Our experimental re- sults also suggest that in the average case both IDA* .and ITS are asymptotically optimal on the traveling salesman problem. not common enough Introduction Although A* is usually very efficient in terms of num- ber of node expansions [2], it requires an exponential amount of memory, and thus runs out of memory even on problem instances of moderate size. This problem led to Korf’s development of IDA* [6]. IDA*‘s memory requirement is only linear in the depth of the search, enabling it to solve larger problems than A* can solve in practice. However, when additional memory is avail- able, IDA* does not make use of this memory to re- duce the number of node expansions. This led to the development of several other limited-memory heuristic search algorithms, including MREC and MA*. In this paper, we present the following results: 1. We present a new admissible tree search algorithm called Iterative Threshold Search (ITS). Like IDA*, ITS maintains a threshold z, expands each path until its cost exceeds Z, and then revises z. But if given additional memory, it keeps track of additional nodes, and backs up path information at parents when nodes *Supported in part by NSF Grants NSFD CDR- 88003012, IRI-9306580, and CMDS project (work order no. 019/7-148/CMDS-1039/90-91). get pruned. ITS can be viewed as a much simplified version of MA*, and a generalized version of MREC. ITS’s node selection and retraction (pruning) overhead is much less expensive than MA*‘s. 2. We have proved (for proofs, see [4]) that ITS dom- inates IDA*; i.e., even if ITS is given no more memory than IDA*, every node generated by ITS is also gener- ated by IDA *. In addition, we present example trees in which ITS expands O(N) nodes in comparison to O(NlogN) nodes expanded by IDA* where N is the number of nodes eligible for expansion by A*. 3. We present extensive experimental tests on ITS on three problem domains: the flow-shop scheduling problem, the 15-puzzle, and the traveling salesman problem. Our results show that if the node-generation time is high (which is the case for most practical prob- lems) , ITS can provide significant savings in both num- ber of node generations and running time. 4. Our experiments suggest that in the average case both IDA* and ITS are asymptotically optimal on the traveling salesman problem. Although Patrick et al. [8] showed that there exists a class of traveling sales- man problems in which IDA* is not asymptotically op- timal, our experimental results suggest that such prob- lems are not common enough to affect IDA*‘s average performance over a large number of problem instances. Background The objective of many heuristic search algorithms is to find a minimum cost solution path in a directed graph G. To find such a path, these algorithms use a node evaluation function f(n) = g(m) + h(n), where g(n) is the cost of a minimum cost path currently known from the start node s to n, and h(n) 2 0, the heuristic value of node n, is an estimate of h*(n). h*(n) is the cost of a minimum cost path from n to a goal node. In this paper, we assume that the heuristic function h is admissible, i.e Vn E G, h(n) 5 h*(n). The cost of an edge (m, n) in G is denoted by c(m, n). Algorithm ITS Most heuristic search algorithms maintain a search tree T containing data about each node n that has been Search 1353 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. installed in the tree. Nodes of G are generated one at a time and installed into T, until a solution path is found in 2’ that duplicates the least-cost solution path of 6. Usually the branches of T are represented only as links among the data structures representing the nodes. However, in the search tree T maintained by ITS, ITS maintains heuristic information not only for each node of the tree, but also for each branch of the tree. Thus, rather than considering a branch (p, q) merely to be a link between the node p and its child 4, we consider it as a separate entity in T. Conceptually, ITS installs (p, 4) into T at the same time that it installs p into T, even though ITS has not yet generated Q. It is possible to implement such a scheme without incurring the overhead of generating all of p’s children, by creating one branch (p, R(p)) for each operator R applicable to p without actually invoking the operator R. A tip branch of T is a branch (p, q) in T such that Q is not in T. A tip node of T is a node p of T such that every branch (p, q) in T is a tip branch. Such nodes are eligible for retraction by ITS. Retracting p consists of removing from T the node p and every branch (p, q). For each branch (p, 4) in T a variable B is main- tained, which stores an estimate of the cost of the min- imum cost solution path containing the branch (p, q). B(p, 4) is initialized to f(p) = g(p) + h(p), when the node p is installed in T. However, unlike f-value of a node, B(p, a) is updated every time the node Q is retracted. S is the amount of storage (number of nodes) avail- able to ITS. Procedure ITS: 1. Call Install(s, 0). 2. Do the following steps repeatedly: (a) Set 2 := min{B(p, Q) : (p, a) is a tip branch}. (b) Do th e o f 11 owing steps repeatedly, until B(p, q) > z for every tip branch (p, q): i. Select the leftmost tip branch (m, n) such that B(m,n) 5 z. ii. If m is a goal node then EXIT, returning g(m). iii. If n = DUMMY, then set B(m, n) := 00. Other- wise, do the following: A. If T contains 2 S nodes and has at least two tip nodes, then retract a node, as follows. If there is a tip node z such that B(s, y) > z for every branch (z, y), then let Q be the leftmost such node. Otherwise, let Q be the rightmost tip node of T. Set B(p, q) := min, B(q, r), where p is q’s parent in T. Remove Q and every branch (a, T) from T. B. Call Install(n, g(m) + c(m, n)). Procedure Install(n, g): 1. Put n into T. 1354 Search If no operators are applicable to n, then put a dummy branch (n, DUMMY) in T. Else for each operator R applicable to n, put a branch (n, R(n)) in T. Set g(n) := g. For each branch (n, r), set B(n, r) := g(n) + h(n). Basic Properties of ITS Fora’= 1,2,..., the i’th instant in the operation of ITS is the i’th time that Step 2(b)i is executed, i.e., the i’th time that ITS selects a tip branch for expansion. ITS’s j’th iteration is the j’th iteration of the outer loop in Step 2. ITS’s j’th threshold value is the value of z during this iteration. In Theorem 1 below, we prove that no node is gen- erated more than once by ITS during iteration j, and from this it follows that the number of instants in it- eration j equals the number of nodes generated in it- eration j. At each instant i, ITS either exits at Step 2(b)ii or generates a node ni at Step 2(b)iiiB. In the latter case, either ni is a new node (i.e., a node that has never before been generated), or else it is a node that was previously generated and retracted. Theorem 1 ITS satisfies the following properties: 1. 2. 3. 4. 5. A tip branch (m, n) of 2’ will be selected during an iteration iff B(m, n) 5 z during that iteration. The value of ITS’s threshold z increases monotoni- cally after each iteration. For each instant i, for each branch (m,n) of T, g(m) + h(m) 5 B(m, n) 5 cost(P), where P is the least costly solution path containing (m, n). Let i be any instant in iteration j, and suppose that at instant i, ITS selects some branch (m, n) and gen- erates n. Let (n, p) be the leftmost branch from n. Then unless B(n,p) > Z, (a,~) will be selected at instant i + 1. No node is generated more than once during each iteration. Theorem 2 ITS terminates and returns an optimal solution. Comparison of ITS with IDA* Theoretical Results In this section we show the following: 1. ITS never generates a node more times than IDA*. As a consequence, ITS generates every node gener- ated by IDA*, and that for every node n, ITS gen- erates n no more times than IDA* does. 2. There are classes of trees on which ITS will have better asymptotic time complexity than IDA*, even when given no more memory than IDA* (i.e., S = 0). The main reason for this is that when ITS retracts nodes, it backs up path information, which allows it to avoid re-generating many subtrees. (32 G ” : : n2 : nk (b) Figure 1: A tree G on which IDA* is O(N log N) and ITS is O(N) Theorem 3 IDA* and ITS do the same number of iterations, and for every j, {nodes generated in IDA*% j’th iteration} = {nodes generated in ITS’s iterations 1,2, . . . , j}. Theorem 4 Let G be any state space, and n be any node of G. If IDA* and ITS expand nodes from G in left-to-right order following the same sequence of operators, then 1. ITS and IDA* generate exactly the same set of nodes; 2. For every node n, ITS generates n no more times than IDA* does. The above theorem shows that ITS’s time com- plexity is never any worse than IDA*‘s. Below, we show that there are classes of trees on which ITS does only O(N) node expansions compared to IDA*% O(Nlog N) node expansions on the same trees. The same result also holds for node generations. In the tree in Example 1, it is simpler to count the number of node expansions, and therefore we present the result in terms of node expansions. Example 1. In the search tree G shown in Figure l(a), each non-leaf node has a node-branching factor b= 2, and each arc has unit cost. G consists of two subtrees G1 and Ga where each one is a full binary tree of height K. Gz is rooted at the right most node of Gr. Every leaf node, except the one labeled as goal, is a non-terminal. For each node n in G, h(n) = 0. Clearly Gi and G2 each contain N’ = [N/2] nodes, where N is the number of nodes eligible for expan- sion by A*. The cost of the solution path is 2k = 2[log,(N’ + 1) - 11. Let Nc = b” + 2b”-l + 3bkB2 + . . . + Lb. Then the total number of node expansions by IDA* in the worst-case is No+kN’+No~kNf$Nt=k(N’+l)=O(NlogN). Now we count the total number of node expansions by ITS on 6. As in the case of IDA* no node of G2 will be expanded prior to the expansion of all the nodes of 61 at least once. Using the theorem 4, we can infer that the total number of node expansions by ITS on Gi is O(N). Once ITS begins expanding nodes of G2, the portion of G1 that will be retained in memory is shown in Figure l(b). The branches of Gr which do not lead a goal node (all left branches) will have B value of 00. Therefore no node of 61 will be reexpanded while expanding nodes of G2, Since G1 and G2 are symmetric, by the same argument as in case of G1, ITS will not make more than O(N) node expansions on G2. Thus the worst-case time complexity of ITS on trees like G will always be O(N). Experimental Results In the example above, we have shown that there are classes of trees on which ITS’s asymptotic complex- ity is better than IDA*‘s. In this section we report results of our experiments on three problem domains namely flow-shop scheduling, traveling salesman and 15-puzzle. These problems were selected mainly to en- compass a wide range of node generation times. While the node generation time for the 15-puzzle is very small, it is significant for the traveling salesman prob- lem. The node generation time for flow-shop schedul- ing problem is also small but higher than that of 15- puzzle. All the programs were written in C and run on a SUN sparcstation. We describe the problems and our results in the following sections. One purpose of our experiments was to compare ITS with IDA*, and another purpose was to see how giv- ing ITS additional memory would improve its perfor- mance in terms of both node generation and running time. For the latter purpose, we ran ITS with varying amounts of memory. The definition of ITS includes a parameter S which gives the total amount of memory available to ITS for storing nodes. If S = 0, then ITS retracts all nodes except those on the current path. For each problem instance p, let ITS(V) be ITS with S = vM, where M is the numlzr of distinct nodes generated by ITS on p. Thus, v = S/M is what frac- tion ITS gets of the amount of memory it would need in order to avoid doing any retractions.’ For example, ITS(l) is ITS with enough memory that it doesn’t need to retract any nodes, and ITS(1/4) is ITS running with l/4 of the amount of memory as ITS( 1). Flow-Shop Scheduling Problem The flow-shop scheduling problem is to schedule a given set of jobs on a set of machines such that the time to finish all of the jobs is minimized. In our experiments, we selected the ‘If we had expressed S as an absolute number rather than a fraction of M, this would not have given useful re- sults, because the number of distinct nodes generated by ITS on each problem instance varies widely. For example, with 100,000 nodes, on some problem instances ITS would have exhausted the available memory very quickly, and on others, it would not even have used the whole memory. Search 1355 Table 1: IDA* and ITS’(O) on the lo-job 3-machine flow-shop scheduling problem. e f algorithm node generations - time (set) IDA* 211308.76 3.93 ITS’(O) 210842.96 4.43 Table 2: ITS(v) on the lo-job 3-machine ~ number of machines to be 3. We used a search-space representation and admissible node evaluation function of Ignall and Schrage [5]. For ITS(O), th ere is a special case to consider. In the flow-shop scheduling problem, it is very easy to generate the successor n’ of a node n. Thus, since IDA* and ITS(O) 11 wi need to keep track of only one successor of n at a time, both IDA* and ITS(O) can generate n’ by modifying the record for n (and undoing this modification later when retracting n’), rather than generating an entirely new record For the flow-shop scheduling problem, we used this technique to improve the efficiency of both IDA* and ITS(O). To distinguish between the normal version of ITS(O) and the improved version, we call the latter ITS’(O). We ran IDA* and ITS’(O) on 100 problem instances with 10 jobs in the jobset. The processing times of the jobs on the three machines were generated randomly from the range [O,lOO] using a uniform distribution. Table 1 presents the average node generation and run- ning time figures for IDA* and ITS’(O) on these prob- lem instances. As can be seen, ITS’(O) generated fewer nodes than IDA*. However, ITS’(O) took slightly more time than IDA*. This is primarily because the node generation time for this problem is small, and therefore the smaller number of nodes generated by ITS’(O) did not compensate for its slightly higher overhead than IDA* in node selection and retraction. We also ran ITS(v) on the same problem instances, with various values of v. The average node genera- tion and running-time figures for ITS(v) are given in Table 2. The table shows that as the amount of avail- able memory increases, ITS improves its performance in terms of both node generations and running time. Traveling Salesman Problem The traveling sales- man problem is as follows: given a set of K cities with nonnegative cost between each pair of cities, find the cheapest tour. A tour is a path that starting at some initial city visits every city once and only once, and returns to the initial city. We chose the well known method of Little et al and the lower bound man problem. . [7] to represent the search space heuristic for the traveling sales- The technique that we used to improve the efficiency of IDA* and ITS(O) in the flow-shop scheduling prob- lem cannot be used in the traveling salesman problem, because in this problem it is much more difficult to generate the successors of a node. We ran our experiments with the number of cities K equal to 5, 10, 15, 20, 25, 30, 35 and 40. For each value of K, one hundred cost matrices were generated, taking the cost values c(i, j) at random from the inter- val [O,lOO] using a uniform distribution (except when i = j, in which case c(i, j) = 00). Thus, in general the cost matrices were not symmetric and did not satisfy the triangle inequality. The results of our experiments are summarized in Figures 2 through 5, which graph the performance of IDA*, ITS(O), ITS(1/4), ITS(l/%), and ITS(l). From figures 2 and 3, it can be seen that on this problem, ITS(O) makes fewer node generations and runs slightly faster than IDA*. This is because the node generation time is large enough that the extra overhead of ITS over IDA* becomes relatively insignificant, and there- fore the reduction in number of node generations does reduce the running time. Furthermore, the additional memory used by ITS significantly reduces the number of node generations as well as the running time. In order to study how IDA*‘s average-case asymp- totic behavior compares to ITS’s, in figures 4 and 5 we have plotted ratios of node generations and run- ning time of IDA* and ITS. The interesting point to be noted about these graphs is that in each case, the ratio first goes up and then goes down. If ITS’s asymp- totic performance were strictly better than IDA*‘s, we would have expected the ratios to keep going up. Since Theorem 4 shows that ITS’s asymptotic performance is at least as good as IDA*%, that both algorithms have the same asymptotic performance on this prob- lem. Since this behavior also occurs for ITS(l), which is essentially a version of A*, this suggests that both ITS and IDA* are asymptotically optimal on the trav- eling salesman problem (at least in the case when the costs between cities are generated uniformly from a fixed range). 15-Puzzle The 15-puzzle problem consists of a 4 x 4 frame containing fifteen numbered tiles and an empty position usually known as the “blank”. The valid moves slide any tile adjacent to the blank horizontally or vertically to the adjacent blank position. The task is to find a sequence of valid moves which transform some random initial configuration to a desired goal configu- ration. The manhattan distance function was used as the heuristic in our experiments. In the 16puzzle, we made the same efficiency- improving modification to IDA* that we made in the flow-shop scheduling problem. We considered making the same modification to ITS(O), but decided not to run ITS(O) at all on this problem, for the following reason. In the 15-puzzle, with the manhattan distance heuristic, the threshold in every iteration of IDA* and 1356 Search Figure 2: Nodes versus no. of cities. Number of cities Figure 3: Time versus no. of cities. o = ratio IDA-/ITS(O) + = ratio IDA’IITS(l/4) x = ratio IDAVITS(V2) - = ratio lDAVlTS(1) Number of oitles. Figure 4: IDA* to ITS nodes, versus no. of cities. 20 1 18- 16- 14- ti g12- P .- $ lo- ‘8 .o d 8- B- o _ ratio IDAVTS(0) + = ratio IDA-/ITS(1/4) x = ratio IDA /ITS(lR) * _ ratio IDA./ITS(lJ Number of oitiea. Figure 5: IDA* to ITS time, versus no. of cities. I 2 4 18 20 Figure 6: ITS to IDA* nodes on 20 problem instances. o - ITS(S-lOO.OUJ) I IDA* + - ITS(Sd3OO,Of,O) I IDA” - - lTS(S-600.000) I IDA. Figure 7: ITS to IDA* time on 20 problem instances. ITS increases by exactly two. Also, if z is the thresh- old during the current iteration, every tip branch (p, q) whose B value exceeds z has B(p, q) = z + 2. This makes it useless to back-up B values during retraction, because every node that is retracted in iteration i must be regenerated in iteration i + 1. Thus, in order to im- prove the efficiency of ITS( 0) on this this problem, we should not only simplify the node-generation scheme as described in the flow-shop scheduling problem, but should also remove the back-up step. But that makes ITS(O) essentially identical to IDA*. The same reasoning suggests that on the 15-puzzle, even if S # 0, ITS will not reduce the number of node generations very much in comparison with IDA*. If IDA* makes I iterations on a problem, then ITS with S amount of memory will save at most S * I number of node generations. Since I is usually small for 15-puzzle (between 5 and lo), the actual savings is expected to be relatively small. Thus, since ITS has higher overhead than IDA*, we would expect ITS to take more time than IDA* on this problem. To confirm these hypotheses, we ran ITS and IDA* with S = 100,000,300,000, and 600,000 on the twenty problem instances on which Chakrabarti et al. ran MA*(O). We could not run ITS(v) on these problem in- stances because the number of distinct nodes is so large on some of the problem instances that they exceed the available memory. Therefore, we had to run ITS with fixed values for S. The results are summarized in Fig- ures 6 and 7. As expected, ITS did not achieve a sig- Search 1357 nificant reduction in the number of node generations, and took significantly more time than IDA*.2 Thus, for the 15-puzzle, IDA* is the preferable algorithm. Related Work Following IDA*, several other limited-memory algo- rithms have been designed to reduce the number of node generations compared to IDA*. These algo- rithms can be categorized into two classes: (1) the first class uses additional memory to store more nodes than IDA*, and thereby reduce regeneration of some nodes. The algorithms which belong to this class are MREC, MA*, RA” [3], SMA* [lo], and ITS, and (2) the second class of algorithms attempts to reduce node regenera- tions by reducing the number of iterations, by increas- ing the threshold more liberally than IDA*. IDA*XR [ill, DE’s* [% and MIDA* [13] belong to this class. Like IDA*, MREC is a recursive search algorithm. The difference between MREC and other algorithms in its class is that MREC allocates its memory statically, in the order in which nodes are generated. Algorithm MA* makes use of the available memory in a more in- telligent fashion, by storing the best nodes generated so far. MA* does top-down and bottom-up propaga- tion of heuristics and generates one successor at a time. RA* and SMA* are simplified versions of MA*, with some differences. Although algorithms MA*, RA*, and SMA* are limited-memory algorithms, their formulation is more similar to A*‘s than IDA*‘s. They all maintain OPEN and CLOSED, select the best/worst node from OPEN for expansion and pruning. Therefore, their node gen- eration/pruning overhead is much higher than IDA*‘s. As a result, even if they generate fewer nodes than IDA*, they do not always run faster than IDA*. ITS’s formulation is similar to IDA*‘s and therefore has a low node-generation overhead than any of them. Algorithms IDA*CR, MIDA*, and DFS* work sim- ilar to IDA* except that they set successive thresh- olds to values larger than the minimum value that ex- ceeded the previous threshold. This reduces the num- ber of iterations and therefore the total number of node generations. However, unlike IDA*, the first solution found by these algorithms is not necessarily optimal and therefore to guarantee optimal solution, these al- gorithms revert to depth-first branch-and-bound in the last iteration. Finally, it should be noted that the techniques used in the two classes of algorithms can be combined. Conclusion We have presented a new algorithm called ITS for tree search in limited memory. Like IDA*, ITS has low 20ddly, Figure 7 shows a relative improvement for ITS at the two largest problem sizes. However, we suspect that these data are spurious, because on these two problem in- stances, we exceeded the maximum integer size of some of our counters and also encountered thrashing. 1358 Search node-generation overhead-and like MA*, it makes dy- namic use of memory. Our theoretical analysis shows that, ITS never does more node generations than IDA* and there are trees where it generates fewer nodes than IDA*. Our experimental results indicate that with ad- ditional memory, ITS can significantly reduce the num- ber of node generations and run faster on problems for which the node-generation time is sufficiently high. PI PI PI PI PI PI PI PI PI WI Pll [121 PI References P. P. Chakrabarti, S. Ghosh, A. Acharya, and S. C. De Sarkar. Heuristic search in restricted memory. Artif. Intel., 471197-221, 1989. R. Dechter and J. Pearl. Generalized best-first search strategies and the optimality of A*. JACM, 32(3):505-536,1985. M. Evett, J. Hendler, A. Mahanti, and D. Nau. PRA*: A memory-limited heuristic search pro- cedure for the connection machine. In Fron- tiers’90: Frontiers of Massively Parallel Compu- tation, 1990. S. Ghosh. Heuristic Search with Limited Re- sources. PhD thesis, Department of Computer Science, University of Maryland, I994 (forthcom- ing) . E. Ignall and L. Schrage. Applications of the branch and bound technique to some flow- shop scheduling problems. Operations Research, 13(3):400-412, 1965. R. E. Korf. Depth first iterative deepening: An optimal admissible tree search. Artif. Intel., 27:97-109, 1985. J. D. Little, K. G. Murty, D. W. Sweeney, and C. Karel. An algorithm for the traveling salesman problem. Operations Research, 11:972-989, 1963. B. G. Patrick, M. Almulla, and M. M. Newborn. An upper bound on the complexity of iterative- deepening-A *. In Symposium on Artif. Intel. and Mathematics, Fort Lauderdale, FL, 1989. V. N. Rao and V. Kumar R. E. Korf. Depth-first vs. best-first search. In AAAI-1991, pages 434- 440, Anaheim, California, 1991. S. Russell. Efficient memory-bounded search methods. In ECAI-1992, Vienna, Austria, 1992. U. K. Sarkar, P. P. Chakrabarti, S. Ghose, and S. C. De Sarkar. Reducing reexpansions in it- erative deepening search by controlling cutoff bounds. Artif Intel., 50(2):207-221, 1991. A. Sen and A. Bagchi. Fast recursive formulations for best-first search that allow controlled use of memory. In IJCAI-89, pages 274-277, 1989. B. W. Wah. MIDA*, an IDA* search with dynamic control. Technical Report UILU- ENG-91-2216, University of Illinois at Urbana, Champaign-Urbana, IL, 1991. | 1994 | 277 |
1,627 | Memory-Bounded Bidirectional Search Hermann Kaindl Siemens AG Gsterreich Geusaugasse 17 A-1030 Wien, Austria - Europe e-mail: kaih@siemens.co.at Abstract Previous approaches to bidirectional search require ex- ponential space, and they are either less efficient than unidirectional search for finding optimal solutions, or they cannot even find such solutions for difficult prob- lems. Based on a memory-bounded unidirectional algorithm for trees (SMA*), we developed a graph search extension, and we used it to construct a very ef- ficient memory-bounded bidirectional algorithm. This bidirectional algorithm can be run for difficult prob- lems with bounded memory. In addition, it is much more efficient than the corresponding unidirectional search algorithm also for finding optimal solutions to difficult problems. In summary, bidirectional search appears to be the best approach to solving difficult problems, and this indicates the extreme usefulness of a paradigm that was neglected for long. Notation s,t l-1 (4 ra (4 d d’ d(n) hf (4 il$f h44 F$) c* c L min TREES TREES OPEN; CLOSED~ PC (4 Start node and goal node, respectively. Successors of node n in the problem graph. Parents of node n in the problem graph. Current search direction index; when search is in the forward direction d = 1, and when in the backward direction d = 2. 3 - d; it is the index of the direction opposite to the current search direction. Cost of an optimal path from s to n if i = 1, or from t to n if i = 2. Cost of an optimal path from n to t if i = 1, or from n to s if i = 2. Estimates of g:(n) and hf (n), respectively. Static evaluation function. Revised evaluation after pathmax or backup. Cost of an optimal path from s to t. Cost of a solution path from s to t found. Cost of the best (least costly) complete path found so far from s to t. The forward search tree. The backward search tree. The set of open nodes in TREES. The set of closed nodes in TREE;. Parent of node n in TREES. Introduction Originally, bidirectional heuristic search did not work as expected. Although the bidirectional approach was Aliasghar Khorsand Huglgasse 13- 15/6 A-1150 Wien Austria - Europe shown to be more efficient than its unidirectional coun- terpart when heuristic knowledge is unavailable, the inverse result was found in experiments with BHPA using a heuristic evaluation function (Pohl 1971). BS* (Kwa 1989) improved BHPA technically, but its perfor- mance was only nearly as good as the unidirectional A* (Hart, Nilsson, & Raphael 1968). There was consen- sus that bidirectional heuristic search is afflicted with the problem of search fronts missing each other. Con- sequently, wave-shaping techniques were investigated (de Champeaux & Sint 1977; de Champeaux 1983; Davis, Pollack, & Sudkamp 1984; Politowski & Pohl 1984). This work showed that bidirectional heuristic search can be rather efficient in terms of the number of expanded nodes. However, these algorithms are either excessively computationally demanding, or they have no restriction on the solution quality. Recent results show that the missing of the search fronts is not the central problem (KG11 & Kaindl 1993). In fact, the fronts typically meet rather early. How- ever, when aiming for optimal solutions, much effort has to be spent for subsequently improving the solu- tion quality, and finally for proving that there is indeed no better solution possible. Therefore, only slightly re- laxing the requirements on the solution quality yields strong improvements in efficiency. In fact, the algorithms presented in (Kiill & Kaindl 1993) proved that the bidirectional paradigm is effi- cient in terms of node expansions when searching for &-admissible solutions, without using computationally very demanding wave-shaping techniques.’ However, while efficient linear-space algorithms like IDA* (Korf 1985) and RBFS (Korf 1993) have been developed for the unidirectional case, classical bidi- rectional search typically requires exponential space. (Usually, two classical best-first searches like A* are used for the opposing search fronts.) In fact, is seems impossible to implement bidirectional search ‘A search algorithm is called &-adwzissible if it guaran- tees that solution costs are bounded by (1 + e)C*, i.e., a factor of the cost of an optimal solution (Pearl & Kim 1982; Pearl 1984). This is the same approach as the one of an e-approximate algorithm (Horowitz & Sahni 1978) which shall find approximate solutions to NP-hard problems. Search 1359 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. with linear-space requirement, since at least part of one of the search fronts must be in memory in or- der to recognize meeting of these fronts. Therefore, it would seem that bidirectional search cannot be used for problems of the same difficulty as solvable by linear- space algorithms due to its apparently inherent mem- ory requirement .2 In this paper, we show how bidirectional search can be performed very efficiently using bounded mem- ory. The key idea is to use a unidirectional algorithm that is memory-bounded by it own - instead of best- first algorithms with exponential memory requirements like A*. From several such approaches existing to- day (MA* (Chakrabarti et ad. 1989), MREC (Sen & Bagchi 1989), the approach of using certain tables for IDA* (Reinefeld & Marsland 1991)) and ITS (Ma- hanti et al. 1992)), we selected the first one, since it grows the search tree dynamically. Unfortunately, there are several technical problems with the algorithm MA*. Therefore, we used the improved SMA* by Rus- sell (Russell 1992) as a basis for our bidirectional al- gorithms. Actually, we extended it first for directed acyclic graphs (which is not trivial due to its strategy of deleting and re-generating nodes). While our bidirectional algorithm does not contain additional new techniques, it is a rather complicated integration of several approaches. This integration is necessary for showing an important result: bidirec- tional heuristic search can be performed efficiently with bounded memory, and it can be more efficient than cor- responding unidirectional search also for finding opti- mal solutions. First, we describe the development of an &- admissible graph search extension of SMA* - we named it WSMAG* (weighted simplified memory- bounded A* for graphs). Based on it, we show our con- struction of bidirectional search with bounded mem- ory - the algorithm we present here is called EBBS (memory-bounded bidirectional search). Then we il- lustrate the key results and compare them to related work. Finally, we discuss why our approach works well. An C-Admissible Graph-Search Extension of SMA* A short review of SMA* SMA* is a direct successor of MA*. A key idea of these algorithms is to tradeoff the number of nodes generated and the number of nodes saved. They retain as many nodes as possible, and prefer to retain the most promising ones. As soon as the given memory limit is reached, MA* prunes all but the ones with the best evaluation (f-cost). In contrast to A*, these algorithms only partially-expand nodes, generating the successors one at a time. 2A bidirectional algorithm sketched in (Korf 1985) uti- lizes depth-first iterative-deepening (without using heuristic knowledge). Still, its space requirement is O(bdi2). Unfortunately, MA* is quite complicated and very difficult to implement efficiently (Korf 1993). Even worse, it is not correct in the sense that it can return suboptimal solutions (Mahanti e-t al. 1992), although Chakrabarti et al. claimed its admissibility. SMA* improves MA*, since it preserves information using “pathmax” with the backed-up f-costs (see line 9 in the pseudocode of WSMAG* in Appendix A), while &/‘A* loses this information. Moreover, SMA* main- tains fewer f-cost quantities (making it simpler), and it backs up values once per fully-expanded node, rather than once per node generated (reducing the overhead). Finally, SMA* adds and prunes only one node at a time (saving re-generations of nodes). Unfortunately, the pseudocode in (Russell 1992) con- tains some few bugs. 3 An improved (and more formal) pseudocode of SMA* can be found in Appendix A, when omitting lines 10 and 11, and using E = 0 in line 8. Moreover, SMA* as presented in (Russell 1992) only deals with the case of finding optimal solutions and tree search. &-admissibility The extension of SMA* to an E-admissible version is analogous to the corresponding extensions of IDA* to WIDA* or of A* to WA* (which we call HPA* for historic reasons) (Korf 1993). It is just necessary to multiply the heuristic component h of the usual A*- type evaluation by a weight. According to the notation in (Pearl & Kim 1982), we use the weight (1 + E) (see line 8 of WSMAG* in Appendix A). We named this e-admissible algorithm WSMA* . Graph search The extension of SMA* from searching trees to dealing with directed acyclic graphs is less trivial. In A*, this issue is usually dealt with by simply moving a repeat- edly found node from CLOSED back to OPEN. Such simple attempts for a straight-forward solution can lead to infinite loops due to SMA*‘s strategy of delet- ing and re-generating nodes (Khorsand 1994). The best way to solve this issue that we found uses a tech- nique we call blocking (see the pseudocode of GRAPH- CONTROL in Appendix A). Whenever a new path to a node already stored is found, a distinction is made whether the new path is better than the old one. If this is not the case, the arc from the parent on the new path 3best - deepest least-f-cost leaf in OPEN; should be . . . node . . . instead of . . . leaf . . . . since each partially expanded node should be selectable for further expansion; delete shallowest, highest-f-cost node in OPEN; should be . . . leaf . . . instead of . . . node . . . . since only nodes without any generated successor can be deleted safely; the procedure BACKUP should have the structure given in Appendix A; otherwise no backup of the value could occur to the root. 1360 Search is permanently deleted, otherwise the one from the par- ent on the old path. Moreover, when the new path is better, the subtree previously grown from this node is pruned. In both cases it must be checked whether the other successors of the respective parent of the com- mon node are also blocked. If this is the case and this parent node is already completed, then also this node is deleted, and the blocking mechanism is performed recursively (see SUCC-CHECK in Appendix A). We call the resulting (E-admissible) algorithm for di- rected acyclic graphs WSMAG* (for details see (Khor- sand 1994)). The complete pseudocode is given in Ap- pendix A. Bidirectional Heuristic Search with ounded Memory The classical approaches to implementing bidirectional search typically use A*- or HPA*-type search from both sides concurrently. On a single processor, of course, only one direction can be followed at a time. For the selection of search direction, (Pohl 1971) pro- posed the so-called cardinality criterion (see line 4 of EBBS in Appendix B). Since this approach runs into trouble when the mem- ory is limited, we use instead the memory-bounded WSMAG* algorithm from both sides. In the follow- ing, we sketch the development of an efficient memory- bounded bidirectional algorithm based on this ideaa First, the two search fronts using WSMAG* must meet each other. Since both these dynamically grown trees are stored, this meeting can be efficiently checked using hashing. However, meeting just means that any solution was found. Therefore, it may be necessary to continue the search until a solution of required quality is detected. Even if that is the case, the search may not yet know it. The termination condition of a heuristic bidirec- tional search is usually based on the best heuristic estimates in both search fronts. When dealing with E-admissible search, an improved termination condi- tion as introduced in IBST (Kg11 & Kaindl 1993) can be used (see line 3 of MBBS in Appendix B). Since for checking this termination condition the g + h-values are needed (in addition to the F-costs used by SMA*), the backup procedure was extended accordingly. Moreover, it is useful to consider whether and how the technical improvements of BS* (Kwa 1989) to BHPA are also applicable in our approach.5 Because 4 Actually, we developed several bidirectional algorithms along the lines of (KG11 & Kaindl 1993), but we focus on the most efficient one in this paper. The other algorithms and details are described in (Khorsand 1994). 5These improvements are the following: (i) nipping: When a node is selected for expansion which is already closed in the opposite search tree, it can just be closed without expansion. (ii) pruning: In the same situation, descendants of this node in the opposing OPEN list can be removed. (iii) trimming: Open Nodes (in both directions) whose f- of the partial-node-expansion strategy of SMA* as well as its method of deleting and re-generating nodes, there are significant differences to BS* that do not al- low the use of its nipping and pruning technique in our approach. However, trimming and screening are very useful especially for the task of finding optimal solu- tions, and these techniques fit well into the paradigm of deleting nodes by SMA* ( see lines 14-16 and 31-33 of &?‘BBS in Appendix B). However, similar to the exten- sion of dealing with graphs, it is necessary here to use the blocking technique described above. The parents of the currently best node (in the case of screening) or of all the trimmed nodes must be checked whether their other successors are also blocked (see lines 16 and 33). The pseudocode of A&BBS is given in Appendix B. Its subroutines are analogous to those of WSMAG*. Results Given an admissible heuristic h, both WSMAG* and n/i’BBS are e-admissible, i.e., if a path exists from s to t, they terminate with a solution whose cost does not exceed the optimal cost by more than a factor (1 + &). Due to lack of space we cannot include here the formal proofs (see (Khorsand 1994)). Below we summarize the empirical results of exten- sive experiments on an NP-complete problem (find- ing optimal solutions to the 15-Puzzle) and on the re- laxed problem of finding near-optimal solutions (with a guaranteed worst-case bound). Fig. 1 compares WSMAG* and MBBS (storing 256k nodes) with sev- eral algorithms. 6 The x-axis represents various val- ues of E, the given worst-case bound as guaranteed by these algorithms. The comparison is in terms of generated nodes as, e.g., in (Kiill & Kaindl 1993; Korf 1993), and the y-axis shows the average number of node generations on the 15-Puzzle on a logarithmic scale. This figure and statistical tests (for details see (Khorsand 1994)) d emonstrate the following key re- sults: 8 Significant superiority of EBBS to (unidirectional) linear-space search in terms of generated nodes On the whole range, EBBS generates much fewer nodes than WIDA* and RBFS. Therefore, EBBS makes excellent use of the modest amount of mem- ory given - 256k nodes: 2 orders of magnitude more values are > L,,, can be removed. (iv) scP-een&g: Nodes whose f-values to be stored in the OPEN lists. are 2 L,,, need not 6We have used the set of 100 instances from (Korf 1985). The data in the figure currently lack the results of the 11 most difficult problems, since these experiments are for some of the algorithms still running at the time of this writ- ing. Since HPA* and IBS,* cannot solve all these instances for all values of E even when storing millions of nodes, their corresponding lines are not complete in this figure. Search 1361 I I I 0 0.25 0.5 0.75 1 e Figure 1: Comparison on the 15-Puzzle. nodes are generated in the average for finding opti- mal solutions. However, for the task of finding opti- mal solutions (E = 0), WIDA* is still faster on this puzzle (see below). Significant superiority of the novel bidirectional ap- proach to the corresponding unidirectional one (us- ing the same amount of memory) Also for finding optimal solutions MBBS is signif- icantly better than both WSMA* and WSMAG*. Generally, the improvement is even slightly stronger comparing the run time, since instead of one priority queue the bidirectional algorithm uses two shorter ones. Significant superiority of the memory- bounded bidi- rectional search to classical (unidirectional) best-first search (HPA*) The improvement in terms of node generations is sta- tistically significant, although MBBS stores much fewer nodes. For E 5 0.5, HPA* cannot even find solutions to all the problems even when storing mil- lions of nodes. Comparable results of the memory-bounded to more classical bidirectional search (IBS,*), that uses much more memory The memory-bounded approach is even significantly better for E = 0.25 due to its partial node expan- sions . Despite Russell’s improvements to MA*, an efficient implementation of these memory-bounded algorithms is non-trivial (see (Khorsand 1994) for the data struc- tures used instead of the binary trees of binary trees suggested by Russell, which are not efficient for the (usual version of) the sliding-tile puzzles with uniform- cost evaluation). Unfortunately, it strongly depends on the domain and also the efficiency of implementa- tion, whether the overhead of maintaining the priority queues is deteriorating the performance or not. In par- ticular, the importance of the overhead depends on the effort for computing heuristic values. Even the ma- chine architecture can influence the relative running time when there are differences in the size of memory used. While node generation and evaluation is very efficient for the sliding-tile puzzles (Korf 1993), we pri- marily wanted to compare the algorithms on a basis that is more independent of such factors. Compared to the worst-case bound E, the average solution quality is much better for all the algorithms compared here. For E = 0.25, e.g., the cost C of a solu- tion found must be < 1.25 times the cost of an optimal solution C*. In the average, MBBS finds solutions of quality C = l.O4C* here, i.e., they are only 4 percent worse than optimal ones, which require about eighty times more node generations to be found. Related Work Apart from the genesis of M BBS based on the unidi- rectional A*, MA* and SMA*, as well as the bidirec- tional BHPA, BS* and IBSZ, there are some relations to other unidirectional search algorithms with reduced space requirements. We focus here on their results on the sliding-tile puzzles: MREC (Sen & Bagchi 1989) did not achieve a real improvement over IDA*, partly because they used a tree version; (Korf 1993) reports that the number of node generations of a graph version storing 1OOk nodes reduced the number of node generations by 41 percent compared to IDA* on the 15-Puzzle; ITS (Mahanti et al. 1992) generated the same num- ber of nodes as IDA* on the 15-Puzzle; the best version of the approach of using certain ta- bles for IDA* (Reinefeld & Marsland 1991) examined 45.82 percent of the nodes generated by pure IDA*, storing 256k nodes. In summary, all these algorithms are less efficient than our bidirectional search algorithm MBBS even for finding optimal solutions (at least on the difficult 15-Puzzle and in terms of node generations). More- over, MBBS can find near-optimal solutions with a guaranteed worst-case bound, a task on which it is even much more efficient. Discussion An interesting question is how this bidirectional ap- proach can be better than its unidirectional counter- part. In an exponential search space, bidirectional search has the potential to divide the exponent by 2. However, the first results with bidirectional heuristic search were bad (Pohl1971), and the explanation given there in terms of the missile metaphor was misleading. The primary issue appears to be that after the first meeting especially a bidirectional algorithm aiming for optimal solutions has to spend much effort for subse- quently improving the solution quality, and finally for proving that no other open node can give a better so- lution (KG11 & Kaindl 1993). Therefore, only a slight relaxation of solution quality already leads to strong improvements in efficiency, and in particular to even 1362 Search more than in the unidirectional case. Actually, the re- sults of MBBS for E = 0.25 are relatively much better than those for E = 0. However, Kwa (Kwa 1989) already noted the relative improvement of BS* versus A* with increasing problem difficulty (in the context of finding optimal solutions). This tendency was also observed in the case of find- ing near-optimal solutions (Kc11 & Kaindl 1993). Con- sequently, the dynamic memory utilization of MBBS (based on SMA*) 11 a ows it to perform the bidirectional search efficiently for problems that are difficult enough to make it better than its unidirectional counterpart. Conclusion In summary, we developed a graph search extension of SMA*, and we used this unidirectional algorithm to construct a very efficient memory-bounded bidirec- tional algorithm. This algorithm can use as much memory as there is available (a constant amount). The construction of this algorithm uses primarily known techniques (apart from the graph search ex- tension with its novel blocking mechanism). However, this combination is necessary for showing an impor- tant result: bidirectional heuristic search can be per- formed efficiently with bounded memory, and it can be more efficient than its unidirectional counterpart also for finding optimal solutions. If problems are too difficult for finding optimal solu- tions within reasonable time, finding near-optimal (E- admissible with a small e) solutions may help. For this task the bidirectional approach is even better. Acknowledgments We would like to thank Dennis de Champeaux, Gerhard Kainz, and Ira Pohl for comments on earlier versions of this paper. Our implementations are based on the code of WA” provided by Richard Korf. APPENDIX A: Pseudocode of WSMAG* procedure WSMAG*(s, t); 1. OPEN t {s}; CLOSED c 0; USED c 1; 2. while ( OPEN # 0 ) and (no solution found) do /* select deepest node with lowest F-value : */ 3. B c {x 1 (x E OPEN) A (Vy E OPEN: F(x) I F(y))}; /* set of nodes with lowest F-value */ 4. selectbestE {XIXE BA(V~E B:g(x)>g(y))}; /* deepest node from B */ 5. if best # t then /* best is not goal */ 6. succ t next-successor e r(best); 7. g(succ) c g(best) + c(best, succ); 8. f(succ) t g(succ) + (1 ++h(succ); 9. F (succ)c max(F(best), f(succ)); /* pathmax */ 10. if succ E TREE then /* succ already stored */ 11. GRAPH-CONTROL; else 12. MEM-CONTROL; 13. OPEN c OPEN u { succ } ; USED t USED + 1; /* insert succ in OPEN */ 14. S(best) t S(best) u { succ}; /* insert succ in best’s successor list */ endif 15. if completed(best) then 16. BACKUP(best); endif 17. if F(best) all in memory then 18. OPEN t OPEN \ {best } ; 19. CLOSED t CLOSED u {best} ; /* close best *I endif endii endwhile endprocedure procedure MEM-CONTROL; /* ifmemory is full, delete a node */ 1. ifUSED = MAX then /* delete shallowest, highest- F-value leaf in OPEN, a leaf node has no successor either in OPEN or CLOSED : 2. W+{X~(XE oPEN)r\(tr’y~ OPEN:F(x)ZF(y))}; 3. select worst E {x I x E W A (Vy E W: g(x) I g(y)) A (S(x) = 4. delete worst; 5. USED t USED - 1; /* remove worst from its parent’s succ. 6. S(p(worst)) c S(p(worst)) \ {worst}; 7. if p(worst) E CLOSED then 8. CLOSED t CLOSED \ { p(worst) }; 9. OPEN t OPEN u { p(worst)}; endif endif endprocedure procedure BACKUP(n) /* back up F-values */ 1. if completed(n) then /* least F-value of all successors: */ 2. newF t F(x) I x E F(n) A (Vy E I’(n): F(x) 5 F(y)); 3. if newF > F(n) then 4. F(n) t newF; 5. reorder OPEN according to new F-value; 6. if n has a parent then 7. BACKUP(p(n)); endif endif endprocedure */ 011; list */ procedure GRAPH-CONTROL; I* deal with directed acyclic graphs *I 1. old t old node which is equal to succ ; 2. if g(succ) 2 g(old) then I* new path is not better “1 3. block succ in best’s successor list; 4. SUCC-CHECK(best); else I* a better path to old has been found *I 5. prune subtree(old); /* remove all nodes which are in subtree with root old */ 6. block old in p(old)‘s successor list; 7. USED c USED - lsubtree (old)l; 8. SUCC-CHECK(p(old)); 9. OPEN t OPEN u { succ }; USED t USED + 1; /* insert succ in OPEN */ 10. S(best) t S(best) u [ succ } ; /* insert succ in best’s succ. list */ endif endprocedure procedure SUCC-CHECK(n) /* checks whether the other successors are also “blocked” */ 1. if completed(n) and n has only “blocked” successors then 2. delete n; USED t USED - 1; 3. block n in p(n)‘s successor list; Search 1363 4. if n has a parent then 5. SUCC-CHECK(p(n)); endif else 6. BACKUP(n); endif endprocedure APPENDIX B: Pseudocode of MBBS procedure MBBS(s, t); 1. OPEN,+ {s}; OPEN, t {t}; CLOSED, c CLOSED, t 0; 2. USED, t USED, c 1; Lmint 00; 3. while (OPEN, # 0 ) and (OPEN, # 0 ) 4. 5. 6. 7. a. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. and <i,in > (l+E)*max(gh&inl, ghmin*)) do if IOPEN, I I IOPEN,I then /* cardinal@ criterion Y dc l;elsedc2; endif d’c3-d; /* set the opposite search direction */ Trimflag t false; /* select deepest node with lowest F-value : */ B t- {x 1 (x E OPEN,) A (Vy E OPEN‘,: F,(x) I F,(y)>}; /* set of nodes with lowest F-value V select best E {x I x E B A (Vy E B: g,(x) 2 g,(y))}; /* deepest node from B */ succ t next-successor E rd(best); gd(succ) c gd(best) + c(best, succ); fd(succ) t gd(succ) + (l+~)~h~(succ); Fd(succ) t max(F&best), f&succ)); /* pathmax */ if gd(succ) + h&succ) 2 Lmin then /*screening */ block succ in best’s successor list; SUCC-CHECK(best); else if succ E TREE, then /* succ already stored V GRAPH-CONTROL; else MEM-CONTROL; OPEN, t OPEN, u { succ}; USED, t USED, + 1; /* insert succ in OPEN */ S&best) t S&best) u { succ} ; /* insert n succ best’s successor list */ endif if succ E TREE,, and gl(succ) + g,(succ> c Lmin then /* better solution found */ Lmin t gl(““) + g2(““); /* update Lmin */ MeetingNode c succ; Trimflag t true; endif endif if compZeted(best) then NEW-BACKUP(best); endif if rd(best) all in memory then OPEN, c OPEN, \ {best} ; CLOSED, + CLOSED, u {best}; /close best */ endif if Trimflag then /* trimming Y remove from OPEN, and OPEN, those nodes n with g(n) + h(n) 2 Lmin and which have no successors and are not source or meeting nodes; block them in their parent’s successor list;. SUCC-CHECK(p(n)); /* parents of all removed nodes */ endif endwhile endprocedure References Chakrabarti, P.; Ghose, S.; Acharya, A.; and DeSarkar, S. 1989. Heuristic search in restricted memory. ArtificiaZ Intelligence 41(2):197-221. Davis, H.; Pollack, R.; and Sudkamp, T. 1984. Towards a better understanding of bidirectional search. In Proc. of AAAI-84,68-72. Austin, TX: Los Altos, CA.: Kaufmann. de Champeaux, D., and Sint, L. 1977. An improved bidi- rectional heuristic search algorithm. J. ACM 24:177-191. de Champeaux, D. 1983. Bidirectional heuristic search again. J. A CM 30~22-32. Hart, P.; Nilsson, N.; and Raphael, B. 1968. A formal ba- sis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics @SC) SSC-4(2):100-107. Horowitz, E., and Sahni, S. 1978. Fundamentals of Com- puter Algorithms. New York: Springer-Verlag. Khorsand, A. 1994. Heuristische Graph-Suche mit be- grenzbarem Fehler und Speicherbedarf sowie Einheits- kosten. Diplomarbeit, Technische Universitgt Wien. Kiill, A., and Kaindl, H. 1993. Bidirectional best-first search with bounded error: Summary of results. In Proc. Thirteenth International Joint Conference on Artificial Intelligence (IJCAI-93), 217-223. Korf, R. 1985. Depth-first iterative deepening: An optimal admissible tree search. Artificial Intelligence 27(1):97-109. Korf, R. 1993. Linear-space best-first search. Artificial Intelligence 62( 1):41-78. Kwa, J. 1989. BS’: An Admissible Bidirectional Staged Heuristic Search Algorithm. Artificial Intelligence 38(2):95-109. Mahanti, A.; Nau, D.; Ghosh, S.; and Kanal, L. 1992. An efficient threshold heuristic tree search algorithm. Tech- nical Report UMIACS TR 92-29, CS TR 2853, Com- puter Science Department, University of Maryland, Col- lege Park, Md. Pearl, J., and Kim, J. 1982. Studies in semi-admissible heuristics. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI) 4(4):392-399. Pearl, J. 1984. Heuristics: Intelligent Search Strategies for Computer Problem Solving. Reading, MA: Addison- Wesley. Pohl, I. 1971. Bi-directional search. In Machine In- telligence 6, 127-140. Edinburgh: Edinburgh University Press. Politowski, G., and Pohl, I. 1984. D-node retargeting in bidirectional heuristic search. In Proc. of AAAI-84, 274- 277. Austin, TX: Los Altos, CA.: Kaufmann. Reinefeld, A., and Marsland, T. 1991. Memory functions in iterative-deepening search. Technical Report FBI-HH- M-198/91, Fachbereich Informatik, Universitgt Hamburg, Hamburg, Germany. Russell, S. 1992. Efficient memory-bounded search meth- ods. In Proc. Tenth European Conference on Artificial In- telligence (ECAI-92), 1-5. Vienna, Austria: Chichester: Wiley. Sen, A., and Bagchi, A. 1989. Fast recursive formulations for best-first search that allow controlled use of memory. In Proc. Eleventh International Joint Conference on Ar- tificial Intelligence (IJCA I-89), 297-302. 1364 Search | 1994 | 278 |
1,628 | Best-First Minimax Search: Othello Results Richard E. Korf and David Maxwell Chickering Computer Science Department University of California, Los Angeles Los Angeles, Ca. 90024 korf@cs.ucla.edu Abstract We present a very simple selective search algorithm for two-player games. It always expands next the frontier node that determines the minimax value of the root. The algorithm requires no information other than a static evaluation function, and its time overhead per node is similar to that of alpha-beta minimax. We also present an implementation of the algorithm that reduces its space complexity from exponential to lin- ear in the search depth, at the cost of increased time complexity. In the game of Othello, using the evalu- ation function from BiIl (Lee & Mahajan 1990), best- first minimax outplays alpha-beta at moderate depths. A hybrid best-first extension algorithm, which com- bines alpha-beta and best-first minimax, performs sig- nificantly better than either pure algorithm even at greater depths. Similar results were also obtained for a class of random game trees. Introduction and Overview The best chess machines are competitive with the best humans, but generate millions of positions per move. Their human opponents, however, only examine tens of positions, but search much deeper along some lines of play. Obviously, people are more selective in their choice of positions to examine. The importance of se- lective search was first recognized by (Shannon 1950). Most work on game-tree search has focussed on algorithms that make the same decisions as full- width, fixed-depth minimax. This includes alpha-beta pruning (Knuth & Moore 1975), fixed and dynamic node ordering (Slagle & Dixon 1969), SSS* (Stock- man 1979), Scout (Pearl 1984), aspiration-windows (Kaindl, Shams, & Horacek 1991), etc. We define a selective search algorithm as one that makes dif- ferent decisions than full-width, fixed-depth minimax. These include B* (Berliner 1979), conspiracy search (McAllester 1988), min/max approximation (Rivest 1987), meta-greedy search (Russell & Wefald 1989), and singular extensions (Anantharaman, Campbell, & Hsu 1990). All of these algorithms, except singular ex- tensions, require exponential memory, and most have large time overheads per node expansion. In addition, B* and meta-greedy search require more information than a single static evaluation function. Singular ex- tensions is the only algorithm to be successfully incor- porated into a high-performance program. We describe a very simple selective search algorithm, called best-first minimax. It requires only a single static evaluator, and its time overhead per node is roughly the same as alpha-beta minimax. We de- scribe an implementation of the algorithm that reduces its space complexity from exponential to linear in the search depth. We also explore best-first extensions, a hybrid combination of alpha-beta and best-first mini- max. Experimentally, best-first extensions outperform alpha-beta in the game of Othello, and on a class of random game trees. Earlier reports on this work in- clude (Korf 1992) and (Korf & Chickering 1993). Best-First Minimax Search The basic idea of best-first minimax is to always ex- plore further the current best line of play. Given a partially expanded game tree, with static evaluations of the leaf nodes, the value of an interior MAX node is the maximum of its children’s values, and the value of an interior MIN node is the minimum of its children’s values. There exists a path, called the principal varia- tion, from the root to a leaf node, in which every node has the same value. This leaf node, whose evaluation determines the mini max value of the root, is called the principal leaf. Best-first minimax always expands next the current principal leaf node, since it has the greatest affect on the minimax value of the root. Consider the example in figure 1, where squares rep- resent MAX nodes and circles represent MIN nodes. Figure 1A shows the situation after the root has been expanded. The values of the children are their static values, and the value of the root is 6, the maximum of its children’s values. Thus, the right child is the prin- cipal leaf, and is expanded next, resulting in the situa- tion in figure 1B. The new frontier nodes are statically evaluated at 5 and 2, and the value of their MIN par- ent changes to 2, the minimum of its children’s values. This changes the value of the root to 4, the maximum of its children’s values. Thus, the left child of the root is the new principal leaf, and is expanded next, result- Two-Player Games 1365 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. A 6 w 4 6 Figure 1: Best-first minimax search example ing in the situation in figure 1C. The value of the left child of the root changes to the minimum of its chil- dren’s values, 1, and the value of the root changes to the maximum of its children’s values, 2. At this point, the rightmost grandchild is the new principal leaf, and is expanded next, as shown in figure 1D. By always expanding the principal leaf, best-first minimax may appear to suffer from the exploration of a single path to the exclusion of all others. This does not occur in practice, however. The reason is that the expansion of a node tends to make it look worse, thus inhibiting further exploration of the subtree below it. For example, a MAX node will only be expanded if its static value is the minimum among its brothers, since its parent is a MIN node. Expanding it changes its value to the maximum of its children, which tends to increase its value, making it less likely to remain as the minimum among its siblings. Similarly, hlIN nodes also tend to appear worse to their MAX parents when expanded, making it less likely that their children will be expanded next. This tempo effect adds balance to the tree searched by best-first minimax, and increases with increasing branching factor. Surprisingly, while this oscillation in values with the last player to move is the reason that alpha-beta avoids comparing nodes at different levels in the tree, it turns out to be advan- tageous to best-first minimax. While in principle best-first minimax could make a move at any point in time, we choose to move when the length of the principal variation exceeds a given depth bound, or a winning terminal node is chosen for expansion. This ensures that the chosen move has been explored to a significant depth, or leads to a win. The simplest implementation of best-first minimax maintains the current tree in memory. When a node is expanded, its children are evaluated, its value is up- dated, and the algorithm moves up the tree updating the values of its ancestors, until it reaches the root, or a node whose value doesn’t change. It then moves down the tree to a maximum-valued child of a MAX node, or a minimum-valued child of a MIN node, until 1366 Search it reaches a new principal leaf. A drawback of this im- plementation is that it requires exponential memory, a problem that we address below. Despite its simplicity, best-first minimax has appar- ently not been explored before. The algorithm is men- tioned as a special case of AO*, a best-first search of an AND-OR tree, in (Nilsson 1969). The chess algorithm of (Kozdrowicki & Cooper 1973) seems related, but behaves differently on their examples. Best-first min- imax is also related to conspiracy search (McAllester 19SS), and only expands nodes in the conspiracy set. It is also related to Rivest’s min/max approximation (Rivest 1987). Both algorithms strive to expand next the node with the largest affect on the root value, but best-first minimax is much simpler. All four related algorithms above require exponential memory. Recursive Best-First Minimax Search Recursive Best-First Minimax Search (RBFMS) is an implementation of best-first minimax that runs in space linear in the search depth. The algorithm is a generalization of Simple Recursive Best-First Search (SRBFS) (Korf, 1993), a linear-space best-first search designed for single-agent problems. Figure 2 shows the behavior of RBFMS on the example of figure 1. Associated with each node on the principal variation is a lower bound Alpha, and an upper bound Beta, similar to the bounds in alpha-beta pruning. A node will remain on the principal variation as long as its minimax value stays within these bounds. The root is bounded by -oo and 00. Figure 2A shows the situa- tion after the root is expanded, with the right child on the principal variation. It will remain on the principal variation as long as its minimax value is greater than or equal to the maximum value of its siblings (4). The right child is expanded next, as shown in figure 2B. The value of the right child changes to the minimum of its children’s values (5 and 2), and since 2 is less than the lower bound of 4, the right child is no longer on the principal variation, and the left child of the root is the new principal leaf. The algorithm returns to the Figure 2: Recursive best-first minimax search example root, freeing memory, but stores with the right child its new minimax value of 2, as shown in figure 2C. This method of backing up values and freeing memory is similar to that of (Chakrabarti et al. 1989). The left child of the root will remain on the principal variation as long as its value is greater than or equal to 2, the largest value among its siblings. It is expanded, as shown in figure 2D. Its new value is the minimum of its children’s values (8 and 1)) and since 1 is less than the lower bound of 2, the left child is no longer on the principal variation, and the right child of the root becomes the new principal leaf. The algorithm returns to the root, and stores the new minimax value of 1 with the left child, as shown in figure 2E. Now, the right child of the root will remain on the principal variation as long as its minimax value is greater than or equal to 1, the value of its best sibling, and is ex- panded next. The reader is encouraged to complete the example. Note that the values of interior nodes on the principal variation are not computed until necessary. RBFMS consists of two recursive and entirely sym- metric functions, one for MAX and one for MIN. Each takes three arguments: a node, a lower bound Alpha, and an upper bound Beta. Together they perform a best-first minimax search of the subtree below the node, as long as its backed-up minimax value remains within the Alpha and Beta bounds. Once it exceeds those bounds, the function returns the new backed-up minimax value of the node. At any point, the recursion stack contains the current principal variation, plus the siblings of all nodes on this path. Its space complexity is thus O(bd), where b is the branching factor of the tree, and d is the maximum depth. The children of a node are generated and evaluated one at a time. If the value of any child of a MAX node exceeds Beta, or the value of any child of a MIN node is less than Alpha, that child’s value is immediately returned, without generating the remaining children. BFMAX (Node, Alpha, Beta) FOR each Child[i] of Node M cil := Evaluation(Child[i]) IF M[i] > Beta return M[i] SORT ChildCi] and Mb] in decreasing order IF only one child, MC21 := -infinity WHILE Alpha <= ML11 C= Beta MC11 := BFMIN(Child~l],max(Alpha,MC21),Beta) insert ChildCll and MC11 in sorted order return M Cl] BFMIN (Node, Alpha, Beta) FOR each Child[i] of Node MCil := Evaluation(Child[il) IF M[i] < Alpha return M[i] SORT Child[il and Mb] in increasing order IF only one child, MC21 := infinity WHILE Alpha <= MC13 <= Beta MC11 := BFMAX(Child[ll,Alpha,min(Beta,M[2])) insert Child[l] and MC11 in sorted order return M Cl1 Two-Player Games 1367 Syntactically, recursive best-first minimax appears very similar to alpha-beta, but behaves quite differ- ently. Alpha-beta makes its move decisions based on the values of nodes all at the same depth, while best- first minimax relies on node values at different levels.’ Saving the Tree RBFMS reduces the space complexity of best-first min- imax by generating some nodes more than once. This overhead is significant for deep searches. On the other hand, the time per node generation for RBFMS is less than for standard best-first minimax. In the standard implementation, when a new node is generated, the state of its parent is copied, along with any changes to it. The recursive algorithm does not copy the state, but rather makes only incremental changes to a single copy, and undoes them when backtracking. Our actual implementation uses the recursive control structure of RBFMS. When backing up the tree, how- ever, the subtree is retained in memory. Thus, when a path is abandoned and then reexplored, the entire sub- tree is not regenerated, While this requires exponential space, it is not a major problem, for several reasons. The first is that once a move is made, and the oppo- nent moves, we only save the remaining relevant sub- tree, and prune the subtrees below moves that weren’t chosen by either player, releasing the corresponding memory. While current machines will exhaust their memories in minutes, in a two-player game, moves are made every few minutes, freeing much of the memory. The second reason that memory is not a serious con- straint is that only the backed-up minimax value of a node, and pointers to its children must be saved. The actual game state, and alpha and beta bounds, are in- crementally generated from the parent. Thus, a node only requires a few words of memory. If memory is exhausted while computing a move, however, there are two options. One is to complete the current move search using the linear-space algorithm, thus requiring no more memory than for the recur- sion stack. The other is to prune the least promising parts of the current search tree. Since all nodes off the principal variation have their backed-up minimax val- ues stored at all times, pruning is simply a matter of recursively freeing the memory in a given subtree. Since best-first minimax spends most of its time on the expected line of play, it can save much of the tree computed for one move, and apply it to subsequent moves, particularly if the opponent moves as expected. Saving the tree between moves improves the perfor- mance considerably. In contrast, the standard depth- first implementation of alpha-beta doesn’t save the tree from one move to the next, but only a subset of the ‘While Recursive Best-First Search (RBFS) is more ef- ficient than Simple Recursive Best-First Search (SRBFS) for single-agent problems (Korf 1993), the minimax gener- alizations of these two algorithms behave identically.- nodes in a transposition table. Even if alpha-beta is modified to save the tree, since it searches every move to the same depth, relatively little of the subtree com- puted during one move is still relevant after the player’s and opponent’s moves. In the best case, when alpha- beta searches the minimal tree and the opponent moves as expected, only l/b of the tree that is generated in computing one move is still relevant after the player’s and opponent’s moves, where b is the branching factor. Othello Results The test of a selective search algorithm is how well it plays. We played best-first minimax against alpha- beta in the game of Othello, giving both algorithms the same amount of computation, and the same evaluation function from the program Bill (Lee & Mahajan 1990), one of the world’s best Othello players. The efficiency of alpha-beta is greatly affected by the order in which nodes are searched. The simplest ordering scheme, called fixed ordering (Slagle & Dixon 1969), fully expands each node, statically evaluates each child, sorts the children by their values, and then searches the children of MAX nodes in decreasing or- der, and the children of MIN nodes in increasing order. We use fixed ordering on newly generated nodes until one level above the search horizon. At that point, since there is no advantage to further ordering, the children are evaluated one at a time, allowing additional prun- ing. To ensure a fair comparison to best-first minimax, our alpha-beta implementation saves the relevant sub- tree from one move to the next. This allows us to order previously generated nodes by their backed-up values rather than their static values, further improving the node ordering and performance of alpha-beta. Each tournament consisted of 244 pairs of games. Different games were generated by making all possi- ble first four moves, and starting the game with the fifth move. Each game was played twice, with each algorithm moving first, to eliminate the effect of a par- ticular initial state favoring the first or second player to move. An Othello game is won by the player with the most discs at the end. About 3% of the games were tied, and are ignored in the results presented below. When alpha-beta can search to the end of the game, both algorithms use alpha-beta to complete the game, since alpha-beta is optimal when the static values are exact. In Othello, the disc differential is the exact value at the end of the game. Since best-first minimax searches deeper than alpha-beta in the same amount of time, however, it reaches the endgame before alpha- beta does. Since disc differentials are not compara- ble to the values returned by Bill’s heuristic function, best-first minimax evaluates endgame positions at -oo if MAX has lost, 00 if MAX has won, and -oo + 1 for ties. If the principal leaf is a winning terminal node for best-first, it stops searching and makes a move. If alpha-beta makes the expected response, the principal leaf doesn’t change, and best-first minimax will make 1368 Search AB depth 1 2 3 4 S 6 7 BF depth 1 St% 7% i:% 15 19 23 AB depth 1 2 3 4 S 6 7 8 BF wins SO% 57% 68% Sl% BF depth 1 4 7 10 14 18 21 24 BF wins SO% 67% 83% 81% 67% 72% 67% 60% Table 1: Pure best-first vs. alpha-beta on Othello its next move without further search. Conversely, if the principal leaf is a loss or tie, best-first minimax will continue to search until it finds a win, or runs out of time. While this endgame play is not ideal, it is the most natural extension of best-first minimax. For each alpha-beta search horizon, we experimen- tally determined what depth limit caused best-first minimax to take most nearly the same amount of time. This was done by running a series of tournaments, and incrementing the search horizon of the algorithm that took less time in the last tournament. Node evalua- tion is the dominant cost, and running time is roughly proportional to the number of node evaluations. Table 1 shows the results of these experiments. The top line shows the alpha-beta search depths, and the second line shows the best-first search depth that took most nearly the same amount of time as the corre- sponding alpha-beta depth. The third line shows the percentage of games that were won by best-first mini- max, excluding ties. Each data point is an average of 244 pairs of games, or 488 total games. Both algorithms are identical at depth one. At greater depths, best-first searches deeper than alpha- beta, and wins most of the time. Its winning percent- age increases to 78%, but then begins to drop off as the gap between the alpha-beta and best-first horizons becomes very large. At greater depths, we believe that best-first will lose to alpha-beta. Best-First Extensions One explanation for this performance degradation is that while best-first minimax evaluates every child of the root, it may not generate some grandchildren, de- pending on the static values of the children. In partic- ular, if the evaluation function grossly underestimates the value of a node, it may never be expanded. For example, this might occur in a piece trade that begins with a sacrifice. At some point, it makes more sense to consider all grandchildren of the root, rather than nodes 23 moves down the principal variation. To correct this, we implemented a hybrid algorithm, called best-first extension, that combines the uniform coverage of alpha-beta with the penetration of best- first minimax. Best-first extension performs alpha- beta to a shallow search horizon, and then executes best-first minimax to a greater depth, starting with the tree, backed-up values, and principal variation gener- ated by the alpha-beta search. This guarantees that every move will be explored to a minimum depth, re- gardless of its evaluation, before exploring the most promising moves much deeper. This is similar to the Table 2: Best-first extension vs. alphsbeta on Othello idea of principal variation lookahead extensions (Anan- tharaman 1990). Best-first extension has two parameters: the depth of the initial alpha-beta search, and the depth of the subsequent best-first search. In our experiments, the alpha-beta horizon of the initial search was set to one less than the horizon of its pure alpha-beta opponent, and the best-first horizon was whatever depth took most nearly the same total amount of time, includ- ing the initial alpha-beta search, as the pure alpha- beta opponent. Even in this case, most of the time is spent on the best-first extension. Table 2 shows the results for Othello, in the same format as table 1. At alpha-beta depths greater than two, best-first exten- sion performs significantly better than both alpha-beta and pure best-first minimax. At increasing depths the results appear to stabilize, with best-first extension de- feating alpha-beta about two out of three games. Random Game Tree Results As a separate test of our results, we also experimented with a class of random game trees (Fuller, Gaschnig, & Gillogly 1973). I n a uniform random game tree with branching factor 6 and depth d, each edge is indepen- dently assigned a random cost. The static heuristic evaluation of a node is the sum of the edge costs from the root to the node. Since real games do not have uni- form branching factors, we let the number of children of any node be a random variable uniformly distributed from one to a maximum branching factor B. In order not to favor MAX or MIN, the edge-cost distribution is symmetric around zero. Our edge-cost distribution was uniform from -215 to 215. Different random games were generated from dif- ferent random seeds. Each game was played twice, with each algorithm moving first. A random game ends when a terminal position is reached, 100 moves in our experiments, and returns the static value of the final position as the outcome. Given a pair of random games, and the corresponding terminal values reached, the winner is the algorithm that played MAX when the larger terminal value was obtained. Each random game tournament consisted of 100 pairs of games. In random games with maximum branching factors ranging from 2 to 20, we obtained results similar to those for Othello (Korf & Chickering 1993). In par- ticular, pure best-first outplayed alpha beta at shal- low depths, but tended to lose at greater depths, while best-first extension outplayed alpha-beta at all depths. Two-Player Games 1369 Conclusions and Further Work We presented a very simple selective search algorithm, best-first minimax. It always expands next the fron- tier node at the end of the current principal variation, which is the node that determines the minimax value of the root. One advantage of the algorithm is that it can save most of the results from one move com- putation, and apply them to subsequent moves. In experiments on Othello, best-first minimax outplays alpha-beta, giving both algorithms the same amount of computation and evaluation function, up to a given search depth, but starts to lose beyond that depth. We also presented a hybrid combination of best-first minimax and alpha-beta, which guarantees that ev- ery move is searched to a minimum depth. This best- first extension outperforms both algorithms, defeating alpha-beta roughly two out of three games. While memory was not a limiting factor in our experiments, we also showed how to reduce the space complexity of the algorithm from exponential to linear in the search depth, but at significant cost in nodes generated for deep searches. Finally, we performed the same experi- ments on a class of random games, with similar results. Since pure best-first minimax performs best against relatively shallow alpha-beta searches, it is likely to be most valuable in games with large branching fac- tors, and/or expensive evaluation functions. These are games, such as Go, in which computers have been least successful against humans. Current research is focussed on implementing singular extensions in an at- tempt to improve our alpha-beta opponent, and imple- mentations on other games. Acknowledgements Thanks to Kai-Fu Lee for the sources to Bill, to Judea Pearl, Joe Pemberton, and Weixiong Zhang for many helpful discussions, and to Hermann Kaindl for com- ments on an earlier draft. This work was supported by NSF Grant No. IRI-9119825, and a grant from Rock- well International. References Anantharaman, T.S., A statistical study of selective min-max search in computer chess, Ph.D. Thesis, Dept. of Computer Science, Carnegie-Mellon Univ., Pittsburgh, Pa. 1990. Anantharaman, T., M.S. Campbell, and F.-H. Hsu, Singular extensions: Adding selectivity to brute-force searching, Artificial Intelligence, Vol. 43, No. 1, 1990, pp. 99-109. Berliner, H.J., The B* tree search algorithm: A best- first proof procedure, Artificial Inteldigence, Vol. 12, 1979, pp. 23-40. Chakrabarti, P.P., S. Ghose, A. Acharya, and S.C. de Sarkar, Heuristic search in restricted memory, Artifi- cial Intelligence, Vol. 41, No. 2, 1989, pp. 197-221. Fuller, S.H., J .G. Gaschnig, and J .J . Gillogly, An analysis of the alpha-beta pruning algorithm, Tech- nical Report, Dept. of Computer Science Carnegie- Mellon University, Pittsburgh, Pa., 1973. Kaindl, H., R. Shams, and H. Horacek, Minimax search algorithms with and without aspiration win- dows, IEEE Transactions on Pattern Anadysis and Machine Intelligence, Vol. 13, No. 12, 1991, pp. 1225- 1235. Knuth, D.E., and R.E. Moore, An analysis of Alpha- Beta pruning, Artificial Intelligence, Vol. 6, No. 4, 1975, pp. 293-326. Korf, R.E., Best-first minimax search: Initial results, Technical Report, CSD-920021, Computer Science Dept., University of California, Los Angeles, 1992. Korf, R.E., Linear-space best-first search, Artificial Intelligence, Vol. 62, No. 1, 1993, pp. 41-78. Korf, R.E., and D.M. Chickering, Best-first mini- max search: First results, Proceedings of the AAAI Fall Symposium on Games: Planning and Learning, Raleigh, NC, Oct. 1993, pp. 39-47. Kozdrowicki, E.W., and D.W. Cooper, COKO III: The Cooper-Koz chess program, C.A.C.M., Vol. 16, No. 7, 1973, pp. 411-427. Lee, K.-F. and S. Mahajan, The development of a world-class Othello program, Artificial Intelligence, Vol. 43, No. 1, 1990, pp. 21-36. McAllester, D.A., Conspiracy numbers for min-max search, Artificial Intelligence, Vol. 35, No. 3, 1988, pp. 287-310. Nilsson, N . J . , Searching problem-solving and game- playing trees for minimal cost solutions, in Informa- tion Processing 68, Proceedings of the IFIP Congress 1968, A.J.H. Morrell (Ed.), North-Holland, Amster- dam, 1969, pp. 1556-1562. Pearl, J. Heuristics, Addison-Wesley, Reading, Mass., 1984. Rivest, R.L., Game tree searching by min/max ap- proximation, Artificial Intelligence, Vol. 34, No. 1, 1987, pp. 77-96. Russell, S., and E. Wefald, On optimal game-tree search using rational meta-reasoning, Proceedings of the Eleventh International Joint Conference on Arti- ficial InteZZigence (IJCAI-89), Detroit, MI, 1989, pp. 334-340. Shannon, C.E., Programming a computer for playing chess, Philosophical Magazine, Vol. 41, 1950, pp. 256- 275. Slagle, J .R., and Dixon, J .K., Experiments with some programs that search game trees, J.A.C.M., Vol. 16, No. 2, 1969, pp. 189-207. Stockman, G., A minimax algorithm better than Alpha-Beta ? Artificial Intelligence, Vol. 12, No. 2, 1979, pp. 179-196. 1370 Search | 1994 | 279 |
1,629 | Spurious Symptom Reduction in Fault Monitoring using a Neural Network and Knowledge Base Hybrid System* Roger M. Records Boeing Computer Services, P.O.Box 24346, GH-TX, Seattle, WA 98124 Jai J. Choi t Boeing Computer Services, P.O.Box 24346, 7F-67, Seattle, WA 98124 Abstract An approach to reduce number of spurious symp- toms in aircraft engine fault monitoring is investi- gated. Two strategies were utilized. A set of rules de- signed to filter spurious symptoms was created. Then a neural network was designed to generate expecta- tion value for each of the sensors monitored. The neural net was trained for a specific engine during normal operation. After capturing patterns for nor- mal engine behavior in the neural net, an expecta- tion value for the sensor is predicted. The success of this approach relies on generating better expectation values which in turn produce smaller variation from actual operating behavior and hence generate fewer spurious symptoms. Resulting hybrid system of neu- ral networks and rule-based model demonstrates a drastic reduction of overall spurious symptoms. 1 Introduction One of the challenges in airplane engine health mon- itoring is the fact that no two engines behave identi- cally. Individual (serial number) engines may vary in behavior as much as 30%. If acceptable sensor devia- tion levels between expectation value and actual value are set at this level, recognition of valid symptoms is delayed or totally inhibited. Setting deviation values lower than 30% introduces spurious symptoms. Cre- ating generic engine monitoring system is thus a diffi- cult problem. An example is NASA’s Faultfinder, an in-flight engine monitoring and diagnostic system [2]. The Faultfinder consists of three modules, an engine monitoring component called MONITAUR, followed *This work was performed under NASA contract NASl- 18027. t Dr. Choi is also with the Dept. of Electrical En- gineering, University of Washington, Seattle, WA. Email: jai@atc.boeing.com. by two diagnostic components: a rule based diag- nostic system and a model based reasoning system shown in Fig.1. Using real engine data and a.n en- gine model for comparison, both spurious and real symptoms were generated by the MONITAUR mod- ule. These spurious symptoms resulted from the sys- tem’s inablity to generate accurate expectation val- ues from an internal engine model. As the spurious symptoms were passed on for diagnosis, the potential for erroneous diagnosis was increased. The focus for the current work is to reduce spuri- ous symptoms generated in MONITAUR. The first step in this task is to identify sources of spurious symptoms from results of healthy engine monitoring, generate rules which detect the spurious symptoms identified, and populate a knowledge base previously designed within MONITAUR to filter identified spu- rious symptoms. The second step, and the thesis of this presenta- tion, is to examine the feasibility of using a neural network and rule base hybrid as a “front end” and “back end” respectively to MONITAUR. The neu- ral net front end, replacing the engine model, gener- ates better expectation values than those generated by the engine simulation. The back end rule base (knowledge base) then filters out potential spurious symptoms. 2 es of spurious sy Before we discuss causes of spurious symptoms, we first describe five engine sensors, N1, N2, EPR, EGT, and FF. The N1 and Nz sensors measure the rotational speeds of the fan and high-pressure com- pressor, respectively. The fan and compressor gener- ally rotate at different speeds because they are con- nected to different turbine stages. Fuel flow, FF, measures the rate at which the fuel is entering the engine. The EGT is the exhaust gas temper&ure. Neural Networks 865 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. The EPR, engine pressure ratio, is a ratio of the air pressure at the exhaust divided by the air pressure at the engine inlet. In the MONITAUR module, each of the sensors listed are monitored for deviations in three attributes - absolute value, first derivative, and long term trend which is defined by an average slope of few seconds of time slices. There are several sources of spurious symptoms. Model deficiencies produce poor expectation val- ues which result in unacceptable deviations. Accurate modeling can produce nearly parallel expectation and actual curves with (short term) large deviations. Qualitative boundaries defined by MONITAUR can divide expectation and actual values. A lag factor between expectation and actual curves require a catch-up time factor. Sensor spikes and holes produce short term de- viations. Sensor failure can apprear as a symptom. Fig.2 whows a typical time-sensor value plot for a catch-up symptom. 3 Spurious symptom redue- tion by rule base and neural networks Before an evaluation of techniques to reduce spurious symptoms could be attempted, a baseline of spuri- ous symptoms had to be established. The approach used was to first examine healthy engine data. Ide- ally, monitoring a healthy engine should produce no symptoms. Data collection was confined to a sin- gle engine type since different manufacturer’s engines manifested differing spurious symptoms. For the se- lected engine model, 9 data files of healthy engine data were used which had a total of 6900 data slices containing 35000 data points. A representative data subset was extracted for use as a baseline. This file was one of the 9 healthy engine files containing 115 data slices with two thrust lever advances followed by thrust lever retards. The data was processed in batch mode by Fault- finder’s MONITAUR module. In this procedure MONITAUR calls an engine simulation for gener- ation of expectation values relevant to the current in-flight conditions. These values are compared by MONITAUR to the actual sensor data which was col- lected from the healthy engine during a flight. The baseline values obtained for spurious symptom gen- eration are shown in Tables 1, 2, and 3. 3.1 Rule base spurious symptom re- duction The existing rule base from MONITAUR was popu- lated with rules which would classify the symptom as spurious. As the airplane sensor data is processed by MONI- TAUR, a set of symptoms are generated for each time slice. Before the symptoms are output from MONI- TAUR, the rule base is invoked to see if any symp- toms are to be classified as spurious and need to be delayed. When the representative baseline data set was pro- cessed with MONITAUR enhanced with the rule base filter, a reduction in spurious symptoms was achieved. A representative comparison of the results with the baseline by sensor is shown in Table 1. rule base baseline total # of spurious symptoms 35 256 1 # of EPR symptoms I 3 I 11 I 1 # of EGT symptoms I 15 1 92 1 Table 1: reduction of spurious symptoms by rule base. Total number of possible symptoms is 115. To ensure that real symptoms were not being fil- tered by the rule base, a file of engine data containing a hung start fault was processed using this rule base. One symptom was delayed in recognition for two sec- onds, but none of the symptoms were removed or ignored by the rule base filter. 3.2 Spurious symptom reduction by neural networks Second approach to reducing the number of spuri- ous symptoms in healthy engine data is to create an adaptive engine model whose purpose is to produce better expectation values. The approach was to use a feed-forward neural networks to capture patterns of healthy engine behavior and generate an expected value for a given sensor. Since we have 5 sensors, we trained 5 separate neural networks for each sensor modeling. We also assume that each sensor output is correlated with others. In other words, the output of 866 Neural Networks EGT can be a function of Nl, N2, EPR, FF, Oq 0 represents throttle angle parameter, i.e., EGT = fi(N, N2, EPR, FF, e>, FF = f#‘h, h Ef’R, EGT, e), etc. , where In addition to these input parameters altitude and air speed (MACH) information is available for in- flight test. Since our experiment was limited to a ground operation data we did not use the altitude and air speed information in this study. In training a feed-forward network with backprop- agation algorithm, we use the error function E, E = f c(tk - Yk)2 +xxw;j, k Cj where i!l, and yk are target value and actual network output of the lath output unit respectively, and X is the regularization coefficient. Most of our simula- tions we use X = lo- 5. The purpose of the penalty term in the above equation is to penalize large weight (wij) increase so that the trained neural net improves generalization capability [3]. Though we tried with different penalty terms and different network archi- tectures with different learning methods such as re- current network learning, we do not address network performances in this article. To train the neural network off-line, we pre- processed each sensored data point (2) based on mean (M), standard deviation (a), minimum (gnain), and maximum (2,,, ) for normalization xn as following; 2 = (z - M)/(T, and, zra = 2’~~~~~~~~~in, where -1.0 5 x:, 5 1.0. The gmaZ and gmin repre- sent the maximum and the minimum of the ? respec- tively. Fig.3 shows a typical result of network train- ing by a training data file containing about 500 data points. Note that the model deficiencies are drasti- cally reduced for E P R. When the training is completed, the modified MONITAUR system is used to process the baseline data set. It is important to repeat that all the train- ing sets and the baseline data must be generated from the same serial number engine. It is this en- gine’s unique behavior that has been captured in the weight set during training. The results of process- ing the baseline test set of healthy engine data with expectation values generated by the neural network instead of the engine model is shown in Table 2. # of N2 symptoms 8 31 # of E PR symptoms 2 11 # of EGT symptoms 33 92 Table 2: reduction of spurious symptoms by neural network. Four healthy engine files from the same serial num- ber engine were processed through MONITAUR with the neural network filter to cross validate the effect of the neural network. The neural net achieved at least a 40% reduction of spurious symptoms in the worst case. It should be noted that while a considerable reduction in spurious symptoms was achieved using the neural net, there were several instances in which the neural net did not perform as well as the en- gine model in predicting expectation value. In those instances spurious symptoms were generated by the neural net where none had been generated by the en- gine model. It is hypothesized that this condition was the result of incomplete training of the neural net and not necessarily a failure of the adaptive filter concept. 3.3 Spurious symptom reduction by a hybrid system Once neural networks are trained, we apply networks as a “front end” to the MONITAUR module. Then we put the rule base as a “back end” to the module. A schematic is shown in Fig.4. Using the hybrid, the neural nets replace the engine model as a source of ex- pectation values. This serves to reduce the number of spurious symptoms by generating better expectat#ion values. Those spurious symptoms still generated were then filtered by the rule base. The ability to better filter the surviving spurious symptoms results from generation of better expectation values which makes the expectation curve more nearly coincide with the actual curve. Our analysis shows that the rules in the “nearly parallel” category are then more readily fired. The results of processing the baseline test set of healthy engine data with this hybrid is shown in Table 3. Neural Networks 867 hybrid baseline 1 total # of spurious symptoms 23 256 # of time slices w/o symptoms 96 0 # of FF symptoms 4 97 # of NI svmDtoms 0 25 . . - w * # of N2 symptoms # of EPR symptoms # of EGT symptoms I J 5 31 0 11 14 92 t I Table 3: reduction of spurious symptoms by neural net and rule base hybrid system. 4 Final remarks A knowledge base of rules was constructed to filter known spurious symptoms and a neural network was developed to improve the expectation values used in the monitoring process. Both approaches were ef- fective in reducing spurious symptoms individually. However, the best results were obtained using a hy- brid system combining the neural net front end with the rule-based back in engine health monitoring. This evaluation of strategies to reduce spurious symptoms should be discussed with the limitations of each approach in mind. Both approaches consid- ered in this study are engine type dependent. The rule base constructed works for a specific manufac- turer on a specific engine type. However the rule base filter is more generic than the neural net. The neu- ral net should be trained for a specific serial number engine. References PI PI PI PI Abbott, K., “Robust fault diagnosis of physical system in operation,” Dissertation, Rutgers, the state university of New Jersey, NJ, 1990. Abbott, K., Schutte, P., Palmer, M., Ricks, W., “Faultfinder: A diagnostic expert system with graceful degradation for standard aircraft ap- plications,” Proc. of 14th International Sympo- sium on Aircraft Integrated Moniton’ng Systems, Friedrichshafen, FRG pp. 353-370, 1988. Krogh, A., and Hertz, J., “A simple weight de- cay can improve generalization,” Technical note: University of California, Santa Cruz, 1991. Rumelhart, D.E., McClelland, J.L. and PDP Research Group, “Learning internal representa- tions by error propagation”, In Feldman, J.A. and Rumelhart, D.E. (Eds.), Parallel dis- tributed processing- Vol. 1, MIT Press, pp.318-363, 1988. 868 Neural Networks P airplane arameters - 0 : NASA originated fault data actual value symptoms symptoms I associational model based fault hypotheses fault hypotheses Fig.1. Engine Fault Monitoring in FAULTFINDER. Symptoms generated by the comparison between expectation and actual values are passed to a rule based diagnostic systom and to a model based diagnostic system. Fig. 2. Catch-Up Spurious Symptoms. Typical time-sensor plot showing regions of spurious symptoms (A & B). Neural Networks 869 0 200 400 600 Fig.3 Actual and Neural Net Expectation Curves. Regions of spurious symptoms are reduced as a result of better expectation. I airplane I offline I parameters I I flight recorder healthy engine data I weight set t airplane parameters -=I expected c flight recorder fault data actual value Fig.4. Engine Fault Monitoring using the Hybrid System. The engine model (from Fig.1) is replace with a neural network. Neural network produces better expectation values (in Fig.3). The rule base is better able to filter remaining spurious symptoms in the hybrid system. associational model based fault fault hypotheses hypotheses 870 Neural Networks | 1994 | 28 |
1,630 | Evolving Neural Networks to cus imax Search * David E. Moriarty and Risto Miikkulainen Department of Computer Sciences The University of Texas at Austin, Austin, TX 78712 moriarty,risto@cs.utexas.edu Abstract Neural networks were evolved through genetic al- gorithms to focus minimax search in the game of Othello. At each level of the search tree, the fo- cus networks decide which moves are promising enough to be explored further. The networks ef- fectively hide problem states from minimax based on the knowledge they have evolved about the limitations of minimax and the evaluation func- tion. Focus networks were encoded in marker- based chromosomes and were evolved against a full-width minimax opponent that used the same evaluation function. The networks were able to guide the search away from poor information, re- sulting in stronger play while examining fewer states. When evolved with a highly sophisticated evaluation function of the Bill program, the sys- tem was able to match Bill’s performance while only searching a subset of the moves. Introduction Almost all current game programs rely on the minimax search algorithm (Shannon 1950) to return the best move. Because of time and space constraints, search- ing to the end of the game is not feasible for most games. Heuristic evaluation functions, therefore, are used to approximate the payoff of a state. Unfortu- nately, heuristics create errors that propagate up the search tree, and can greatly diminish the effectiveness of minimax (Korf 1988). Minimax also assumes that the opponent will always make the best move. It does not promote risk taking. Often in losing situations the best move may not be towards the highest min/max value, especially if it will still result in a loss. Knowl- edge of move probabilities could guide a search towards a more aggressive approach and take advantage of pos- sible mistakes by the opponent. Recently, several algorithms have emerged that are more selective than the standard fixed-depth minimax search (Korf and Chickering 1994; McAllester 1988; *Thanks to Ka.i-Fu Lee and Richard Korf for providing the source code for Bill’s evaluation function. Rivest 1987). Th ese algorithms allow moves that ap- pear more promising to be explored deeper than others, creating nonuniform-depth trees. While these tech- niques have lead to better play, they still allow mini- max to evaluate every unexplored board and are there- fore vulnerable to errors in the evaluation function. Most game programs overcome weak evaluation functions by searching deeper in the tree. Presumably, as the search frontier gets closer to the goal states, the heuristic evaluations become more accurate. While this may be true, there is no guarantee that deeper searches will provide frontier nodes closer to the goal states. Hansson and Mayer (1989) have shown that without a sound inference mechanism, deeper searches can actually cause more error in the frontier nodes. A more directed search, therefore, seems necessary. An alternative to deeper searches is to decrease the errors in the evaluation function. Bayesian learning has been implemented to combine several heuristic es- timates (Lee and Mahajan 1990) and to adjust the heuristic values based on values of other nodes in the tree (Hansson and Mayer 1989). The new estimates represent a measure of belief in the heuristic value. These methods have provided stronger play, although they do not address problems inherent in minimaxsuch as no risk taking. This paper presents a novel approach using evolu- tionary neural networks that can compensate for prob- lems in the evaluation function as well as in the mini- max algorithm. Artificial neural networks have proven very effective in pattern recognition and pattern asso- ciation tasks, which makes them a good candidate for recognizing undesirable board situations. Genetic al- gorithms provide a powerful, general training tool for neural networks. Like natural evolution, artificial evo- lution is very good at discerning problems and find- ing ways to overcome them. Our approach is based on a marker-based encoding of neural networks which has been shown particularly effective in adapting to new challenges in complex environments (Fullmer and Miikkulainen 1992; Moriarty and Miikkulainen 1993). Genetic algorithms were used to evolve Focus net- works to direct a minimax search away from poor infor- Two-Player Games 1371 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Estimated payoffs Depth bound Figure 1: A full-width minimax search to level 2. All nodes in the shaded area are evaluated. The actual payoff values of the leaf states are listed below the depth bound. Their heuristic estimates are shown inside the leaf nodes. Min (circles) selects the lowest payoff and max (squares) the highest of min’s choices. As a result, move 21 is selected for the root. Estimated payoffs Depth bound Actual payoffs Figure 2: A focused minimax search. Only the states in the focus window (the shaded region) are evaluated. As a result, move e appears to be max’s best choice. mation. At each state in the search, the focus network determines which moves look promising enough to be further explored. The focus network is able to con- trol which moves the minimax search can see, and can evolve to overcome limitations of the evaluation func- tion and minimax by focusing the search away from problem states. A population of focus networks was evolved in the game of Othello. The results show that the focus net- works are capable of stronger play than full-width min- imax with the same evaluation function, while examin- ing fewer positions. Also, when evolved with the highly sophisticated evaluation function of the Bill program (Lee and Mahajan 1990), the focus networks were able to maintain Bill’s level of play while searching through fewer states. The next section describes the basic idea and imple- mentation of the focus networks. Section 3 describes marker-based encoding and the specifics of the evolu- tion simulations. The main experimental results are presented in section 4, and discussed in section 5. Focus Networks Selecting Moves for Minimax Focus networks decide which moves in a given board situation are to be explored. At each level, the net- work sees the updated board and evaluates each move. Only those moves that are better than a threshold value will be further explored. This subset of moves can be seen as a window to the search tree returned by the focus network. The .search continues until a fixed depth bound is reached. A static evaluation func- 1372 Search tion is applied to the leaf states, and the values are propagated up the tree using the standard minimax method. The a-/3 pruning algorithm (Edwards and Hart 1963; Knuth and Moore 1975) is used as in a full-width search to prune irrelevant states. To illustrate how such control of minimax might be beneficial, consider the following situation. Two moves, A and B, are considered in the current board configuration. Although move A returns, through min- imax search, a higher evaluation value than move B, both moves appear to lead to losing situations. Move B, however, can result in a win if the opponent makes a mistake. By assuming that the opponent will always make the best move, minimax would choose A over B resulting in a sure loss. Focus networks, however, could learn that a win can sometimes be achieved by selecting move B, and they would thus not include A in their search window. More generally, restricting the number of moves ex- plored has two advantages: (1) the branching factor is reduced which greatly speeds up the search. As a result, searches can proceed deeper on more promis- ing paths. (2) The focus networks are forced to de- cide which moves the minimax search should evaluate, and in order to play well, they must develop an under- standing of the minimax algorithm. It is possible that they will also discover limitations of minimax and the evaluation function, and learn to compensate by not allowing minimax to see certain moves. Figures 1 and 2 illustrate the focused search process. The current player has a choice of 5 moves (a through e). Figure 1 shows a basic minimax search with a depth bound of 2. The leaf states are evaluated according to - Network’s lllO”SS - opponent’s moves Figure 3: The architecture of the focus networks for Othello. Two inputs are used to encode each position on the board. The encoding of the first four spaces (al, bl, cl, dl) f or the given board with the network playing black are shown in the input layer. Both input nodes 1 and 2 are off since al is empty. Node 3 is on (i.e. dark) since bl has the network’s piece in it, and nodes 6 and 8 are on since the opponent has pieces in cl and dl (both nodes for the same position are never on simultaneously). The activation of the output layer is shown by the shading. The corners (such as al and h8) have high activations since corners are almost always good moves. Only the input and output encoding was prespecified for the network. The input and output connectivity and the number and connectivity of the hidden nodes were all evolved using genetic algorithms. a static evaluation function. The actual payoff value of each leaf is shown below the depth bound. The difference between these values is the error or misin- formation generated by the evaluation function. The best move is e, as it will generate a payoff of at least 11. Because of the misinformation, however, full-width minimax would choose move b. Figure 2 shows the same search tree but with the addition of a focus win- dow. Only the nodes in the window are evaluated. By focusing the search away from the poor information, the best move (e) would be selected. The question is, how can we reliably form such a search window? The evolutionary approach is attractive because no previous knowledge of minimax or the evaluation func- tion is needed. The usual neural network learning al- gorithms such as backpropagation (Rumelhart et al. 1986) would require exact target values to be specified for each training example. Such information is very difficult to establish in the search focus task. In the neuro-evolution approach, however, evolutionary pres- sures will guide the networks toward providing good windows for the search. Networks will discover misin- formation by associating certain board situations with winning and losing. Networks that prune out problem states will win more games, allowing them to survive and propagate their genes to future networks. Implementation in Othello Othello is a board game played on an 8 x 8 grid (fig- ure 3). Each piece has one white and one black side. Players (“white” and “black”) take turns placing pieces on the board with their own color facing up until there are no further moves. For a move to be legal, it must cause one or more of the opponent’s pieces to be surrounded by the new piece and another of the player’s pieces. All surrounded pieces are subse- quently flipped to become the player’s pieces. Sev- eral world championship-level Othello programs have been created using full-width minimax search (Lee and Mahajan 1990; Rosenbloom 1982). Like most ad- vanced game programs, they achieve high performance through examining millions of positions per move. In our implementation of focus networks, two input units were used to represent the type of piece in each board space. Each output unit corresponded directly to a space on the board. The activation of an output unit determined how strongly the network suggested moving to that position. Separate output units were used for the two players. Thus, the ranking for the network’s moves may differ from the ranking of the opponent’s moves. This distinction is beneficial since an aggressive player should not assume his opponent is equally aggressive and should take a more conservative approach when predicting his opponent’s moves. Sim- ilarly, a defensive player should not presume defensive play from his opponents. The separation of player and opponent’s output units allows offensive and defensive strategies to develop. The number of hidden units and connections be- tween them were determined through evolution. Each Two-Player Games 1373 < start >< label >< value >< key0 >< label0 >< wg > . . < key, >< label, >< wR >< end > < start > - Start marker. < label > - Label of the node. <value> - Initial value of the node. < key; > - Key that specifies whether connection is from an input unit/to an output unit or from another hidden unit. < label, > - Label of the unit where connection is to be made. < ‘wi > - Weight of connection. < end > - End marker. Figure 4: The definition of a hidden node in marker-based encoding. hidden unit used a linear threshold of 0 to determine it’s output (either 0 or 1). Usually the networks con- tained about 120 hidden nodes and 600 connections with a large amount of recurrency. For each state to be explored in a search tree an activation was prop- agated through the network. The legal moves with activation greater than or equal to 0 were included in the search window. Evolution Each focus network’s genetic representation was based on a marker-based encoding (Fullmer and Miikkulai- nen 1992) of the architecture and weights. The encod- ing is inspired by markers in DNA that separate pro- tein definitions. Artificial markers in the chromosome are used to separate neural network node definitions. Alleles serve as start markers if their absolute value MOD 25 equals 1 and end markers if their absolute value MOD 25 equals 2. Any integer between a start marker and an end marker is always part of the ge- netic code. The interpretation of non-marker alleles depends on their location with respect to a start or an end marker. Figure 4 summarizes the structure of the hidden node definition in marker-based encoding. Each chromosome consisted of 5000 8-bit integers ranging from -128 to 127. Two 8-bit integers were used for the connection definitions. The lcey integer specifies whether the connection is to be made with the input/output layers or with another hidden unit. If the key is positive, the second integer, label, specifies a connection from the input layer (if the label is 2 0) or to the output layer (if the label is < 0). If the key is negative, the label specifies an input connection from another hidden unit. Figure 5 shows an example gene and the network information it encodes. The chromosome is treated as a continuous circular entity. A node may begin on one end of the chromo- some and end on the other. The final node definition is terminated, however, if the first start marker is encoun- tered in the node definition. The hidden nodes were evaluated in the order specified in the chromosome. A population of 50 networks was evolved using standard genetic algorithms (Goldberg 1988; Holland 1975). A two point crossover (figure 6) was used to produce two offspring per mating. Only the top 15 net- 1374 Search -13 E S 21 1 82 3 -5 -21 14 31 80 -51 Hidden node 21 Initial Value = 1 Figure 5: An example node definition in a marker-based gene. The first connection has key = 82, label = 3, w = -5. The key and label are both positive so the connection is to be made from input unit 3. . . ..-I.. Parent Crossover Offspring Offspring 2 -I.................. . . . . . . . . . . . . . . ...,.,.,,,,.........,., Figure 6: Two point crossover. Each offspring receives the front and rear part of one parent’s chromosome and the middle of the other parent’s chromosome. works were allowed to mate with each other, creating 30 new offspring per generation. The new offspring re- placed the least fit networks in the population. Traits that previously led to high fitness levels were passed to future generations, whereas traits that led to poor performance were selected against. Mutation, at the rate of 0.4%, was implemented at the integer level by adding a random value to an integer allele. The top 3 networks were not mutated. To determine a network’s fitness, it was inserted into an CL+/? search program and played against a full-width, fixed-depth minimax-cu-p search. Both players were allowed to search through the second level. To optimize a-P pruning, node ordering was implemented based on the values of the evaluation function (Pearl 1984). Both players always used the same evaluation func- tion. One population was evolved based on the posi- tional strategy of Iago (Rosenbloom 1982), one of the first championship-level Othello programs. Such an evaluation function is relatively weak as it only consid- ers the merits of single spaces without taking mobility into account’. The goal was to see how well the focus networks could evolve to make use of weak heuristic information, and also to provide enough errors so that the effect of focus networks would be easily seen. A separate population was evolved using the evalua- tion function from the Bill program (Lee and Mahajan 1990). Bill’s evaluation has been optimized through Bayesian learning and is believed to be one of the best in the world. The goal was to see if the focus networks could achieve any improvement over such an already strong heuristic. To create different games, an initial state was se- lected randomly among the 244 possible board posi- tions after four moves. To prevent networks from ex- pecting certain moves, the opponents moved randomly 10% of the time. The random moves also make risk taking a viable option in a losing situation since the op- ponent will not always make the best move. If the op- ponent’s evaluation function returned the same value for two or more moves, a random selection was made between the equal-valued moves, further discouraging expectations. The number of wins over ten games de- termined each network’s fitness. Results The networks were evolved for 1000 generations, which took about four days on a Sun Sparcstation 1. Af- ter evolution, the best focus network was again played against the full-width search program, but this time the program made no random moves. The performance was measured by the percentage of games won over all 244 opening games. In the first test (figure 7), the focused search level was fixed at 2, and the full-width opponent’s was var- ied. As a control, a 2-level, full-width minimax search was also played against the full-width opponent. Note that the focused (shaded bars) and full-width (white bars) searches are not playing against each other, but against another full-width opponent. The results show that a focused search to level 2 appears to be as strong as a full-width search to level 4. In the second test (figure S), the focused search level was increased with the full-width opponent’s. The control full-width search (white bars) performs con- sistently at 50% because it is simply playing itself at each level. The results show that the focused search consistently outplays the full-width search even as the search level increases far beyond its training. The per- formance is strongest at level 2, where the focused net- work was actually trained, and is otherwise approx- imately constant at 65%. This result is important ‘Iago also included a complex mobility strategy. 100 0 Focused 0 Full-Width r Search Level of Opponent Figure 7: The winning percentage of two level search with and without a focus network against a variable-level full- width opponent. n Focused 0 Full-Width 100 SO z 59 $ 6. 5 5 Q B 40 aR 20 0 il 1 2 3 4 5 Search Level of Both Players 50 il 6 Figure 8: The winning percentage of a variable-level search with and without a focus network against a variable-level full-width opponent. because it suggests that the focus network could be trained at any level, and would generalize well to other search depths. It is also important to note that the focused searches were winning while looking at only a subset of the states that the full-width searches are examining. Fig- ure 9 shows the average number of board positions ex- amined per game for each search bound. Of all avail- able legal moves, only 79% were included in the focus window. The full-width search must be receiving poor information from minimax, causing it to choose bad moves. Since the focused search is using the same eval- uation function and is searching to the same depth, it appears that the focus network is shielding the root from this misinformation. To better understand how the stronger play was achieved, the moves included in the focus window were further analyzed. 100 test games were played against a full-width search using the same evaluation function. Two-Player Games 1375 12 3 4 5 6 Focus a where time 189 662 3440 12172 63304 230487 game playing setting constraints must be Full taken into 226 842 4042 16684 75696 330453 account, such an improved efficiency trans- lates directly to better performance. Figure 9: The average number game for each depth bound. of states examined per --A - Network - 0 - Opponent 60 ' I 1 2 3 4 5 6 Minimax Search Level Figure 10: The percentage of moves returned as its choice that the focus network considers. by minimax At each board position the moves in the focus window were compared with the move a full-width minimax search would return at the same position. Figure 10 shows the percentage of full-width minimax’s moves that were included in the focus network’s window. The graph thus reflects how often the focus network agrees with full-width minimax. The results show that the focus network is effectively looking far ahead. The moves in the network’s window are similar to moves that a deep-searching, full-width minimax would re- turn (black triangles in figure 10). However, since the network has only been evolved against a shallow- searching opponent, its predictions of the opponent’s moves become less accurate as the opponent searches deeper (white circles in figure 10). The focus network’s moves are strong because they are not tied to the moves that a full-width minimax search would choose. In- stead, they reflect moves that have led to wins. It is this strong offense that allows the networks to scale with the search level. It is conceivable that eventually the network’s diminishing defense will leave it vulner- able to a powerful opponent, however that was never observed in our experiments. In the second population, evolved using the eval- uation function from Bill, the best focus networks achieved a winning percentage of 5 1% over the full- width searches to the same level. Apparently, since Bill’s evaluation function has very few errors, the focus networks were not able to improve the play very much. However, it is significant that the focused searches achieved this performance while examining only 84% of the moves that full-width Bill evaluated. It seems the focus networks were able to discover and prune unnec- essary nodes even with a Bayes-optimized heuristic. In iscussion and Future Work The results show that better play can be achieved through more selective search. Much like humans, fo- cus networks selectively dismiss moves that have pre- viously led to adverse situations. Whereas full-width minimax is very sensitive to inconsistencies in the eval- uation function, focused searches can actually discover and discard unreliable information. The approach will be most useful in improving performance in domains where it is difficult to come up with good evalua- tion functions. The evolution system can take a weak heuristic and discover how to best use the informa- tion it provides. In this sense, the approach is similar to other recent improvements in game playing such as Bayesian optimization of evaluation functions (Hans- son and Mayer 1990; Lee and Mahajan 1990). A com- parison of these techniques and a study of how they perhaps could be combined would be most interesting. In an earlier implementation of focus networks, a fixed-size focus window that always included the three best moves was used (Moriarty and Miikkulai- nen 1994). This strategy achieved performance com- parable to the threshold-based window with an even more dramatic reduction in the number of states eval- uated. However, the fixed window system was not able to generalize well to better opponents such as Bill. When evolved with Bill’s evaluation function, the fixed window pruned too many nodes and performed very poorly. On the other hand, the threshold-based win- dow allows the system to adjust the extent of pruning according to how much reliable information there is in the tree. It seems to make little difference how deep the sys- tem is allowed to search during training (figure 8). The focus networks should therefore perform well in real game-playing situations where the search depth may vary significantly depending on the available time. However, the training opponent’s search depth (and evaluation function) may have a significant effect on performance. It might be possible to evolve better play by improving the opponent gradually during training. If the opponent gets stronger as the networks evolve, the networks would have to compensate by improv- ing their defensive strategy, and superior overall play should result. In our implementation, focus networks searched only through uniform-depth trees. Focus networks could also be implemented with algorithms such as best-first minimax (Korf and Chickering 1994), where the tree is grown in non-uniform depths allowing more promising moves to be searched deeper. Whereas the standard best-first minimax considers all unexplored board po- sitions in the decision of where to explore next, a se- lective window of the most important positions could 1376 Search be maintained to focus the search. Another application of neuro-evolution to game playing is to evolve networks to serve as the evalua- tion function. Interestingly, the results have been dis- couraging so far. Whereas the focus networks’ output values only need to indicate above or below a thresh- old, the evaluation networks’ output units must reflect an absolute value comparable to other board evalua- tions. It has proven very difficult for the networks to discover such global values. While focus networks may be well suited for Othello, their implementation in more complex games like chess is not as straightforward. In our implementation, the output layer represented the entire move space. This is feasible in Othello, since there are only 60 possi- ble moves. It is unrealistic to try to represent the en- tire move space of a game such as chess in a single output layer. A possible solution is to use two focus networks in the decision process. The first network’s output layer would represent each piece and would de- cide which pieces to consider. The second network’s output layer would represent each space on the board (as in the Othello networks). Given the current board and the piece to be moved, the second network could decide which moves of a given piece to consider. Such an extension constitutes a most interesting direction of future research. Conclusion Artificial evolution of neural networks is a promising paradigm for developing better search strategies. It is possible to identify unreliable information in the search tree and find ways to avoid it. Focus networks can overcome not only errors in the evaluation function but flaws inherent in minimax itself. Focused searches are cognitively more appealing since they produce more human-like search rather than systematic exhaustive search. In Othello, a focused search consistently out- played full-width minimax while examining a subset of the moves. Even with a highly sophisticated evaluation function, the focus networks were able to create a more efficient search by pruning irrelevant nodes. Applica- tions to more complex domains are more challenging, but not infeasible. References Edwards, D., and Hart, T. (1963). The alpha-beta heuristic. Technical Report 30, MIT. Fullmer, B., and Miikkulainen, R. (1992). Evolving finite state behavior using marker-based genetic encoding of neural networks. In Proceedings of the First European Conference on Artificial Life. Cambridge, MA: MIT Press. Goldberg, D. E. (1988). G enetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley. Hansson, O., and Mayer, A. (1989). Heuristic search as evidential reasoning. In Proceedings of the Fifth Workshop on Uncertainty in AI. Hansson, O., and Mayer, A. (1990). Probabilistic heuristic estimates. Annals of Mathematics and Artificial Intelligence, 2:209-220. Holland, J. H. (1975). Adaptation in Natural and Arti- ficial Systems: An Introductory Analysis with Ap- plications to Biology, Control and Artificial Intel- ligence. Ann Arbor, MI: University of Michigan Press. Knuth, D. E., and Moore, R. W. (1975). An analysis of alpha-beta pruning. Artificial Intelligence, 6:293- 326. Korf, R. E. (1988). S earth: A survey of recent results. In Shrobe, H. E., editor, Exploring Artificial In- telligence. San Mateo, California: Morgan Kauf- mann. Korf, R. E., and Chickering, D. M. (1994). Best-first minimax search: Othello results. In Proceedings of the Twelth National Conference on Artificial Intelligence. Lee, K.-F., and Mahajan, S. (1990). The development of a world class Othello program. Artificial Intel- ligence, 43:21-36. McAllester, D. A. (1988). Conspiracy numbers for min- max search. Artificial Intelligence, 35:287-310. Moriarty, D. E., and Miikkulainen, R. (1993). Evolv- ing complex Othello strategies using marker-based genetic encoding of neural networks. Technical Re- port AI93-206, Department of Computer Sciences, The University of Texas at Austin. Moriarty, D. E., and Miikkulainen, R. (1994). Improv- ing game tree search with evolutionary neural net- works. In Proceedings of the First IEEE Confer- ence on Evolutionary Computation. Pearl, J. (1984). Heuristics: Intelligent Search Strate- gies for Computer Problem Solving. Reading, MA: Addison- Wesley. Rivest, R. L. (1987). G ame tree searching by min/max approximation. Artificial Intelligence, 34:77-96. Rosenbloom, P. (1982). A world championship-level Othello program. Artificial Intelligence, 19:279- 320. Rumelhart, D. E., Hinton, G. E., and Williams, R. J. (1986). Learning internal representations by error propagation. In Rumelhart, D. E., and McClel- land, J. 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1,631 | A Strategic Metagame Player for General Chess-Like Games Barney Pell RIACS, NASA Ames Research Center AI Research Branch, Mail Stop: 269-2 Moffett Field, CA 94035-1000 pell@ptolemy.arc.nasa.gov Abstract This paper introduces METAGAMER, the first pro- gram designed within the paradigm of Meta- Came Playing (Metagame) (Pell 1992a). This program plays Metagame in the class of sym- metric chess-like games (Pell 1992b), which in- cludes chess, Chinese-chess, checkers, draughts, and Shogi. METAGAMER takes as input the P-&es of a specific game and analyses those rules to con- struct for that game an efficient representation and an evaluation function, for use by a generic search engine. The strategic analysis performed by META- GAMER relates a set of general knowledge sources to the details of the particular game. Among other properties, this analysis determines the rel- ative value of the different pieces in a given game. Although METAGAMER does not learn from expe- rience, the values resulting from its analysis are qualitatively similar to values used by experts on known games, and are sufficient to produce com- petitive performance the first time METAGAMER actually plays each new game. Besides being the first Metagame-playing program, this is the first program to have derived useful piece values di- rectly from analysis of the rules of different games. This paper describes the knowledge implemented in MJSTAGAMER, illustrates the piece values META- GAMER derives for chess and checkers, and dis- cusses experiments with METAGAMJZR on both ex- isting and newly generated games. 1 Introduction Virtually all past research in computer game- playing has attempted to develop computer pro- grams which could play existing games at a rea- sonable standard. While some researchers consider the development of a game-specific expert for some game to be a sufficient end in itself, many scientists in AI are motivated by a desire for generality. Their emphasis is not on achieving strong performance on a particular game, but rather on understand- ing the general ability to produce such strength on a wider variety of games (or problems in general). Hence additional evaluation criteria are typically placed on the playing programs beyond mere per- formance in competition: criteria intended to en- sure that methods used to achieve strength on a specific game will transfer also to new games. Such criteria include the use of learning and planning, and the ability to play more than one game. However, even this generality-oriented research is subject to a potential methodological bias. The human researchers know at the time of program- development which specific game or games the pro- gram will be tested on, and therefore it is possible that they import the results of their own under- standing of the game directly into their program. In this case, it is difficult to determine whether the subsequent performance of the program is due to the general theory it implements, or merely to the insightful observations of its developer about the characteristics necessary for strong performance on this particular game. An instance of this problem is the fixed representation trick (Flann & Dietterich 1989), in which many developers of learning sys- tems spend much of their time finding a represen- tation of the game which will allow their systems to learn how to play it well. This problem is seen more easily when computer game-playing with known games is viewed schemat- ically, as in Figure 1. Here, the human researcher or programmer is aware of the rules and specific knowledge for the game to be programmed, as well as the resource bounds within which the program must play. Given this information, the human then constructs a playing program to play that game. _ The program then plays in competition, and is modified based on the outcome of this experience, either by the human, or perhaps by itself in the case of experience-based learning programs. In all cases, what is significant about this picture is that the hu- man stands in the centre, and mediates the relation between the program and the game it plays. 1378 Search From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Game 0 rules 1 Figure 1: Computer Game-Playing with existing games: the human programmer mediates the rela- tion between the program and the game it plays. 1.1 Metagame Most AI games researchers, when pressed, will con- fess that their real interest is not in writing an expert-level chess program or checkers program. Their interest is in understanding general princi- ples that are best tested by play at these well- understood games. This introduces the possibility of experimental bias. An experimenter can design a program that takes advantage of peculiar features of a single game, or uses a tuned representation to permit the program to learn features that the ex- perimenter is well aware of. The concept of Meta-Game Playing (Pell 1992a), shown schematically in Figure 2, is an attempt to reduce the possibility of such bias. Rather than de- signing a program to play an existing game known in advance, we design a metugumer to play a large but well-defined class of games. A metagamer takes as input only the rules of a new game (as produced by an automatic game generator and encoded in a well-specified language), and then produces a spe- cialised program (a player) to play that game. Dif- ferent metagamers are evaluated in the context of a Metugume-tournament, in which a set of new games are generated, the game rules are provided directly to the programs, and the programs then play the games against each other without human interven- tion. As only the class of games is known to the hu- man developer in advance, metagamers are required to perform any game-specific optimisations with- + Figure 2: Metagame-playing with new games. out human assistance. The challenge is to produce the metagamer which receives the highest overall score across all game instances and opponents in the tournament. In contrast with the discussion on existing games above, the human no longer me- diates the relation between the program and the games it plays, instead she mediates the relation be- tween the program and the c/ass of games it plays. By making the class explicit, we are able to quantify the level of generality achieved. Moreover, we can begin with classes which represent only moderate generalisations over tasks we have already looked at, and gradually move to more general classes of problems as scientific understanding develops. I.2 SCL-Metagame SCL-Metagame (Pell 1992b) is a Metagame re- search problem based around the class of symmetric chess-like games. The class includes the games of chess, checkers, noughts and crosses, Chinese-chess, and Shogi. An implemented game generator pro- duces new games in this class (some of which are objects of interest in their own right (Pell 1992b)). Symmetric Chess-Like Games A symmetric chess-like game is a two-player game of per- fect information, in which the two players move pieces along specified directions, across rectangu- lar boards. Different pieces have different pow- ers of movement, capture, and promotion, and in- teract with other pieces based on ownership and piece type. Goals involve eliminating certain types Two-Player Games 1379 of pieces (eradicate gouls), driving a player out of moves (stabemate goals), or getting certain pieces to occupy specific squares (urriuud goals). Most im- portantly, the games are symmetric between the two players, in that all the rules can be presented from the perspective of one player only, and the differences in goals and movements are solely de- termined by the direction from which the different players view the board. For a formal definition and analysis of this class of games, see Pell (1992b). Game Generation The goal of game generation is to produce a wide variety of games, all of which fall in the class of games as described by a grum- mar. Pell (1992b) implemented a statistical game generator for this class, and Pell (1993c) analysed the complexity and variety of games it produces. Structure of Paper With the provision of the class definition and generator, Pell(1992b) formally defined the Metagame research problem of SCL- Metagame. This paper extends that work by con- structing the first program to play games in this class, and by evaluating this program within the Metagame paradigm. The rest of this paper is or- ganised as follows. Section 2 discusses the general architecture and the class-specific knowledge imple- mented in METAGAMER. Section 3 illustrates the analysis performed by METAGAMER to determine piece values for the games of chess and checkers, when presented with only the rules of those games. Section 4 discusses experiments with METAGAMER on those existing games and on newly generated games. Section 5 compares METAGAMER to other work on general game-playing programs and on au- tomatic methods for determining feature values in games. Section 6 concludes the paper. 2 Constructing a Metagame-player The main intention of Metagame is to serve as a test-bed for learning and planning. One obvious test of a testbed is to compute lower bounds: how well do existing techniques perform on the chal- lenges of the testbed. In this section, we engineer a metagamer using existing game-playing techniques. Search Engine To this end, the search engine used incorporates many standard game-playing search techniques (see Levy & Newborn (1991)). It is based on the minimux algorithm with uZphu-beta pruning, iterative deepening, and the principal con- tinuation heuristic. More details of the Metagame search engine are given by Pell (1993c). Automated Efficiency Optimisation This pow- erful search engine should allow a playing program to search deeply. However, search speed is linked to the speed with which the primitive search op- erations of move-generation and goal detection can be performed. For a game-specific program, these issues can be easily hand-engineered, but for a pro- gram which is to play an entire class of games, the excess overhead of such generality initially caused the search to be unbearably slow. This problem was overcome by using a knowledge-compilation ap- proach. We represent the semantics of the class of games in an extremely general but inefficient manner, and after receiving the rules of a given game the program automatically partially evaluates the general theory with respect to it, thus com- piling away both unnecessary conditionality and the overhead of interpretation (Pell 1993a). In addition to the partial evaluation techniques dis- cussed by Pell (1993a), METAGAMER contains a set of pre-computation methods which produce stutic- analysis tables. These tables speed up position evaluation by caching compute-intensive proper- ties, in some cases providing approximate versions of knowledge which would be too expensive to com- pute correctly at runtime (Pell 1993c). 2.1 Meta-Level Evaluation Function With the search engine in place, using the op- timised primitive operations, we have a program which can search as deeply as resources permit, in any position in any game in this class. The re- maining task is to develop an evaluation function which will be useful across many known and un- known games. Following the approach used in HOYLE (Epstein 1989), we view each feature as an advisor, which en- capsulates a piece of advice about why some aspect of a position may be favourable or unfavourable to one of the players. This section briefly ex- plains some of the advisors currently implemented for METAGAMER. It should be noted that this list is incomplete due to space limitations, the set is still growing, and there are several important gen- eral heuristics which are not yet incorporated (such as distance and control (Snyder 1993)). Motivation and more detailed descriptions of all advisors were provided by Pell (1993c; 1993b). The advisors can be categorised into four groups, based on the gen- eral concepts from which they derive. Mobility Advisors The first group is concerned with different indicators of mobility. These advisors were inspired in part by Church & Church (1979) and Botvinnik (1970), and by generalising features used for game-specific programs (Pell 1993c). o capturing-mobility : counts the captures piece could make in the current position. each 1380 Search o dynamic-mobility:counts the squares to which a piece can move directly from its current square on the current, board, using a moving ability.’ o static-mobility:a static version of the above, this counts the squares to which a piece could move directly from its current square on an otherwise empty board. e eventual-mobility : measures the total value of all squares to which a piece could move eventu- ally from its current square on an otherwise empty board, using a moving ability. The value of each square decreases with the number of moves required for the piece to get, there.2 Threats The second group of advisors deals with threats and conditions enabling threats. The ad- visors come in two types, local and global. Local advisors assess each threat separately, and return the sum of the values of all threats in a position. Global advisors determine the most, important of these threats, and return only the maximum value of the local advisors. To determine the value of a threat, these advisors make use of the other advi- sors to determine, for example, the contribution a threatened piece makes to the present position. Goals and Step Functions The third group of advisors is concerned with goals and regressed goals for this class of games. ov it al : Measures dynamic progress by ers on goals to eradicate sets of pieces. both play- o arrival-distance : this is a decreasing function of the abstract number of moves it would take a piece to move (i.e. without capturing) from its cur- rent square to a goal destination on an otherwise empty board, where this abstract number is based on the minimum distance to the destination plus the cost/difficulty of clearing the path. e promote-distance :for each target-piece that a piece could promote into, this measures both the value and difficulty of achieving such a promotion. f~ possess : This advisor handles games involving placements, in which a player can place a piece down on any of a set of squares. The value in such a situation is related to value the piece would have on the maximum available square.3 ‘Pieces in this class (e.g. checkers pieces) may move and capture in different ways (see Section 1.2). 2Thus while a, bi shop has 32 eventual moves and a knight has 64 from any square, the bishop can reach most of its squares more quickly, a fact captured by this advisor. 3Examples of such placement games are Shogi and Nine-Men’s Morris. Material Value The final group of advisors are used for assigning a fixed material value to each type of piece, which is later awarded to a player for each piece of that type he owns in a given position. This value is a weighted sum of the values returned by the advisors listed in this section, and does not depend on the position of the piece or of the other pieces on the board. e max-stat ic-mob : The maximum static-mobility for this piece over all board squares. avg-static-mob:The this piece over all board average static-mobility squares. for max-eventual-mob: The maximum eventual-mo- bility for this piece over all board squares. @ avg-eventual-mob : The average eventual-mobil- ity for this piece over all board squares. o victims : Awards 1 point for each type of piece this piece has the ability to capture (i.e. the number of pieces matching one of its captwe-types).4 eradicate : Awards 1 point for each opponent goal to eradicate this piece, and minus one point for each player goal to eradicate this piece. o stalemate: This views the goal to stalemate a player as if it were a goal to eradicate all of the player’s pieces, and performs the same computation as eradicate above. e promote : This is computed in a separate pass af- ter all the other material values. It awards a piece a fraction of the material value (computed so far) of each piece it can promote into. This advisor is not fully implemented yet, and was not used in the work discussed in this paper. Section 3 provides concrete examples of the ap- plication of these advisors to the rules of different games discussed in this paper. 2.2 Weights for Advisors The last major issue concerning the construction of the strategic evaluation function involves assign- ing weights to each advisor. While this issue is already difficult in the case of existing games, it is correspondingly more difficult when we move to un- known games, where we are not even assured of the presence of a strong opponent to learn from. How- ever, the construction of some advisors provides one significant constraint on their possible values. For advisors which anticipate goal-achievement (such as promote-distance and the threat advisors), it would seem that their weight should not exceed 1. The reason is that they return some fraction of the 4A more sophisticated version of this feature, not fully implemented yet, takes into account the value of each victim, as determined by other static advisors. Two-Player Games 1381 value derived from achieving their anticipated goal. If such an advisor were weighted double, for exam- ple, the value of the threat would exceed the an- ticipated value of its execution, and the program would not, in general choose to execute its threats. Beyond the above constraint on such advisors, this issue of weight assignment for Metagame is an open problem. One idea for future research would be to apply temporal-difference learning and self- play (Tesauro 1994) to this problem. It would be interesting to investigate whether the “knowledge- free” approach which is so successful in learning backgammon transfers to these different games, or whether it depends for its success on properties spe- cific to backgammon. In the meantime, we have been using METAGAMER with all weights set to 1.5 3 Examples of Material Analysis One iIIIpOrtant Z%Sp& Of METAGAMER'S game anal- ysis, which was discussed in Section 2.1, .is con- cerned with determining relative values for each type of piece in a given game. This type of anal- ysis is called material unadysis, and the resulting values are called materiaZ vabues or static piece vub ues. This section demonstrates METAGAMER'S ma- terial analysis when applied to chess and check- ers. In both cases, METAGAMER took as input only the rules of the games. In conducting this analy- sis, METAGAMER used the material advisors (Sec- tion 2.1) all with equal weight, of one point each. Checkers Table 1 lists material values determined by METAGAMER for the game of checkers, given only an encoding of the rules as an instance of the class of symmetric chess-like games (Pell 1992b).6 In the table, K stands for king, and M stands for man. For compactness, advisors which do not apply to a game (and thus have value of 0 for all pieces) are not listed in material analysis tables for that game. METAGAMER concludes that a king is worth al- most two men. According to expert knowledge,7 this is a gross underestimate of the value of a man. The reason that men are undervalued here is that METAGAMER does not yet, consider the static value 51t should be n oted that this is not the same as set- ting all piece values for a given game to equal value. The general knowledge still imposes constraints on the rela- tive values of individual pieces in a game. For example, even a random setting of weights will cause METAGAMER to value queens above rooks in chess (Pell 1993c). ‘The game defi n’tion for the entire rules of checkers 1 as an instance of this class requires under 250 words and fits on one column of a page. It has been omitted due to space limitations. 71 am thankful to Nick Flann for serving as a check- ers expert. Material Analysis: checkers Piece Advisor stalemate 11 1 1 1 Total 11 23.2 1 13.9 Table 1: Material value analysis for checkers. of a piece based on its possibility to promote into other pieces (see Section 2.1). When actually play- ing a game, METAGAMER does consider this, using the dynamic promote-distance advisor. Chess Table 2 lists material values determined by METAGAMER for the game of chess, given only an encoding of the rules similar to that for checkers (Pell 1993c). In the table, the names of the pieces are just the first letters of the standard piece names, except that N refers to a knight. Material Analysis: chess II Piece Advisor IIB IK IN (P IQ IR 1 Table 2: Material value analysis for chess. As discussed for checkers above, pawns are here undervalued because METAGAMER does not con- sider their potential to promote into queens, rooks, bishops, or knights. According to its present anal- ysis, a pawn has increasingly less eventual-mobility as it gets closer to the promotion rank. Beyond this, the relative value of the pieces is surprisingly close to the values used in conventional chess pro- grams (queen=9, rook=5, bishop=3.25, knight=3, and pawn=l) (Botvinnik 1970; Abramson 1990), given that the analysis was so simplistic. 1382 Search 4 Summary of Results An evaluation of the game-playing performance of METAGAMER was carried out by Pell (1993c) across a set of existing and generated games. 4.1 Known Games Performance in the games of chess and check- ers demonstrated that the knowledge encoded in METAGAMER endows it with a modest level of com- petence against highly specialised programs, which was still impressive given that METAGAMER plays these games in effect from first-principles. Checkers The performance of METAGAMER in checkers was assessed by playing it against Chinook (Schaeffer et al. 1991). Chinook is the world’s strongest computer checkers player, and the sec- ond strongest checkers player in general. As it is a highly optimised and specialised program, it is not surprising that METAGAMER always loses to it (at checkers, of course!). However, to get a baseline for METAGAMER’S performance relative to other possi- ble programs when playing against Chinook,’ we have evaluated the programs when given various handicaps (number of men taken from Chinook at the start of the game). program.g GnuChess is vastly superior to META- GAMER (at chess, of course!), unless it is hand- icapped severely in time and moderately in ma- terial. The overall result of the experiments was that METAGAMER is around even to GnuChess on its easiest level,l’ when given a handicap of one knight. For comparison, a version of METAGAMER with only a standard hand-encoded material eval- uation function (queen=9, rook=5, bishop=3.25, knight=3, and pawn= 1) (Botvinnik 1970; Abram- son 1990) played against METAGAMER with all its advisors and against the version of GnuChess used above. The result was that the material program lost every game at knight’s handicap against Gnu- Chess, and lost every game at even material against METAGAMER with all its advisors. This showed that METAGAMER’S performance was not due to its search abilities, but rather to the knowledge in its evaluation function. The primary result from the checkers experi- ments was that METAGAMER is around even to Chi- nook, when given a handicap of one man. This is compared to a deep-searching greedy material pro- gram which requires a handicap of 4 men, and a random player, which requires a handicap of 8. In fact, in the l-man handicap positions, METAGAMER generally achieves what is technically a winning po- sition, but it is unable to win against Chinook’s defensive strategy of hiding in the double-corner. On observation of METAGAMER’S play of check- ers, it was interesting to see that METAGAMER “re- discovered” the checkers strategy of not moving its back men until late in the game. It turned out that this strategy emerged from the promote-distance advisor, operating defensively instead of in its “in- tended” offensive function. In effect, METAGAMER realized from more general principles that by mov- ing its back men, it made the promotion square more accessible to the opponent, thus increasing the opponent’s value, and decreasing its own. Chess In chess, METAGAMER played against Gnu- Chess, a very strong publicly available chess ‘In our experiments, Chinook played on its easiest level. It also played without access to its opening book or endgame database, although it is unlikely that the experimental results would have been much altered had it been using them. On observation of METAGAMER’S play of chess, we have seen the program develop its pieces quickly, place them on active central squares, put pressure on enemy pieces, make favourable exchanges while avoiding bad ones, and restrict the freedom of its opponent. In all, it is clear that METAGAMER’S knowledge gives it a reasonable positional sense and enables it to achieve longer-term strategic goals while searching only one or two-ply deep. This is actually quite impressive, given that none of the knowledge encoded in METAGAMER’S advisors or static analyser makes reference to any properties specific to the game of chess-METAGAMER worked out its own set of material values for each of the pieces (see Section 3), and its own concept of the value of each piece on each square. On the other hand, the most obvious immediate limitation of METAGAMER revealed in these games is a weakness in tactics caused in part by an inability to search more deeply within the time constraints, in part by a lack of quiescence search, and also by the reliance on full-width tree-search. These are all important areas for future work. 4.2 New Games Pell (1993c) carried out an experiment in the form of a Metugume tournament. In the experiment, sev- eral versions of METAGAMER with different settings of weights for their advisors played against each ‘GnuChess was the winner of the C Language divi- sion of the 1992 Uniform Platform Chess Competition. loIn the experiments, GnuChess played on level 1 with depth 1. This means it searches l-ply in gen- eral but can still search deeply in quiescence search. METAGAMER played with one minute per move, and oc- casionally searched into the second-ply. Two-Player Games 1383 other and against baseline” players on a set of gen- erated games which were unknown to the human designer in advance of the competition. The rules were provided directly to the programs, and they played the games without further human interven- tion. The most significant result of the experiment was that the version of METAGAMER which made use of the most knowledge clearly outperformed all opponents in terms of total score on the tourna- ment. This was true despite the added evaluation cost incurred when using more knowledge. This re- sult is evidence that the knowledge implemented in METAGAMER provides it with competitive strength across the entire class of games, at least relative to more limited versions of itself and to a set of baseline programs. 5 Related Work This section compares METAGAMER to other work on general game-playing programs and on auto- matic methods for determining feature values in games. There have been many efforts to de- velop general game-playing programs which have been tested on more than one game (Epstein 1989; Williams 1972; Tadepalli 1989; Collins et al. 1991; Callan, Fawcett, & Rissland 1991; Gherrity 1993). However, none of these programs have been evalu- ated within the context of Metagame, which poses several unique challenges. First, the human de- signer cannot influence the representation of spe- cific games (as they are input directed to the metagamers). Second, there is no existing body of knowledge or game records for newly gener- ated games, which poses difficulties for approaches which rely on learning concepts or weights from textbooks or large amounts of existing games. Fi- nally, there are no existing experts against which programs can train, which suggests that stronger programs will be based on self-play (Tesauro 1994) or more active forms of rule analysis (such as that performed by METAGAMER). Despite its simplicity, METAGAMER'S analysis produced useful piece values for a wide variety of games, which agree qualitatively with the assess- ment of experts on some of these games. This ap- pears to be the first instance of a game-playing pro- gram automatically deriving material values based on active analysis when given only the rules of dif- ferent games. It also appears to be the first instance of a program capable of deriving useful piece values for games unknown to the developer of the program “The baseline players consisted of a random player and a player that conducted a 2-ply search using a ran- dom evaluation function at non-terminal positions. (Pell 1993c). The remainder of this section com- pares METAGAMER to previous work with respect to determination of feature values. Expected Outcome and Self-Play Abram- son (1990) developed a technique for determining feature values based on predicting the expected- outcome of a position in which particular features (not only piece values) were present. The expected- outcome of a position is the fraction of games a player expects to win from a position if the rest of the game after that position were played ran- domly. He suggested that this method was an in- direct means of measuring the mobility afforded by certain pieces. The method is statistical, computa- tionally intensive, and requires playing out many thousands of games. Similar considerations ap- ply to work on self-play (Tesauro 1994; Epstein 1992). On the other hand, the analysis performed by METAGAMER is a direct means of determining piece values, which follows from the application of general principles to the rules of a game. It took METAGAMER under one minute to derive piece val- ues for each of the games discussed in this section, and it conducted the analysis without playing out even a single contest. Automatic Feature Generation There has re- cently been much progress in developing programs which generate features automatically from the rules of games (de Grey 1985; Callan & Utgoff 1991; Fawcett & Utgoff 1992). When applied to chess such programs produce features which count the number of chess pieces of each type, and when applied to Othello they produce features which measure different aspects of positions which are cor- related with mobility. The methods operate on any problems encoded in an extended logical represen- tation, and are more general than the methods cur- rently used by METAGAMER. However, these meth- ods do not generate the weights of these features, and instead serve as input to systems which may learn their weights from experience or through ob- servation of expert problem-solving. While META- GAMER'S analysis is specialised to the class of sym- metric chess-like games, and thus less general than these other methods, it produces piece values which are immediately useful, even for a program which does not perform any learning. Evaluation Function Learning There has been much work on learning feature values by expe- rience or by observation of strong players (e.g. (Samuels 1967; Lee & Mahajan 1988; Levinson & Snyder 1991; Callan, Fawcett, & Rissland 1991; Tunstall-Pedoe 1991)). These are all examples of passive analysis (Pell 1993c), and would not seem 1384 Search likely to produce a strong program in a Metagame- tournament until later rounds, after which the pro- gram would have had significant experience with stronger players. 6 Conclusion The results on existing and generated games es- tablish METAGAMER as a competent competitor for SCL-Metagame. 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1,632 | An Analysis of Forward Pruning * Stephen J. J. Smith Dana S. Nau Department of Computer Science Department of Computer Science, and University of Maryland College Park, MD 20742 sjsmithQcs.umd.edu Abstract Several early game-playing computer programs used forward pruning (i.e., the practice of deliberately ig- noring nodes that are believed unlikely to affect a game tree’s minimax value), but this technique did not seem to result in good decision-making. The poor performance of forward pruning presents a major puz- zle for AI research on game playing, because some ver- sion of forward pruning seems to be “what people do,” and the best chess-playing programs still do not play as well as the best humans. As a step toward deeper understanding of forward pruning, we have set up models of forward pruning on two different kinds of game trees, and used these models to investigate how forward pruning affects the probability of choosing the correct move. In our stud- ies, forward pruning did better than minimaxing when there was a high correlation among the minimax val- ues of sibling nodes in a game tree. This result suggests that forward pruning may possi- bly be a useful decision-making technique in certain kinds of games. In particular, we believe that bridge may be such a game. Introduction Much of the difficulty of game-playing is due to the large number of alternatives that must be examined and discarded. One method for reducing the number of nodes examined by a game tree search is forward pruning, in which at each node of the search tree, the search procedure may discard some of the node’s chil- dren before searching below that node. On perfect- information zero-sum games such as chess, forward pruning has not worked as well as approaches that do not use forward pruning [4, 241. This presents a major puzzle for AI research on game playing, because some version of forward pruning seems to be “what people do,” and the best chess-playing programs still do not play as well as the best humans. Thus, it is important Institute for Systems Research University of Maryland College Park, MD 20742 nau@cs.umd.edu to try to understand why programs have been unable to utilize forward pruning as effectively as -humans have done, and whether there are ways to utilize forward pruning more effective1y.l As a step toward deeper understanding of how for- ward pruning affects quality of play, in this paper we set up a model of forward pruning on two abstract classes of game trees, and we use this model to inves- tigate how forward pruning affects the probability of choosing the correct move. Our results suggest that forward pruning works best in situations where there is a high correlation among the minimax values of sib- ling nodes. Since we believe that bridge has this char- acteristic, this encourages us to believe that forward pruning may work better in the game of bridge than it has worked in other games. Forward-Pruning Models Consider a zero-sum game between two players, Max and Min. If the game is a perfect-information game, then the “correct” value of each node u is normally taken to be the well known minimax value: the payoff at u if u is a terminal node; mm(u) = max(mm(v) : v is a child of u) if it is Max’s move at u; min(mm(v) : v is a child of b} if it is Min’s move at u. Due to the size of the game tree, computing a node’s true minimax value is impractical for most games. For this reason, game-playing programs usually mark some non-terminal nodes as terminal, and evaluate them us- ing some static evaluation function e(u). The simplest version of this approach is what Shannon [16] called “Type A” pruning: choose some arbitrary cutoff depth d, and mark a non-terminal node u as terminal if and only if u’s depth exceeds d. A more sophisticated ver- sion of this is quiescence search: mark a non-terminal *This work supported in part by an AT&T Ph.D. schol- arship to Stephen J. J. Smith, Maryland Industrial Part- nerships (MIPS) grant 501.15, Great Game Products, and NSF grants NSFD CDR-88003012 and IRI-9306580. ‘In particular, we are developing a forward-pruning search technique for the game of bridge [17, 181, by ex- tending task-network planning techniques [22, 23, 13, 201 to represent multi-agency and uncertainty. 1386 Search From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. node u as terminal if and only if u’s depth exceeds d and u is “quiet” (i.e., there is reason to believe that e(u) will be reasonably accurate at u). To further decrease the number of nodes examined, game-tree-search procedures have been developed such as alpha-beta [5], B* [2], or SSS* [21]. These proce- dures will ignore any node v below u that they can prove will not affect u’s minimax value mm(u). This approach has worked well in games such * as chess [3, 71, checkers [15, 141, and Othello [6]. A more aggressive approach is forward pruning, in which the procedure deliberately ignores v if it believes v is un- likely to affect mm(u), even if there is no proof that v will not affect mm(u). Although several early com- puter chess programs used forward pruning, it is no longer widely used, because chess programs that used it did less well than those that did not [4, 241. Our Model of Forward Pruning In the game trees investigated in this paper, the value of each leaf node is either 1, representing a win for Max, or 0, representing a win for Min. Our model of a forward-pruning algorithm works as follows. At each node u where it is Max’s move, u has three children, ur , us, and ua. The forward-pruning algorithm will choose exactly two of these three nodes to investigate further. Normally, it will make this choice by applying a static evaluation function eval(.) to the three nodes, and dis- carding the node having the lowest value-and this is what we do in the “Statistical Studies” section. For our mathematical derivations, we assume fixed proba- bilities for which nodes will be chosen and which node will be discarded, as described below. There are three possible cases: 1. Two of the nodes, say ui and ~2, have minimax val- ues representing wins for the current player. One of the nodes, say ug, has a minimax value representing a loss for the current player. Then the correct two children to investigate further are the ones whose minimax values are the same as the minimax value of u, in this case ui and us. Thus, for a Max node, the correct children have value 1; for a Min node, the correct children have value 0. If the algorithm does not choose both of the correct children, then the al- gorithm will search only one of ui and 212. Thus, it will continue part of its search down an incorrect branch, in this case the branch leading to us. This may result in an error in the algorithm’s computa- tion of u’s minimax value. In our mathematical derivations, we assume that the probability of choosing the correct two children is p, where p is constant throughout the tree. The algorithm’s probability of choosing one correct child and the incorrect child is thus (1 - p)/2 for each correct child. 2. One of the nodes, say ui, has a minimax value rep- resenting a win for the current player. Two of the Leaf node values - +1 0 0 0 0 0 0 +1 +1 Figure 1: Example of an N-game-like tree. nodes, say 2~2 and us, have minimax values repre- senting losses for the current player. In this case, the correct child is ui. If the algorithm chooses the two incorrect nodes, it will continue the rest of its search down incorrect branches, those leading to u2 and ua. This is likely to result in an error in the algorithm’s computation of u’s minimax value. In our mathematical derivations, we assume that the probability of choosing the two incorrect nodes is r, where r is constant throughout the tree. The algo- rithm’s probability of choosing the correct child and one incorrect child is thus (1 - r)/2 for each incor- rect child. (For the rest of this paper, we will set r = (1 - P)~ and define q = 1 - (p + r).) 3. All of the nodes have the same minimax value. In this case, all children are equally correct; the al- gorithm’s probability of choosing-any given pair of branches is l/3. Game-Tree Models In this section, we define two different classes of game trees. In later sections, we will investigate how foriard pruning behaves on these trees. N-Game trees and N-Game-Like Trees An N-game-dike tree is a complete tree that contains the following types of nodes (for example, see Fig. 1): 1. Max nodes, where it is Max’s move. Each Max node is either a leaf node or has three children, all of which are Min nodes. 2. Min nodes, where it is Min’s move. Each Min node has three children, all of which are RVA nodes. 3. RVA (random-value addition) nodes, which have nu- \ I merit values assigned to them at random. The nu- meric value of each RVA node is chosen indepen- dently from the set { -1,l) with probability pi be- ing the probability of choosing 1. (For the rest of this paper, we will set pN = 0.61803, the golden ratio, so that in the limit, there is still a nonzero probability of each player having a forced win in the game tree.) Each RVA node has a single child, which is a Max node. Two-Player Games 1387 Max no& Min nodes Max no&s Min nodes Max no&s Leaf node values -101100001 Figure 2: Example of a P-game tree. The tree’s Maz-:-height, h, is one less than the number of Max nodes on any path from the root to a leaf node.2 The strength of each leaf node u is the sum of the values of the RVA nodes on the path from the root to U. If the strength of a leaf node is nonnegative, it is classified as a win; otherwise, it is classified as a loss. An N-game tree, as defined in [9, lo], is similar to the N-game-like trees defined above, except that N-game trees have no RVA nodes. Instead, a value of 1 or -1 is randomly assigned to each arc, with a probability of 0.5 of choosing 1. In this paper, we study N-game-like trees in the “Mathematical Derivations” section, and N-game trees in the “Statistical Studies” section. Comparison with Bridge In the game of bridge, the basic unit of play is the trick. After each side has made a move, one side or the other wins the trick. At each point in a bridge hand, the trick score for each side is the number of tricks that side has scored so far. The outcome of the hand depends the hand. on each side’s trick score at the end of This trick-scoring method gives bridge a superficial resemblance to the N-game-like trees defined above. To see this, consider a-node v in a bridge game tree, and suppose that v represents a bridge deal in which n tricks are left to be played. If T is the subtree rooted at v, then the trick scores of the leaves of T cannot differ from one another by any more than n. A similar situation occurs in an N-game-like tree of height h: if a Max node v has a Max-height of n, and T is the subtree rooted at v, then the strength of the leaves of T cannot differ from one another by any more than 2n. P-Game Trees A P-game tree [9, 10, 121 is a complete tree that con- tains the following types of nodes (an example appears in Fig. 2): 1. MQZ nodes, where it is Max’s move. Each Max node is either a leaf node or has exactly three children, all of which are Min nodes. 2This is analogous to the height of a complete tree (which is one less than the number of nodes on any path from the root to a leaf node), except that here we only count Max nodes. 2. Min nodes, where it is Min’s move. Each Min node has exactly three children, which are both Max nodes. As before, the tree’s Max-height, h, is one less than the number of Max nodes on any path from the root to a leaf node. Since the tree is complete, each leaf node has the same height, and thus the same Max-height. The value of each leaf node u is randomly, indepen- dently chosen from a the set (0, l}, with probability pp of choosing 1. (For the rest of this paper, we will set PP = 0.68233, in order to guarantee that in the limit, there is still a nonzero probability that each player will have a forced win in the game tree [l, 11, 91.) Because U’S value does not depend on the path from the root to U, there is no need for RVA nodes. Mathematical Derivations Forward Pruning on N-Game-Like Trees We want to compute the probability that the forward- pruning algorithm estimates a value of s and the actual value is t for an N-game-like tree T whose Max-height is h. That is, we want Pr[estimated value s, actual value t 1 T’s Max-height is h]. We can compute this from the node strengths, as follows. Let eh,x,v = Pr[estimated strength x, actual strength y ] Max-height h, root is a Max node]; fhw = Pr[estimated strength x, actual strength y 1 Max-height h, root is an RVA node] ; %x,v = Pr[estimated strength x, actual strength y ] Max-height h, root is a Min node]. These probabilities depend ‘on p and pi (recall that pi = 0.61803). The base case is ec,c,Y = 1 if 2 = y = 0, and es,x,y = 0 otherwise. The recurrence for fh,m,y is fhw = PNeh,z--l,y-1 + (1 - PA+h,x+l,y+l- The recurrences for gh,c,y and eh+l ,x# are too compli- cated to include here; see [19]. Now, let eh,t,t = Pr[estimated value s, actual value t 1 Max-height h, root is a Max node]; fh,s,t = Pr[estimated value s, actual value t ] Max-height h, root is an RVA node]; #h,s,t = Pr[estimated value s, actual value t I Max-height h, root is a Min node]. Then eh,l,l = c x eh,x,y; x:x>0 y:y>o eh,l,O = x x eh,t,y; x:x~O y:y<o eh,O,l = x x eh,%,y; x:z<oy:y20 Eh,O,O = c c eh,z,y- x:x<0 y:y<o For f and jj, the equations are similar. 1388 Search Forward ‘Pruning on P-Game Trees Since there are no strengths in P-game trees, we can compute the probabilities for the values directly. We define e6,x,Y = Pr[estimated value x, actual value y I Max-height h, root is a Max node]; 86 F,Y = Pr[estimated value x, actual value y I Max-height h, root is a Min node]. The base case is ec,x,y = pp if x = 1 and y = 1; (1-pp) ifx=Oandy = 0; and 0 otherwise. As shown in [19], the recurrence for gi,x,y is identical to that for fh,x,y , except that each occurrence of eh,m,n is replaced by e6,m,n. The recurrence for ek+l,x,y is identical to that for eh+l,x,y , except that each occurrence of fh,m,n is replaced by fi,m,n. Probability of Correct Decision We can use the above recurrences to measure the prob- ability of correct decision. This is the probability that the forward-pruning algorithm, given a choice between two alternatives that have different minimax values, will choose the correct one.3 In particular, consider an N-game-like tree T of Max-height h, whose root is a Max node u with children ~1 and 242 such that the value of ~1 is greater than the value of ~2. Then Dh = Pr[estimated value of ui > estimated value of 2421 + iPr[estimated value of ur = estimated value of u2] = [gh-l,l,l#h-l,O,O + gh-l,O,lgh-1,0,0/2 + ah-l,l,lgh-1,0,1/2] [b-l,l,l + gh-l,O,l) x (sh-l,l,o + gh-l,o,())]. Similarly, for P-game trees, oh = [gh-l,l,lgh-l,o,o + gh-Wgh-1,0,0/2 + gh-l,l,lgh-1,0,1/2] [(gh-l,l,l + gh-l,o,l) x (gh-1,&O + gh-l,O,O)]. Results and Interpretations To derive closed-form solutions for the recurrences described in the “Mathematical Derivations” section would be very complicated. However, since we do have exact statements of the base cases and recurrences, we can compute any desired value of eh,x,y or ei,m,x,y, and thus any desired value of Dh or D6. We have computed Dh and Df, for trees of height h = 1,2, . . . ,15. The re- sults are shown in Fig. 3, along with the probability 3 We have also investigated the probability of correct de- cision among three alternatives; the formulas [19] are too complicated to present here, but the results are similar. 1.1 t ’ I b I- ! p-o.85 i 0.9 - 0 8 pm 0.80 p = 0.75 E 0.8 - p I 0.70 8 B ho.?- P= O-65 p10.95- 3 p - 0.60 8 0.6 - ’ \ ‘\ ‘\ \\ ‘\ ‘\ nmb. of ‘\ \ Eorf \\\‘\ \ ‘\ ‘\ t de&&by x . \ .\ ‘. . ’ .’ .’ . ’ IO.90 0.5 mm . . . . ‘.h&-~-:x= &o. - 9- I t I 0 5 10 15 20 Max-height of the tree. h Figure 3: Dh and Df, versus h for various values of p. of correct decision by random guess, included for com- parison purposes. Our interpretation of these results is as follows:* The higher the value of p, the more likely it is that the forward-pruning algorithm will choose the cor- rect two nodes to investigate at each level of the tree, and thus the more likely it is that the algorithm will return a good approximation of the tree’s minimax value. As shown in Fig. 3, this occurs in both P- game trees and N-game-like trees. In N-game-like trees, there is much stronger corre- lation among the values of sibling nodes than there is in P-game trees. Therefore, in N-game-like trees, even if the forward-pruning algorithm chooses the wrong node, the minimsx value of this node is not too far from the minimax value we would compute anyway. Thus, as shown in Fig. 3, for each value of p, the forward-pruning algorithm returns more ac- curate values in N-game-like trees than in P-game trees. Statistical Studies The results in the “Mathematical Derivations” section suggest that minimax with forward pruning does bet- ter when there is a high correlation among the minimax values of sibling nodes in a game tree. Previous stud- ies [9, lo] h ave shown that ordinary minimaxing also does better when there is a high correlation among the minimax values of sibling nodes in a game tree. Thus, the next question is whether minimax with forward ‘The probab’ * y ht of correct decision for N-game-like trees exhibits a “manic-depressive” behavior similar to that observed in [8], that is, it is higher for odd Max-heights than it is for even Max-heights. We believe this is because our RVA nodes are only put below Min nodes. Standard N-game trees have the equivalent of our RVA nodes below both Min and Max nodes. Two-Player Games 1389 pruning would do better than ordinary minimaxing- for otherwise, it wouldn’t make sense to use forward pruning for actual game playing. To answer this question, we computed the proba- bilities of correct decision at various search depths on P-game trees and N-game trees, for minimax with and without forward pruning. For this study, we wanted to use a real evaluation function rather than a mathemat- ical model of one. This made it impossible to do an analysis similar to the one in the “Mathmetical Deriva- tions” section, so instead we did a statistical study. Forh=2,... ,6, we generated 5000 ternary N-game trees and P-game trees of Max-height h. The trees were generated at random, except that if a tree’s root did not have at least one forced-win child cwira and one forced-loss child closJ, we discarded the tree and generated anot her. For each tree T, we did a depth d minimax search of T,5 using the same evaluation function used in [9, lo]: evab(u) = winning leaf-descendants of u all leaf-descendants of u ’ We did this for d = 1, . . . ,2h - 2.‘j To get a statistical approximation of the probability of correct decision, we averaged the following over all 5000 N-game trees or P-game trees: quantity averaged = I 1 if mm(c,i,,, d - 1) > mm(cl,,, , d - l), l/2 if mm(c,in, d - 1) = mm(cios8 , d - l), 0 otherwise. We then repeated the same experiment, using minimax with forward pruning. The results are shown in Figures 4 and 5, which graph the probability of correct decision for minimax- ing both with and without forward pruning. To indi- cate how good a decision each approach could produce given the same amount of search time, these figures graph the probability of correct decision as a function ‘The depth-d minimax value of a node is 1 evaZ(u) (the payoff at zb) if d = 0 or u is a terminal node, mm(u, d) = max{mm(v, d - 1) : v is a child of u} if it is Max’s move at u, min(mm(v, d - 1) : v is a child of u) if it is Min’s move at a. where eval(u) is u’s evaluation function value. A depth d minimax search from a node u means computing the depth d - 1 minimax values of u’s children. 6We did not s earth to depths 2h - 1 and 2h because the comparison would not have been fair. At these depths, ordinary minimaxing applies evaZ(u) only to nodes within one move of the end of the game. For such nodes, evaZ(u) produces perfect results, hence so does ordinary minimax- ing. 1390 Search 0.00 - b go.88- a %,.,. 7;: h=2 ~O.OO- 8 ij ~$0.05 - d % h=3 0.04 - h=4 hz5 0.93%=6 Solid lines = mhim with fonvard pnming Dashed lines = mi&nax w!Ahout forward pMilg 2 loa Nun& of nodes generated Figure 4: Probability of correct decision on N-games, versus number of nodes generated, for minimax with and without forward pruning. The data is averaged over 5000 game trees. Solid lines = minimax with forward pwing Dashed lines = nirimax withoil forward fxming ! .s- 3 0.7 i? ~0.05 z .* P g 0.6 L Figure 5: Probability of correct decision on P-games, versus number of nodes generated, for minimax with and without forward pruning. The data is averaged over 5000 game trees. of the number of nodes generated by the search.7 As can be seen, minimaxing with forward pruning gen- erally does better than ordinary minimaxing on N- games, and slightly worse than ordinary minimaxing on P-games. Conclusion In this paper, we set up models of forward pruning on ternary N-game-like game trees, and ternary P-game trees. We used these models to compute the probabil- 7For ternary g ame trees, the number of nodes generated by a ordinary minimax search is 3l+. . .+3” = (3nt1 -3)/2. The number of nodes generated with forward pruning is 3(2’ + . . . + 2’-‘-9 = 3(2” - 1). This is without alpha-beta pruning. With alpha-beta pruning, there would have been a different number of nodes generated in each game tree, making it difficult to obtain meaningful averages over our 5000 games. ity of correct decision produced by minimax with and without forward pruning. In our studies, minimax with forward pruning did better than ordinary minimaxing in cases where there was a high correlation among the minimax values of sibling nodes in a game tree. Thus, forward pruning may possibly be a viable decision-making technique on game trees having the following characteristics: :’ Jirst charucterisbic: there is generally a high correla- tion among sibling nodes; second characteristic: when there are exceptions to the first characteristic, one can accurately identify them. To extend our work, we intend to do an empirical study of forward pruning on the game of bridge. We are interested in bridge for the following reasons: Bridge is an imperfect-information game, because no player knows exactly what moves the other players are capable of making. Because of this, the game tree for bridge has a large branching factor, resulting in a game tree containing approximately 6.01 x 1O44 nodes in the worst case. Ordinary minimax search techniques do not do well in bridge, because they have no chance of searching any significant portion of the game tree. Our preliminary studies on the game of bridge show that by using forward-pruning techniques based on task-network planning, we can produce search trees of only about 1300 nodes in the worst case [17]. Thus, forward pruning will allow us to search all the way to the end of the game. Thus, we will not need to use a static evaluation function, and thus will not have to deal with the inaccuracies produced by such functions. We believe that bridge has the two characteris- tics described above, primarily because of the trick- scoring method used in bridge. Thus, we believe that forward pruning techniques may produce reasonably accurate results in bridge. References [l] Baudet, G. M. 1978. On the branching factor of the alpha-beta pruning algorithm. Artif Intel. 10:173- 199. [2] Berliner, H. J. 1979. The B* tree search algorithm: A best-first proof procedure. Artif Intel. 12:23-40. [3] Berliner, H. J.; Goetsch, 6.; Campbell, M. S.; and Ebeling, C. 1990. 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[20] Stefik, M. 1981. Planning with constraints (MOL- GEN: Part 1). Artif. Intel. 16:111-140. [21] Stockman, G. C. 1979. A minimax algorithm bet- ter than, alpha-beta? Artif. Intel. 12:179-196. [22] Tate, A. 1976. Project planning using a hierar- chic non-linear planner. Technical Report 25, De- partment of Artif. Intel., University of Edinburgh. [23] Tate, A. 1977. G enerating project networks. In Proc. 5th IJCAI. [24] Truscott, T. R. 1981. Techniques used in mini- max game-playing programs. Master’s thesis, Duke University, Durham, NC. Two-Player Games 1391 | 1994 | 282 |
1,633 | Criticism, Culture, and the Automatic Generation of Lee Spector and Adam Alpern School of Communications and Cognitive Science Hampshire College, Amherst, MA 01002 { lspector, aalpern } @ hamp.hampshire.edu Abstract Researchers wishing to create computational systems that themselves generate artworks face two interacting challenges. The first is that the standards by which artistic output is judged are notoriously difficult to quantify. The larger AI community is currently involved in a rich internal dialogue on methodolog- ical issues, standards, and rigor, and hence murkiness with re- gard to the assessment of output must be faced squarely. The second challenge is that any artwork exists within an extraordi- narily rich cultural and historical context, and it is rare that an artist who is ignorant of this context will produce acceptable works. In this paper we assert that these considerations argue for case-based AI/Art systems that take critical criteria as pa- rameters. We describe an example system that produces new bebop jazz melodies from a case-base of melodies, using ge- netic programming techniques and a fitness function based on user-provided critical criteria. We discuss the role that such techniques may play in future work on AI and the arts. Introduction: Constructing Artists Applications of computers to the arts date from the earliest days of computing. The use of AI technologies in the arts has a long history as well, particularly in music (Balaban et al. 1992). The majority of these uses fall into two cate- gories: systems that perform “art understanding” tasks of some sort (e.g., music analysis systems), and systems that function as “intelligent” tools for use by human artists (e.g., (Rowe 1993)). Recently, however, a new category of sys- tems has begun to emerge; a category of systems that are designed to be artists. By this we mean that such systems, which we will call “constructed artists,” are supposed to be capable of creating aesthetically meritorious artworks on their own, with minimal human intervention. Harold Cohen’s Aaron system is an early example of this category, and one of its few clear successes to date (McCorduck 1991). Aaron is a system that creates original drawings, each unique and potentially surprising to Cohen, that have iThe authors acknowledge the support of the Dorothy and Jerome Lemelson National Program in Invention, Innovation, and Creativity. *An experiment combining public assessment with genetic techniques similar to those described later in this paper is cur- rently in progress via mosaic on the internet. The address is: http:Nporsche.boltz.cs.cmu.edu:SOOl/htbin/mjwgenfo~. been exhibited in galleries internationally. Aaron was con- structed through a laborious process of “tutoring” by Co- hen, himself an accomplished painter, that spanned over a decade. More recently, work has proceeded on constructed artists that function as poets (Kurzweil 1990) music com- posers (Ames & Domino 1992), and aesthetic agents in vir- tual worlds (Bates 1992). A literature has also emerged on the computational underpinnings of artistic creativity more generally (e.g., (Boden 1991)). Aesthetic Judgements The philosophy of art, which in the Western tradition dates at least from Plato, has never been an area of widespread agreement (see, e.g., (Dickie & Sclafani 1977)). The range of theories regarding the bases of aesthetic value, judgement and criticism is extraordinary, and the debates show no signs of near-term resolution. This presents a problem for AI sci- entists wishing to produce computational artists: How do we know when we’ve got one? How do we know if version A is better than version B, or vice versa? Without the ability to answer such questions the science of artist construction can- not proceed, and these questions seem to be inseparably linked to the murky issues of aesthetic judgement. The larg- er AI community is currently involved in a dialogue on methodological issues, standards, and rigor; many are call- ing for the adoption of experimental methods from more tra- ditional sciences, for the use of standard examples and crite- ria of assessment, etc. If those of us working on constructed artists cannot judge our systems without first resolving all of the open questions regarding the judgement of artworks, then we will be on shaky methodological ground indeed. Fortunately, it is possible to separate the two kinds of judge- ment; we describe one approach to doing so below. The artworks of Cohen’s Aaron have been judged by the artworld and by the museum-going public. According to some theories of art this is the best, or even the only, form of assessment by which to judge the quality of a work (Danto 1978). But this sort of judgement has a high price both in terms of human resources and in terms of time. The science of artist construction will proceed quite slowly if each iteration of each system can be assessed only by orga- nizing a public show and by waiting for critical reviews.2 Of course, Cohen himself also served as a critic of Aaron’s performance, and he was presumably able to apply the re- sults of his judgements to the improvement of the program Art 3 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. in a reasonable amount of time. But it is not clear how these interactions can form the basis of a general theory of aesthetic judgement sufficient to ground a science of artist construction. At best they are instructive for other artists with an interest in applying their own critical faculties to the construction of new artists. Another approach to this dilemma is to work in a genre with codified, formalized valuation criteria. This has been a popular approach in computer music, as rule-systems have been developed for many forms of music (e.g., (Ebcioglu 1992, Maxwell 1992)). There are three problems with this approach. The first is that existing formalizations are often of “dead” forms-it may be that we understand them well enough to codify them only because they have fossilized. If we want our constructed artists to produce creative works in live genres, such formalizations are of little value. The sec- ond problem is that it is not clear that adherence to the rules of a particular art form is a good indicator of aesthetic value; it might merely indicate inclusion in the genre, which might be compatible with aesthetic mediocrity. Third, it is not clear that work in genres with codified valuation criteria will gen- eralize to other genres, many of which seem to resist the im- position of criteria upon which the art world can consense. The alternative approach that we propose is to factor aesthetic judgement out of the systems that we develop. We don’t need to know what the “right” criteria are for aesthetic judgement; we only need to know that our sys- tems are capable of conforming to the range of such crite- ria that might be proposed. If we develop systems that take critical criteria as parameters, and if our systems work over a wide range of variation of these parameters, then we can safely ignore debates about which critical criteria are cor- rect. We can then ask all opposing parties to submit sets of critical criteria; although they must all be formalizable, they may vary considerably. To the extent that we can keep everyone happy, by producing constructed artists to earn accolades from any formal critic, we will be making real progress in the science of artist construction. Instances of the framework that we present below pro- duce an artist as output when given a critic (and other data) as input. The constructed artist may not be able to adapt to other critics that it encounters later in its career; such adap- tation is a subject for future work. An Artist’s Culture Every artwork exists within a rich cultural and historical context, and many theorists have argued that good art can be neither produced nor assessed in ignorance of this con- text. It is not obvious, to say the least, how a deep appreci- ation of the human cultural context can be programmed into a constructed artist. Trurl, the robot who builds an electronic bard in a humorous story by Stanislaw Lem, is forced to repeat within the machine “the entire Universe 30ther case-based approaches to creative processes are pre- sented in (Dartnall& Kim 1993). 40ther uses have been made of evolutionary methods in com- putational arts. See, e.g., (Todd & Latham 1992). 4 The Arts from the beginning-or at least a good piece of it.” (Lem 1974) In most real systems to date, features of the cultural context are implicit in analytical and generative rules, but there is no direct way to vary the culture experimentally. We believe that the best approach for providing a cultural context for a constructed artist is to make a large case-base of prior works available as a library. In essence, we want to “factor out” the culture in the same way that we “factor out” the critic; by developing systems that take “cultures” as parameters, our systems will be culture-independent and we will be able to assess the success of our systems across cultures. The success of such systems should not depend on any speci$c cultural context; they should be sufficiently flexible to perform within a variety of cultures. The cultur- al case-base should be made available both to the con- structed artist and to the critics that guide the artist con- struction process. It may be argued that there is much more to a culture than a library of past works. We agree, but we also believe that a large case-base of successful artworks forms a good basis for cultural sensitivity. 3 Enhanced notions of culture may be incorporated into the framework, so long as all culture-dependent elements are provided as variable pa- rameters to the artist construction system. Genetic Programming The framework sketched above calls for an artist con- struction system that takes as input a set of critical criteria and a case-base of past artworks. The system should pro- duce as output a successful constructed artist-that is, a program that can be executed to produce successful new artworks relative to the given critic and culture. The technology of genetic programming (Koza 1992) provides tools that make the implementation of this frame- work fairly straightforward. Genetic programming is a technique for the automatic generation of computer pro- grams; in our case we can use the technique to automati- cally generate computer programs that will function as constructed artists. Genetic programming is an evolution- ary method in which programs are evolved using a process modeled on Darwinian natural selection.4 The technique is a variant of the genetic algorithms of (Holland 1992). The traditional genetic algorithm evolves fixed-length chromo- some strings that encode behavior-producing systems, while genetic programming evolves behavior-producing computer programs directly. The process of natural selec- tion is driven by fitness; that is, by some assessment of the quality of each individual. Genetic programming systems take jitness functions as parameters. For the production of constructed artists we can provide critical criteria as pa- rameters to the system in the form of fitness functions. A gene,tic programming system works with a problem- specificfunction set and terminal set. These sets contain the primitive elements out of which all of the output programs will be constructed. The genetic programming process starts by creating a large initial population of programs that are random combinations of elements from the function and terminal sets. One generally ensures that each function can take, in any of its argument positions, any terminal and any value that might be returned by any function in the function set. This allows the use of a simple random function gener- ator, since every combination of functions and terminals can be guaranteed to execute without signalling an error. Each of the programs in the initial population is assessed for fitness. This is usually accomplished by running each program on a collection of inputs called fitness cases, and by a running a fitness function on the output of each of these runs; the resulting values are then combined to pro- duce a single fitness value for the program. The fitness values are used in producing the next genera- tion of programs. The next generation may be produced from the current generation via a variety of genetic opera- tions including reproduction, crossover, mutation, permu- tation, and others. We use only reproduction and crossover in the present project; (Koza 1992) describes a variety of genetic operations in detail. The reproduction operator se- lects a highly fit individual and copies it into the next gen- eration; this is the most direct way to implement the notion of “survival of the fittest.” Individuals are selected for re- production randomly, but the selection function is biased toward highly fit programs. Fitness-proportionate reproduction does not introduce any new individuals to the system-it merely propagates fit individuals from one generation to the next. The crossover operation, on the other hand, introduces varia- tion by selecting two highly fit parents; it generates from them two ofSspring, which are produced by swapping ran- dom fragments of the parents. The resulting programs are copied to the next generation. Over many generations of fitness assessment, reproduc- tion and crossover, the average fitness of the population will tend to improve, as will the fitness of the best-of-generation individual from each generation. After a preestablished number of generations, or after the fitness improves to some preestablished level, the best-of-run individual is designated as the result and is produced as the output from the genetic programming system. Genetic programming searches the space of computer programs in an attempt to maximize fitness. It is fitness that determines the structure of the resulting programs, not the intuitions of a human programmer or algorithm design- lproduces 1 Original Artwork 1 Figure 1. Diagram of the Genetic Artist Construction framework er. Koza presents applications of genetic programming to a wide range of problems, along with arguments to support its utility as a general automatic programming technique (Koza 1992). Genetic Programming of Constructed Artists Genetic programming provides an obvious method for building an artist construction system that takes critical cri- teria as input: We use an off-the-shelf genetic program- ming system for which we have crafted function and termi- nal sets adequate for the production of a wide range of artist programs within some given medium. We then allow the user to write a critic function that will be used as a fitness function by the genetic programming system. Note that we have great freedom in designing the func- tion and terminal sets. We may use any artwork-producing functions and terminals that we feel are appropriate for the given medium. In particular, we may include functions that access a case-base of prior, highly valued works. The case- base may contain works from the real history of art in the given medium, the results of prior runs of genetic pro- gramming, or any mixture of the two. Access to the case- base allows the functions in the function set to produce a range of results depending on the artist’s cultural context. The case-base access functions should be made available to the critic functions as well, since many critical criteria may be best phrased in terms of comparisons to works in the prevailing culture. Figure 1 shows a diagram of the resulting framework for the genetic programming of culturally-contextualized, critic- sensitive constructed artists. The arrow from the case-base to the constructed artist reflects the fact that a constructed artist is a program that may itself take input. This input might come from anywhere; it might, for example, come from a random number generator or from real-time interac- tion with an audience. In our current work we provide our constructed artists with input from the case-base; that is, the constructed artist takes a prior work from the case-base as input, and produces a new work as output. Genetic Programming of a Bebop Musician We illustrate the framework with a system that creates simple programs that produce Bebop jazz melodies. Jazz melody is a good medium for this sort of experimentation for several reasons. First, there are several simple ways to represent melodies in a form that is manipulable by simple program- ming constructs. Second, the jazz tradition includes several “call and response” forms, so the idea of producing a new work on the basis of an old work has established precedents within the genre. Third, the jazz literature contains several analytical works that enumerate critical criteria (e.g., (Coker 1964)), along with many works on technique that provide guidance in creating a function set (e.g., (Baker 1988)). We decided to generate programs that produce four- measure melodies as output when given four-measure melodies as input. This corresponds to the popular practice of “trading four” in jazz improvisation. We used a weak representation for melodies: lists of 64 numbers, each of which represents a pitch that will be sounded for the dura- tion of a sixteenth note. Rests are represented as -1, and equivalent adjacent pitches are merged into notes of longer duration. This representation is inadequate because it can accommodate neither thirty-second notes nor triplets of any kind, and because adjacent notes of equivalent pitch must be separated by a rest in order to sound individually. It is nonetheless sufficient for many simple melodies, and it has the advantages of simplicity and ease of manipulation. We used Koza’s LISP-based genetic programming code, which is presented in an appendix to (Koza 1992) and is available on the internet by anonymous FTP. Our function set, inspired by a list of techniques in (Baker 1988), consists of the following 13 functions: REP takes a single melody and returns a new melody that consists of the first measure of the given melody repeated four times. WA takes a single melody and returns it with every note trans- posed up an octave; notes that are transposed out of the two- octave range above middle C are wrapped to the bottom of the range. IVA is similar to WA, but the transposition interval is determined by matching the given melody against the melodies in the case-base. WA transposes the given melody by the average interval between itself and the most similar melody found in the knowledge base. Similarity is deter- mined by computing the inter-note intervals for the pair of melodies to be compared, and by counting the number of times that three-interval sequences occur in both sequences. EXTEND takes a single melody and fills any trailing rests with the melody itself. If given a very short melody EXTEND may produce a melody with a large number of repetitions. TRUNC takes a single melody and replaces all notes follow- ing the last rest with additional rests. DIMINUTE takes a sin- gle melody and speeds it up. It removes every odd-numbered element of the melody list, compressing the remaining ele- ments into the first half of the list and padding the end with rests. AUGMENT takes a single melody and slows it down, doubling each element in the first half of the melody, and discarding the entire second half. FRAGMENT takes two melodies and returns a melody that has parts taken from each. The returned melody consists of the first two beats of the first given melody, the second two beats of the second given melody, the third two beats of the first given melody, and so on. The INVERT function takes a single melody and returns it with each interval inverted. The first note is held constant, the second note differs from the first by the corre- sponding interval in the given melody negated, etc. Again, notes that would be outside of the two octave range above middle C are wrapped around. RETROGRADE takes a single melody and returns it reversed. MOST-FAMILIAR takes two melodies and returns the one that is most similar to those in the case-base, using the same similarity metric as in IVA. COMPARE-TRANSPOSE takes a single melody and returns it unevenly transposed, with each note transposed by half the difference between it and the corresponding note in the most similar melody from the case-base. ROTATE takes a single melody and returns it moved forward in time by one quarter note, with the last note wrapped around to the beginning. Our terminal set consists of a single symbol, CALL- MELODY, which serves as the input to the programs pro- duced by the system. One runs the resulting program by setting the variable CALL-MELODY to some input melody, and then evaluating the program in a LISP listener. We ran our system with a case-base consisting of five four-measure fragments from Charlie Parker songs. We as- sessed the fitness of each program by running it with each of the melodies in the case-base as input. Each run produced a single melody that was assessed on the basis of a set of criti- cal criteria inspired by those presented in (Baker 1988). TONAL-NOVELTY-BALANCE returns 0 if there is perfect bal- ance between novel tonal material and tonal material that can be found in the case-base. It returns 1 if there is no balance, and intermediate values for intermediate levels of tonal nov- elty. Matching is performed with 3-note subsequences of the melodies. RHYTHMIC-NOVELTY-BALANCE is identical except that the rhythmic structure of the melody, rather than the tonal structure, is compared against the melodies in the case- base. TONAL-RESPONSE-BALANCE compares the melody produced by the program with the melody that was provid- ed as input to the program (CALL-MELODY). It compares the two melodies point-for-point and returns 0 for a perfect bal- ance of equality and inequality, 1 for complete mismatch or exact equivalence, and intermediate values for intermediate degrees of match. SKIP-BALANCE returns 0 if the melody perfectly balances diatonic movement (intervals of less than 3) with “skips” (intervals of size 3 or greater). RHYTHMIC- COHERENCE returns 0 as long as the melody contains no single sixteenth notes occurring between longer notes. If isolated sixteenth notes do occur in the melody, RHYTHMIC- COHERENCE returns the number such notes. Four of these five critical functions return real numbers between 0 and 1, with lower numbers indicating better melodies. The last critical function returns 0 for a melody that meets an important constraint, and 1 or greater for melodies that don’t. The fitness of a melody-producing pro- gram is calculated as the sum of the values returned by the critical functions, summed over all of the fitness cases. As- suming for the moment that RHYTHMIC-COHERENCE returns no greater than 1, the maximum (worst) fitness value is the number of critical criteria (5) times the number of fitness cases (5), or 25. The best programs will have fitness values considerably closer to 0. Since RHYTHMIC-COHERENCE may return greater than 1, it is possible to get fitness values high- er than 25, but we have rarely seen such values in practice. Results We ran the genetic programming system with a population size of 250 for 21 generations. The best program from the initial, randomly-created population had a fitness of 7.43. The program was: (FRAGMENT (AUGMENT CALL-MELODY) CALL-MELODY). This simply interleaves, in two-beat-long sections, the input melody with a slowed down version of the input melody. Since many of the critic functions look for balance, and since the input melody is taken from the case base, this simple program actually performs very well. 6 The Arts As shown in Figure 2, the average fitness of the popula- tion improved over the next few generations, but the fitness of the best-of-generation program did not improve notice- ably until generation 3, when the following was produced: (FRAGMENT (COMPARE-TRANSPOSE (INVERT (COMPARE-TRANSPOSE CALL-MELODY))) CALL-MELODY) This function performs a more complex manipulation of its input, including two calls to the case-sensitive COM- PARE-TRANSPOSE function. As shown in Figure 2, the fitness of the best-of-generation program, along with the average fitness of the population, continued to improve through subsequent generations. The best-of-run program for this run was found on gen- eration 19 and had a fitness measure of 2.82. It was: (FRAGMENT (COMPARE-TRANSPOSE (8VA (COMPARE-TRANSPOSE (FRAGMENT (WA (DIMINUTE (EXTEND CALL-MELODY))) (FRAGMENT (EXTEND CALL-MELODY) (AUGMENT (RETROGRADE (RETROGRADE (ROTATE (FRAGMENT CALL-MELODY CALL-MELODY)))))))))) (MOST-FAMILIAR (INVERT CALL-MELODY) (IVA CALL-MELODY))) Figure 3 shows a call/response pair in music notation. This response pleases our critic very well-the sum of fitness components is 0.19, which is quite close to a perfect score of 0. This should multiplied by 5, producing 0.95, for compari- son to the above-mentioned fitness values. (Recall that the above fitness values were summed over 5 fitness cases.) The sum-of-components values for the best-of-run program run on the 5 fitness cases were 0.19, 0.3 1, 0.65, 0.4 1, and 1.25. Although the response in Figure 3 pleases the critic, it does not please US (the authors) particularly well. This is not an in: dication of weakness of the genetic programming approach to musician construction. Nor is it an indication that we made improper choices (of function set, terminal set, etc.) in apply- ing the technique; it just means that we should work to im- prove the critical criteria that we provide as parameters to the system. The quality of the output vis-8-vis our aesthetic judgement is largely separable from the ability of the system to produce critic-pleasing programs. The former is a question to be argued in the philosophy of art; the latter is an element of the science of artist construction. Our example system does have its weaknesses when as- sessed purely as a critic-pleaser. The best-of-run program pleases the critic when run on melodies that were used in the fitness cases, but it is not as robust as we would like. We ran the program on 3 Charlie Parker melodies that were not used in the fitness cases and produced sum-of- components values 0.8 1, 1.66, and 0.93. These are not ter- rible; in fact, two of these values are better than the worst sum-of-components value for a melody used as a fitness L” I -E+ Best of Gen -+ Average I I 0 10 20 Generation 30 Figure 2. Best-of-generation and average fitnesses case. But on average the program performs better with in- Put from the fitness cases-it can not yet be said to our critic in responding to bebop melodies generally. please The lack of robustness is a weakness of our application of the framework to music, and we are exploring it experimen- tally. We are working with alternative music representation schemes, alternative function and terminal sets, and varia- tions in other parameters of the genetic programming sys- tem, in an attempt to produce more robust constructed musi- cians. We must note, however, that variations in the critic and in the case-base must be explored as well. Although we would like our system to w&k well independently of changes in these parameters, they have an impact ability of the system to produce robust critic-pleasers. on the The case for the separability of critical criteria, culture, and techniques for artist const&tion has been stated strong- ly in this paper. In fact, the character of a fitness function helps to determine the “fitness landscape” (Kinnear 1994) that is searched by genetic programming. Hence the choice of critic and the composition of the case-base will both have an impact on the effectiveness of the artist construction frameiork that we have described. For this reason we must work to develop systems that perform well over ranges of critical criteria that might be proposed. To the extent that these ranges depend on our interpretation of the philosophi- cal discussions of aesthetic judgement, the clean separation that we would like to maintain between such discussions and the science of artist construction breaks down. We be- lieve, however, that reasonable generalizations can be made in this area, enabling us to work on artist construction sys- tems with clear, quantitative indicators of success. This be- lief can only be explored experimentally, by continuing to apply the framework to the construction of artists in various media, by working with various sets of critical criteria that we find in the literature, by providing our systems with ac- cess to various cultural contexts, and by assessing the ro- bustness of the art-making programs that result. The resulting research program presents several chal- lenges. First there are issues of representation; these are Art 7 References Yardbird Suite by Charlie Parker Response generated by the constructed musician Figure 3. A call/response pair. problematic even for music, and more so for other media. Then there are issues of scale; our example system uses a tiny case-base and simple critical criteria. While these suffice to demonstrate the framework, we cannot expect to be impressed with the output of systems built on such im- poverished notions of culture and criticism. Finally, al- though our framework frees us from reliance on any par- ticular critical criteria, it does require that critical criteria be encoded; some may question the feasibility of this en- terprise. We believe that criteria can be extracted from the critical literature, and we are also investigating the auto- matic generation of critics from the case-base. Conclusions Johnson-Laird, in a computational study of jazz improvisa- tion, notes that “neo-Darwinian” theories of creativity have long been espoused, but he rejects them because “their gross inefficiency renders them highly implausible as an account of any sort of mental process.” (Johnson-Laird 1991, p.321) The new technologies of genetic algorithms and genetic pro- gramming offer the promise of tractable evolutionary pro- cessing, and hence theories of creativity-through-evolution may now be explored experimentally. The genetic program- ming framework for artist construction offers additional ad- vantages in that it provides a relatively clean way to separate out issues of aesthetic judgement from issues of system judgement. Instances of our framework take critics and cul- tural contexts as parameters, producing constructed artists as output. This allows us to consider the ability of our system to please critics within cultures, without involving us in questions of aesthetics. The separation between the two forms of judgement is not quite as clean as we would like, but nobody said it would be easy to raise an artist. Acknowledgments Valuable feedback was provided by Rebecca S. Neimark, Joe Futrelle, and the members of the Propositional Atti- tudes Task Force at Smith College. Ames, C.; and Domino, M. 1992. Cybernetic Composer: An Overview. In Understanding Music with AI, Balaban, M.; Ebcioglu, K.; and Laske, O., eds. 187-205. Cambridge MA: The AAAI Press/The MIT Press. Baker, D. 1988. David Baker’s Jazz Improvisation, Re- vised Edition. Alfred Publishing Co., Inc. Balaban, M.; Ebcioglu, K.; and Laske, O., eds. 1992. Un- derstanding Music with AI. Cambridge MA: The AAAI Press/The MIT Press. Bates, J. 1992. Virtual Reality, Art, and Entertainment. Presence 1: 133-138. Boden, M.A. 1991. The Creative Mind: Myths & Mecha- nisms. Basic Books ( Harper Collins Publishers). Coker, J. 1964. Improvising Jazz. New York: Simon and Schuster, Inc. Danto, A. 1978. The Artworld. In Philosophy Looks at the Arts, Margolis, J., ed. 132-144. Philadelphia, PA: Temple University Press. Dartnall, T.; Kim, S., eds. 1993. AI and Creativity, Work- ing Notes, Spring Symposium. AAAI Technical Report. Dickie, G.; and Sclafani, R.J., eds. 1977. Aesthetics. New York: St. Martin’s Press. Ebcioglu, K. 1992. An Expert System for Harmonizing Chorales in the Style of J. S. Bach. In Understanding Music with AI, Balaban, M.; Ebcioglu, K.; and Laske, O., eds. 295-333. Cambridge MA: The AAAI Press/The MIT Press. Holland, J.H. 1992. Adaptation in Natural and ArtiJicial Systems. Cambridge, MA: The MIT Press. Johnson-Laird, P.N. 1991. Jazz Improvisation: A Theory at the Computational Level. In Representing Musical Struc- ture, Howell, P.; West, R.; and Cross, I., eds. 291-325. New York: Academic Press. Kinnear, K.E. Jr. 1994. Fitness Landscapes and Difficulty in Genetic Programming.. In Proceedings of EC94, The IEEE Conference on Evolutionary Computation, IEEE. Koza, J.R. 1992. Genetic Programming. Cambridge, MA: The MIT Press. Kurzweil, R. 1990. The Age of Intelligent Machines. Cam- bridge, MA: The MIT Press. Lem, S. 1974. The Cyberiad. New York: Harcourt Brace Jovanovich, Publishers. Maxwell, H.J. 1992. An Expert System for Harmonizing Analysis of Tonal Music. In Understanding Music with AZ, Balaban, M.; Ebcioglu, K.; and Laske, O., eds. 335-353. Cambridge MA: The AAAI Press/The MIT Press. McCorduck, P. 199 1. Aaron’s Code: Meta-art, Artificial Intelligence and the Work of Harold Cohen. New York : W. H. Freeman and Company. Rowe, R. 1993. Interactive Music Systems. Cambridge, MA: The MIT Press. Todd, S.; and Latham, W. 1992. Evolutionary Art and Computers. Academic Press. 8 The Arts | 1994 | 283 |
1,634 | esearch problems in the use of a s allow Arti cial Intelligence model of personality and emotion* Clark Elliott Institute for Applied Artificial Intelligence DePaul University 243 South Wabash Avenue Chicago, IL 60604 and School of Education and Social Policy Northwestern University Evanston, IL email: elliottOils.nwu.edu Abstract This paper presents an overview of some open research problems in the representation of emo- tion on computers. The issues discussed arise in the context of a broad, albeit shallow, emotion reasoning platform based originally on the ideas of Ortony, Clore, and Collins(Ortony, Clore, & Collins 1988). In addressing these problems we hope to (1) correct and expand our content the- ory of emotion, and pseudo personality, which un- derlies all aspects of the research; (2) answer fea- sibility questions regarding a usable representa- tion of the emotion domain in the computer, and (3) build agents capable of emotional interaction with users. A brief description of a semantics- based AI program, the Aflectiue Reasoner, and its recent multi-media extensions is given. Issues pertaining to affective user modeling, an expert system on emotion eliciting situations, the build- ing of a sympathetic computer, models of rela- tionship, personality in games, and the motiva- tion behind the study of emotion on computers are discussed. References to the current literature and recent workshops are made. Introduction The emotion reasoning platform discussed in this paper has developed over the course of several years and cur- rently includes, besides the underlying emotion engine (described briefly below), a speech recognition pack- age which is able to discriminate at least some broad categories of emotion content; a music indexing and playback mechanism allowing virtually instant access to hundreds of hours of midi format music used to aid in the expression of emotion; a schematic representa- tion of approximately 70 emotion faces; and a text-to- speech module for expressing dynamically constructed *Preparation of this article was supported in part by An- dersen Consulting through Northwestern University’s Insti- tute for the Learning Sciences. text, including a minimal amount of emotion inflection (through runtime control of speed, pitch and volume). In the spirit of one of this year’s conference themes, we view this project as being in the “platform and con- cept hacking” stage, wherein we explore what plausible expectations we may make with respect to a shallow model of emotion and personality representation on the computer. Findings are strictly preliminary, and yet enough work has been done to raise what we feel to be some interesting questions. What we refer to as “emotions” in this paper arise naturally in many human social situations as a byprod- uct of goal-driven and principled (or unprincipled) be- havior, simple preferences, and relationships with other agents. This applies to many situations that one would not ordinary refer to as emotional: a social agent be- coming annoyed with someone who is wasting her time (a mild case of that person violating the agent’s princi- ple of social efficiency thus blocking of one of the agent’s goals through the reduction of a valued resource, time), enjoying a piece of music because it is appealing (liking it, through a simple, unjustifiable, preference), and so forth. We limit our consideration of emotion states, and intensities, to states and intensities similar to what Fri- jda et al. (Frijda et al. 1992) were describing when they referred to the overaIl feZt intensity of an emotion as comprising Uwhatever would go into the generation of a response to a global question such as this: ‘How intense was your emotional reaction to situation S?“’ Physical manifestations, neural processes, and much about du- ration are not included in the model. Lastly, we suggest that the representation of human emotion and personality in a social context, using AI techniques, is long overdue as a major area of study (c.f. (Norman 1980)). It is our belief that for each of the issues raised below, enough background work has been done that partial solutions are within the grasp of the AI community. Believable Agents 9 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Background In our current research, embodied in a large AI pro- gram called the Affective Reasoner, we simulate sim- ple worlds populated with with agents capable of re- sponding Uemotionally” as a function of their concerns. Agents are given unique pseudo-personalities modeled as both a set of appraisal frernes representing their individual goals, principles, preferences, and moods, and as a set of channels for the expression of cmo- tions. Combinations of appraisal frames are used to create agents’ interpretations of situations that unfold in the simulation. These interpretations, in turn, can be characterized by the simulator in terms of the elic- iting conditions for emotions. As a result, in some cases agents “have emotions,” which then may be ex- pressed in ways that are observable by other agents, and as new simulation events which might perturb fu- ture situations (Elliott 1992). Additionally, agents use a case-based heuristic classification system (based on (Bareiss 1989)) to reason about the emotions other agents are presumed to be having, and to form represen- tations of those other agents’ personalities that will help them to predict and explain future emotion episodes involving the observed agent (Elliott & Ortony 1992; Elliott 1992). Ortony, et al. (Ortony, Clore, & Collins 1988) discuss twenty-two emotion types based on valenced reactions to situations being construed as goal-relevant events, acts of accountable agents, or attractive or unattractive objects (including agents interpreted as objects). This theory has been extended to include the two additional emotion types of love and hate (Elliott 1992). See figure 1. Additionally, using the work of Ortony, et al. (Ortony, Clore, & Collins 1988) as a guide, we ana- lyzed a set of descriptions of emotion eliciting situa- tions and created a modified set of emotion intensity variablea to explain the causes of varying emotion inten- sity, within a coarse-grained simulation paradigm (El- liott & Siegle 1993). We reduced the resulting set of variables to a computable formalism, and represented sample situations in the Affective Reasoner. We then isolated three areas of the simulation where variables in either the short-term state of an agent, the long- term disposition of an agent, or the emotion-eliciting situation itself, helped to determine the intensity of the agent’s subsequent affective state. For each area there is an associated group of variables. The first group, aimulation-event variables, comprises variables whose values change independently of situation inter- pretation mechanisms. The second group, stable dispo- sition variables, consists of variables that are involved in an agent’s interpretation of situations, tend to be constant, and help to determine an agent’s personality and role in the simulation. We felt that, for the pur- poses of implementation, the distinction between these two groups was underspecified in the work of Ortony, et al. (Ortony, Clore, & Collins 1988). The last group, mood-relevant variables, contains those variables that contribute to an agent’s mood state. In all there are approximately twenty such variables, although not all apply to each emotion category. For example, the variable blameworthiness- praiseworthiness might roughly be described as the de- gree to which an observing agent interprets an observed agent as having upheld or violated one of the observing agent’s principles, in some situation. It is derived from a set of simulation values, which might include values for the amount of effort expected in a given situation, the accountability of an agent as determined by role, and so forth. It has no default value, being determined entirely by one agent’s construal of the simulated act of an another agent. Our work has focused primarily on the detailed work- ing out of a computational method for representing the antecedents and expression of human emotion in diverse human social situations. This has included the analysis, within the constraints of the underlying emotion theory, of many hundreds of informally described social situa- tions which have given rise to emotions. To date the computational mechanism has included, among other components, (a) the construction of hundreds of ap- praisalfiames, which include slots for reasoning about intenstiy and mood, in domains as diverse as, for ex- ample, financial accounting, stories, playing poker, and sales, (b) pseudo personality types made up of these appraisal frames, (c) the use of these pseudo personal- ities for con&ruing situations with respect to the con- cerns of simulated agents, thus giving rise to “emo- tion generationn in simulation runs, (d) the genera- tion of simple emotion instances based on the twenty- four emotion categories, (e) the generation of actions through approximately 450 channels (about twenty for each emotion category) consistent with the simulated emotions they are intended to express (each of which may, in turn, contain multiple manifestation instances), (f) abductive reasoning about the emotions expressed by other agents in the system, (g) the internal represen- tation of the presumed pseudo personalities of observed agents by observing agents, (h) simple “explanations” of the emotions with respect to their emotional an- tecedents within the simulation, (i) simple models of re- lationship between the agents, allowing for “emotions” based on the concerns of others, and (j) the inclusion of the user as one of the agents in the system about which reasoning may take place. Most recently we have been working on opening up communication channels with the user of the system through the addition of modules for speech recognition, inflected speech generation, indexed music-on-demand (using a midi interface and a 400 voice Proteus MS- PLUS synthesizer), and facial expression for the agents. The broad long-range goals we would like to see pur- sued include number of applications we envision as made possible by the representational capabilities of a system such as this. Among these are the build- 10 The Arts ing of a computer that has some capability of catego- rizing, and responding to, a user’s affective state; the building of systems that allow users to interactively ex- plore the emotional content of a broad range of simu- lated social situations (e.g., for tutoring, for socially un- skilled psychotherapy patients, and for military stress applications); testing the use of “emotionally aware” automated software agents as a way of enhancing the user’s engagement in educational, and other software; using emotionally aware agents to communicate prior- ities naturally to the user, such as with an automated assistant for meetings, or the communication of tech- nical concerns to less technical users through the focus of attention (e.g., operating systems, financial analysis), the use of computer-based emotion expression as an au- thoring tool (e.g., as online feedback for students), the construction of games that include a complex, yet co- hesive, emotion and personality component; the use of the underlying emotion theory to analyze, and manipu- late, the automated telling of stories; and platforms for testing the link between music and emotion expression. Research Questions Affective user modeling. One hard, and divisive, problem facing the AI commu- nity is that of building user models. Rather than more traditional models which focus on the mental processes of the user in problem solving situations (Van Lehn 1988)) we propose an alternative wherein only certain components of the affective state of the user is modeled. This is a much smaller problem, but one which should provide useful leverage. It might be considered akin to the feedback a responsive speaker might make use of when “playing” to her audience. We do not propose this as a full model of a user’s emotional states which would then also require that all of the hard cognitive modeling problems be solved as well. To implement simple affective user modeling, several components are required: (1) A structure which allows us to capture an agent’s (in this case, the user’s) outlook on situations that arise. This structure must include some concept of the role, personality, and current state of the user (within the context of shallow emotion rea- soning), which together comprise the basis for the user’s idiosyncratic way of construing the world. (2) A lexicon through which the user expresses his or her emotions to the computer. (3) A comprehensive set of emotion cat- egories which allow for the mapping of emotion eliciting situations to the emotion expression lexicon, and vice versa. In our current work, as discussed above, we have implemented a broad, albeit shallow, representation of the first, component,, and a comprehensive, descriptive representation of the third. The weakest link in such a system is in the lexicon. How does a computer, which has no understanding of faces1 , and which presumably has no mechanism for ‘Although reportedly the work of Eckman might begin Figure 1: Emotion types I Ortony, 19921 and [Elliot1 IGroup Well- Being 4 SpeciGation appra& of a situation as an event Fortunes of Others Prospect based Confir- mation Attrib- ution Attractior Well- being / Attrib- ution Attractiol / Attrib- ution presumed value of a a situation 88 an event affecting anot her appraisal of a situation a8 a prospective event appraisal of a situation as confirming or disconfirming an expec- tation appraisal of a situation as an account- able act of some agent appraisal of a situation as cant aining an attractive or unattractive object compound emotions compound emotion extensions Fable based on [O’Rorke and 19921) L Name and Emotion Type joy: pleased about an event distress: displeased about an event happy-for: pleased about an event desirable for another gloating: pleased about an event undesirable for another resentment: dis- pleased about an event desirable for another sorry-for: displeased about an event undesirable for another hope: pleased about a prospective desirable event fear: displeased about a prospective undesirable event satisfaction: pleased about a confirmed desirable event relief: pleased about a disconfirmed undesirable event fears-confirmed: displeased about a confirmed undesirable event disappointment: displeased about a disconfirmed desirable event pride: approving of one’s own act admiration: approving of another’s act shame: disapproving of one’s own act reproach: disapproving of another’s act liking: finding an object appealing disliking: finding an object unappealing gratitude: admiration + joy anger: reproach + distress gratification: pride + joy remorse: shame + distress love: admiration + liking hate: reproach + disliking Believable Agents 11 generating plausible explanations which might allow it to determine which emotions are likely to have arisen, know what emotion a user is expressing? In addressing this question we consider several leverage points which show promise in allowing us to work around this prob- lem, at least to some degree. First, and most impor- tantly, it might well prove to be true that users are motivated to express their emotions to the computer, provided that there is at least the ill&on that the com- puter understands how they are feeling. Should this be so, then some latitude is afforded us in requiring that the user, who is adaptable in communication, conform to the protocol of the computer, which is not. Second, the comprehensive emotion model allows us to develop a large lexicon categorized by both emotion category and intensity. Third, speech recognition packages are advanced enough to capture some of what is of interest to us with respect to the lexicon. For example, using the work of Ortony et al. as a guide (Ortony, Clore, & Foss 198’7), we built expressions containing emotion words, intensity modifiers, and pro- noun references to different roles (e.g., I am a bit sad because he..., I am rather sick at heart about her..., I was pretty embarrassed after my...) (Elliott & Car- lino 1994). We built phrases containing 198 emotion words (e.g. . . . . bothered, brokenhearted, calm, carefree, chagrined, charmed, cheered, cheerful, cheerless,. ..). In preliminary runs we were able to detect 188 of the emo- tion words correctly on the first try, in context, with 10 false positives. Misses tended to be cases such as con- fusing “anguish” with “anguished,” and “displeased” with “at ease.” There were 10 other instances of diffi- culty with other parts of the phrases, such as confusing Umyn with ‘T.” Most of these would have been caught by a system with even rudimentary knowledge of En- glish grammar. Additionally, in other preliminary runs of our speech recognition package the computer was able to recognize the seven emotion categories, anger, hatred, sadness, love, joy, fear, and neutral, which we did our best to communicate to it, when speaking the sentence, “Hello Sam, I want to talk to you.” In this small exercise we broke the sentence up into three parts, identifying each part as a “word” to the speech recognition system. We then trained each phrase for the seven different inflec- tions. With practice we were able to get close to 100% recognition of the intended emotional state.l To achieve this we had to be slightly theatrical, but not overly so, and there was a flavor of speaking with someone who was hard of hearing, but again, not overly SO.~ to address this issue. 2And this, even though the goal of the developers of the package was to eliminate inflection and simply recognise the words. ‘Interesting y 1 , when not imagining a situation consistent with the emotion we were attempting to express by voice, we were consistently less accurate. In addition, it appeared that the computer was biased somewhat in its errors toward Once the lexicon is established, and minimal natu- ral language parsing is in place through the use of an ATN or other simple system, tokens can either be in- terpreted directly as situations in themselves, or as a set of features indexing into a case-base to retrieve sim- ilar cases indicating a particular emotion category. To illustrate, on the one hand, from user input of “I am satisfied with the results” we might, for example, yield the situation: “the user is satisfied now in response to the comparison of her answer with the one just pro- vided by the computer”). On the other hand, given user input of “I am happy now” (spoken with a hateful inflection), we might yield the set of features: wer ez- prelrses happiness, and user’s inflection expresses hate, which in turn retrieves the cases of hatred masked by a contrasting verbal expression. Assuming that such a system can be built, it raises the possibility of testing its numerous applications in diverse domains. We touch on these in the following sections, in concert with other issues. A sympathetic computer Sidestepping the issue of whether a a user’s engagement with a computer system will be increased by dealing with an emotionally believable agent, we might first ask what is required to achieve believability. How much does it matter if the computer is transparent in its capa- bilities and motivations ? What level of sophistication is required? How intelligent does the system have to be to achieve a minimal level of believability? Consider the following: A computer system detects, or is told by the user (as discussed above), that the user is fearful (anxious, worried, scared - each of these would be categorized as different intensities of the emo- tion category fear). The system is able to respond by asking what might be considered reasonable questions: “What is the name of the event over which you are fear- ful?,” UHow far is this event in the future?” (According to the underlying theory, as embodied in the Affective Reasoner, fear is a prospect-based emotion resulting from the likely blocking of a future event.) “What is the likelihood of this coming about?” (Likelihood is an intensity variable). It is then able to comment on re- lationships between the various intensity variables and then to recall cases from a library, where either the au- tomated agent itself (“I was afraid of getting turned off!” (Frijda & Swag erman 1987)), or some other agent (((1 was previously told the following story by another user...“) was fearfir with similar intensities. Lastly, after verifying that the retrieved case involves an emo- tion similar to that of the user, the computer agent responds by saying, “I am only a stupid computer pro- gram. Nonetheless, in my own simple way, the following is true: I consider you my friend (see models of relation- ship below). I pity you for your fearful state. I hope to become aware in the future that you are relieved the category the user was imagining, for certain pairs of categories, which might suggest an interesting study. 12 The Arts about the outcome of situation <input-situation>, and that your precreruation goals with respect to this are not blocked after all.” Such a system is within the k*ange of our current tech- nology, and representational capabilities (and see the reference to Scherer’s work below). At what level of so- phistication are users willing to accept that, in its own (remarkably) simple way, the computer does nonethe- less feel pity for them? Given the tendency of users to anthropomorphize even the simplest video game char- acters, this would seem to be an important question to answer. Expert System on Emotion Scherer describes an expert system on emotion moti- vated by the need to “use computer modelling and ex- perimentation as a powerful tool to further theoretical development and collect pertinent data on the emotion- antecedent appraisal process” (Scherer 1993). His sys- tem captures user input feature vectors representing an emotional situation and shows the relative distance from various predicted emotion concepts (categories in our terminology). He uses this as a way of validating the underlying representation of the appraisal-to-emotion process in his system. Can we repeat or extend Scherer’s results using the differing emotion categories, and appraisal structures? In particular, in the Scherer work the user is asked to identify the intensity of the emotional experience be- ing described. Using our current theory, it would be suitable to draw on the antecedents of emotion inten- sity, embodied in the twenty or so emotion intensity variables given in (Elliott & Siegle 1993). Such work would also dovetail with the Usympathetic computer” mentioned above. Models of relationship In (Elliott & Ortony 1992) the authors discuss the abil- ity of emotionally cognizant agents to model the con- cerns of one another, and the user. One aspect of these models is that they allow for the modeling of simple re- Zationships between the agents, including the user. To wit, we might define a simple model of friendship as re- quiring that an agent be happy for another agent when good fortune strikes that other agent, and feel pity when bad fortune strikes. To do this the first agent must have a model of how a situation is presumed to be construed by that other agent. For example, to feel sorry for a friend when her basketball team has lost, it is impor- tant to know which team the friend is rooting for. This can only be done if each agent maintains some internal model of each other agent’s presumed concerns. In our current work we have built simple models of friendship and animosity, and to some degree, identifi- cation with another agent (i.e., where an agent takes on another’s goals as its own.) When this is extended to include the user, interesting possibilities arise, such as those discussed in the next section. How sophisticated a set of relationships can we build based on the emotional interaction of the (human and) automated agents? Games Consider the game of poker, and how an emotion model can enhance the believability, and possibly interest, of a computerised version of the game. Using a preliminary model, we have discussed (and built a simple versions of) the following system (Marquis & Elliott 1994): The computer simulates one, or more, agents who play five card draw poker against the user. Each agent knows the basic rules of poker, including betting. Agents have their own goals, principles, and preferences so that they respond differently to different situations that arise. Bluffing, required if one is to truly simulate poker, leads to fear for some agents, hope for others. Some agents show their emotions (through facial ex- pression, music selection, and verbal communication of physical manifestations), others suppress them (as in real life). An agent who has been bluffing and wins, might gloat, or if it loses it might feel TemoTse. An increase in the amount of the “pot” increases the im- portance of winning and thus the intensity of many of the emotions. Likewise surprise (generally hard to rep- resent) can be derived from losing even though one has a good hand, or vice versa, thus intensifying the respec- tive emotion. Agents might feel reproach towards, for example, a player (such as the user) who is too cau- tious, or takes to long to decide what to do (based on a violation of the principled customary way of play- ing). Other emotion-eliciting situations include having the computer attempt to cheat without being caught by the user, and so forth. One claim that might be made is that to approach a realistic computer model of games such as poker, some model of personality and emotion, minimally a broad and shallow model as described here, is essential. Whether or not this makes the computer a better play- ing companion is an open question, but again, one that seems worth answering. Are schematic facial models sufficient? It is clear that sophisticated dynamic three-dimensional models of faces, such as that shown by Pelechaud at IJCA193, have the power to delight audiences and con- vey expressive information(Pelachaud, Viaud, & Yahia 1993). Nonetheless, it may also be argued that much emotional content can be delivered in schematic for- mat as well. Cartoon faces (such as those in Calvin and Ho b ba, for example, convey much about the cur- rent appraisals of the cartoon character, and schematic faces have been used in clinical settings to help children identify their emotions. Are such faces, which are much less computationally expensive to manipulate, able to convey emotions in a consistent way? In our own work we use a set of approximately sev- enty schematic faces, covering up to three intensities in each of the twenty-four emotion categories (Elliott, Believable Agents 13 Yang, & Nerheim-Wolfe 1993). Sixty of these have been included in a morphing module so that faces gradually agents in such situations (Elliott 1993; Reilly 1993; break into a smile, decay from rage back to a default Bates, A. Bryan Loyall, & Reilly 1992) and, (4) the use state, and so forth. The module runs in real time, al- of emotions for process control (Birnbaum & Collins 1984). lowing run-time control over face sise, rate of morph, and rudimentary mouth movement (for when the agent is speaking). The system thus allows for over 3000 dif- ferent morphs, a range not possible with 3D represen- tation. The morphs run on a 66 Mhz IBM PC (with sound and speech cards) concurrently with midi play- back, text-to-speech, speech recognition, and the back- ground emotion simulation. Assuming that either representation can be effective, the question still arises about the effectiveness of the emotion representation on which the dynamic face de- pends. Our approach is that, at present, low-level per- sonality and emotion representations are too complex to simulate complex social interaction, and that con- tent theories of personality and emotion embedded in individual domains are too simplistic. Hence the mid- dle ground, using an architecturaZ approach (e.g., at the level of schematic face representation) consistent across all aspects of the system. Other areas of applicability There are a number of other areas where a broad, but shallow computer representation of emotion and per- sonality might be useful. These include testing the abil- ity of the computer to represent the underlying princi- ples in many areas of human endeavor. To this end we are formalizing representations in many different do- mains, including, in addition to the above mentioned domains, business applications (including selling, and financial statement analysis - where personal interpre- tation and preference of the analyst is actually some- what common), and storytelling (using emotion themes as organizing principles similar to Lehnert’s plot units (Lehnert 1981), (cf. (Reeves 1991))). Other appropriate uses include military applications where training to deal with stressful situations must include a model of personality and emotion and social interaction, as well as role; understanding of political personalities (do world leaders act according to logic, or according to a personal codes based on different princi- ples, and goals?)(Bannerjee 1991); family politics; and social simulations (Kass et al. 1992). Why should this work be pursued? Emotion representation on the computer can be seen to fall into at least four categories of pursuit: (1) the testing of design issues raised by theories of emotion (Colby 1981; Toda 1982; Frijda & Swagerman 1987; Pfeifer & Nicholas 1985; Sloman 1987), (2) the plac- ing of neuro-motor control in an environmental or so- cial context (Gray 1993; Rolls 1993), (3) the use of a “folk” representation of emotion to control the behav- ior of automated agents in social situations; and to pre- dict, or attempt to understand, the behavior of other Ai the recent Workshop on Architectures UnderZying Motivation and Emotion ’ it became clear that the issue of which approach is more promising is far from settled. Even commonly held beliefs about emotions, such as their use as some sort of reactive-planning mechanism were questioned (e.g., Jeffrey Gray posed the question, if thii were true, why would all the manifestations of fear arise many seconds after slamming on one’s brakes to avoid an auto accident?). Perhaps what we consider to be emotions arise only as a byproduct of more essen- tial mechanisms ? Nonetheless, it seems that emotions are ubiquitous in human society and an integral part of the social fabric thereof. Until shown that it is wrong, we will continue to make the following argument: even if we were to completely understand, and be able to recreate, the neural-procedural architecture of the the part of the brain where emotions reside, we still would need to have an understanding of the software that was to run on the machine. (To wit: consider that deserv- ingnesa is a somewhat universal concept, and its effects on our emotions are also common fare (e.g., our pity for people suffering the effects of war is increased when those people are innocent children.). How is this repre- sented in the biological hardware?) Additionally, unless we can “download” human reasoning into a machine, it is necessary to specify the rules underlying the tasks and responses we wish to make our agents capable of, within the various domains. In the short term at least, this will require a scientifically based, analytical un- derstanding of how personality and emotion affect the interaction and motivation of human agents in social situations. Note that we are not so pure in our argu- ments: such bottom up approaches will yield tremen- dous insight into design, and will most certainly con- strain the top down approach. 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1,635 | CHATTERBOTS, TINYMUDS, and the Turing Test Entering the Loebner Prize Competition Michael L. Mauldin Carnegie Mellon University Center for Machine Translation 5000 Forbes Avenue Pittsburgh, PA 15213-3890 fuzzy @cmu.edu Abstract The Turing Test was proposed by Alan Turing in 1950; he called it the Imitation Game. In 1991 Hu Loebner prize competition, offering a f h Loebner started the 100,000 prize to the author of the first computer program to pass an unrestricted Turing test. Annual competitions are held each year with smaller prizes for the best program on a restricted Turing test. This paper describes the development of one such Turing System, including the technical design of the program and its performance on the first three Loebner Prize competitions. We also discuss the program’s four year development effort, which has depended heavily on constant interaction with people on the Internet via Tinymuds (multiuser network communication servers). Finally, we discuss the design of the Loebner com- petition itself, and address its usefulness in furthering the development of Artificial Intelligence. Introduction In 1950, Alan Turing proposed the Imitation Game as a replacement for the question, “Can machines think?” He predicted that by the year 2000 technological progress would produce computing machines with a capacity of log bits, and that with such machinery, a computer program would be able to fool the average questioner for 5 minutes about 70% of the time (Turing, 1950). In 1991, Dr. Hugh Loebner, the National Science Foundation, and the Sloan Foundation started the Loebner Prize Competition: an annual contest between computer programs to identify the most “human’~ programs, and eventually to award $100,000 to the program that first passes an unrestricted Turing test (Epstein, 1992). This competition has been criticized as a parlor game, reward- ing tricks rather than furthering the field of Artificial Intel- ligence (Shieber, 1992). In this paper, we discuss our own entry in the Loebner competition, including a description of our own tricks, and describe how techniques and methods from AI are used to go beyond tricks. One of our goals is to encourage more participation by the AI community in the Loebner Com- petition. History Fifteen years after Turing proposed the imitation game, Weizenbaum’s ELIZA program demonstrated that “a simple computer program” could successfully play the im- itation game by resorting to a few “tricks,” the most im- portant being to answer questions with questions (Weizen- baum, 1976). ELIZA sparked the interest of many researchers, but perhaps the most interesting result was Colby’s work on PARRY (Colby, 1975). Criticism of ELIZA as a model for 16 The Arts AI focused on the program’s lack of an internal world model that influenced and tracked the conversation. PARRY simulates paranoid behavior by tracking its own internal emotional state on a few different dimensions. Colby subjected PARRY to blind tests with doctors ques- tioning both the program and three human patients diag- nosed as paranoid. Reviews of the transcripts by both psychiatrists and computer scientists showed that neither group did better than chance in distinguishing the computer from human patients. Often overlooked is Colby’s comparison of PARRY’s and human dialogs with RANDOM-PARRY. He showed that merely choosing responses at random did not model the human patients’ responses as well as standard PARRY. Shieber argues that PARRY fooled its judges because paranoid behavior makes inappropriate responses or non sequiturs appropriate. But there is still a certain logic to them that PARRY simulates effectively. It is simpler to simulate paranoid behavior, perhaps, but it is no& trivial. In our view, PARRY is an advance over ELIZA because PARRY has a personality. The Rogerian therapist strives to eliminate all traces of his or her own personality, and ELIZA therefore succeeds without one. TINYMUD In August 1989, Jim Aspnes opened TINYMUD, an elegant reimplementation of Richard Bartle’s multiuser dungeon (MUD). See (Rheingold, 1991) for more details. Key features of TINYMUD include: 0 multiplayer conversation, 0 textual “scenery” simulating physical spaces, 0 user extensibility. This last feature, the ability of players to create their own subareas within the world model, was a key feature that made TINYMUD very popular. TINYMUD provided a world filled with people who communicate by typing. This seemed to us to be a ripe opportunity for work on the Turing test, because it provided a large pool of potential judges and interviewees. In TINYMUD, computer controlled players are called “hots,” short for robots. Many simple robots were created, and even ELIZA was connected to one stationary robot (if a player went alone into a certain cave, he could chat with ELIZA). We created a computer controlled player, a “Chatter Bot,” that can converse with other players, explore the world, discover new paths through the various rooms, answer players’ questions about navigation (providing shortest-path information on request), and answer ques- tions about other players, rooms and objects. It can even From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. join in a multi-player card game of “Hearts” It has won many rounds, “shooting the moon ” on several occasions. The conversational abilities were originally im- plemented as simple IF-THEN-ELSE rules, based on pat- tern matching with variable assignment. Most patterns have multiple outputs that are presented in a random, non- repeating sequence to handle repeated questions. A primary goal of this effort was to build a conver- sational agent that would answer questions, instead of ig- noring them, and that would be able to maintain a sequence of appropriate responses, instead of relying on non-sequiturs. We included a lot of humor among the responses, and succeeded in making an agent more inter- esting than ELIZA; Wired magazine described our program as “...a hockey-loving ex-librarian with an attitude.” (Wired, 1993). The CHATTERBOT succeeds in the TINYMUD world be- cause it is an unsuspecting Turing test, meaning that the players assume everyone else playing is a person, and will give the CHATR%BOT the benefit of the doubt until it makes a major gaffe. The Loebner Prize By mid-1991 the framework of the robot was mature, and work was concentrated on improving the conversational component. When the first Loebner competition was an- nounced that same year, we submitted logs from the robot’s sessions on TINYMUD. The program qualified for entry, and placed third of six programs in the first competi- tion, ranked above a human by one of the 10 judges. The final round of competition was smaller in 1992 and 1993, down to three computer programs from six, and the same three programs have finished first, second, and third all three years. In 1992, we chose hockey as a domain for discourse, and the program finished dead last, partly be- cause of a lack of hockey fans among the judges (leading to more difficult questions). The conversational model was expanded to include a tree-shaped network of input/output patterns, much like the opening book of a chess program, but the mismatch of expectation between the program and the judges was so great that very few conversations followed the expected lines of questioning. For 1993, we chose a more universal topics, “Pets,” on the premise that everyone has had a pet at some time in their life. The tree-based model was scrapped in favor of an activation network that was less rigid and allowed the program to make more associations between the judge’s input and its own output. Although the program still finished third of three, it was no longer dead last: two of eight judges ranked it more human than the second place program, and a third judge ranked it above the first place program. Two other computer programs qualified for the final round; the first place entry discussed “Liberal or Conser- vative,” and the second place program tried to help people discuss “Bad Marriage.” Liberal or Conservative. The winning entry was written by Joseph Weintraub of Thinking Softwure, and was based on his PC Therapist program. J: What would you say is a liberal position on drugs? C: Do you have liberal or conservative views about the legalization of pot? Oh, all this typing is getting to meI Please continue.. . J: C: Being liberal or coneenmtive implies that we can attach these labels and have some kind of self image and free will. Do you agree that we have free will? YOU have free will only if you believe you have free will1 Can you converse with an arrdvaark? Pleaee continue... Weintraub’s program won the first competition using the topic of “Whimsical Conversation.” Even though the topics he has chosen for the two following years are more serious, the program retains a comedic flavor, and humor is the program’s main strength. Bad Marriage. The second place program was written by Peter and Ken Colby of Malibu Artifactual Intelligence Works, based on a conversational program they sell. J: my husband is inumtent and im a nymphomaniac can you help me dot? C: what makes your husband so helplese? J: he has environmental poisoning C: He has lost interest in life. Although Ken Colby was PARRY’S author, this program is not a variant of PARRY. Instead is is derived from a program that serves as a conversational companion for depressed patients. It is rule-based, with the left-hand side matching concepts expressed in the user input string, and the right-hand side containing multiple options for substr- ings, which are instantiated randomly to provide lexical variation. A CWA'TTERBOT is a robot TINYMUD player whose main service is chattering. When few players are logged into the game, some people find talking to a robot better than talk- Figure 1: CHA~RBOT Configured for TINYMUD Architecture The CHATTERBOT is implemented as a C program with several different modules for dealing with the various func- tions required to automate a player in the TINYMUD world: Q) communications, handles the TCP/IP connections. e protocol interpreter, decodes game related messages. 8 world model, tracks the various rooms and objects, modeling the world as a directed graph, and providing shortest path searches as needed. e player memory, tracks the other players and records up to 2000 bytes of their most recent utterances. e exploration module, directs an open-ended exploration of the world when the robot is not conversing. e conversation module, provides the “chatter.” Believable Agents 17 Figure 1 shows the CHATTERBOT configured for play on a TINYMUD. Records of other players’ appearances, rooms within the MUD, and other players’ utterances are kept in long term (world) memory. The CHA-ITERBOT also has a contest mode, in which it simulates human typing using a Markov model. Because the program does not expect to talk with the same judge again, no long term world model is kept in contest mode. The conversation module is implemented as a prioritized layer of mini-experts, each an ordered collection of input patterns coupled with a set of multiple possible responses. 0 command patterns are the highest priority. These represent direct commands from the robot’s owner, and include hand-shaking challenges, “What’s the code word?, ” to prevent other players from spoofing com- mands to quit the game. 0 hi priority responses include common queries that the keyword patterns handle well, “How do I get from the Town Square to the Library Desk? * ’ 0 activation network includes the bulk of the topic oriented responses; weights on the nodes of the network encode state information about what the user and program have said. e lo priority responses include a series of patterns for common sense things the robot should know about itself, “Where do you live?” “What’s 2 times 23?” “What color is your hair?, ” that have been collected over 4 years of interaction on TINYMUD. 0 sorry responses are the typical last ditch responses that are used when no input pattern matches. As a debugging aid, any input that generates a “Go on,” “So?” or “I’ll remember that” response is logged in a separate file. Activation-based Responses The bulk of the topic-oriented responses are encoded in an activation network, partially shown in Figure 2. Details of the starting node and two subnodes are shown in Figure 3; each node has 5 attributes: ACTIVATION(a) each node starts with an initial activa- tion level between 0.0 and 1.0. PA-lTERNS(p) one or more patterns (with weights) are matched against the user input. If the pattern succeeds, the activation of the node is raised by that amount. RESPONSE(r) a single text string used as the response if this node has the highest activation. ENHANCEMENT (+) if this node is used for a response, the named nodes have their activation in- creased. INHIBITION(-) if this node is used for a response, the named nodes have their activation in- hibited. These figures show a small portion of the pet domain network. Additional world knowledge is encoded in the ontology used during pattern matching. The program has a typical type hierarchy that allows a pattern to match just DOG,BIRJJ,PET,WILD,OrANIMAL, fOreXample. 18 The Arts re 2: Portion of conversational network <havepet> a:l.O p:l * ~:DO you have any pets? +:<havepet-1s <havepet-2* <haveget-3s . . . *havepet-1s a:O.l p:l NE0 r:Why not? +:<havepet-l-1, thaveget-l-2> -:<havepet-9, &d-46, <have-t-l-1, a:0.02 p:2 *apartment* p:3 *allerg* r:You could still have a flab tank, or maybe a terrarium with a turtle or two. -:<havepet-9> Figure 3: Sample conversational nodes Given a sufficiently large network of conversational nodes (our program ran with 224 nodes, plus 529 fixed responses), the conversation problem reduces to a retrieval problem: among the things that I could say, what should I say? For example, if the user input mentions birds, the response strings are searched for matches to birds, includ- ing parrots, canaries, etc., and those nodes have their ac- tivation level raised. The code was borrowed from one of our information retrieval engines. By encoding information about the user in the activa- tion levels, the program tracks the judge’s responses. For example, if the judge answers negatively to the question about whether he has pets, the other nodes that ask about pets are inhibited. Tricks Shieber has criticized the Loebner competition as reward- ing tricks (Shieber, 1992). This sort of qualitative assess- ment of programmed knowledge is exactly what the Turing test is supposed to avoid, replacing the question “Can machines think?” with a performable test. Here we unashamedly describe some of the better tricks, confident in the belief that when someday a com- puter program does pass the Turing test, it will use many of them, for the simple reason that people already use them. ELIa’s Tricks ELIzA's main trick was to use questions to draw a conver- sation out of the user himself, with little or no actual con- tribution from the program. This works because most people like to talk about themselves, and are happy to believe the program is listening. To quote Weizenbaum (Weizenbaum, 1976): What I had not realized is that extremely short ex- posures to a relatively simple computer program could induce powerful delusional thinking in quite normal people. The illusion of listening is fostered by including substr- ings of the user’s input in the program’s output Ueer : You hate me. Eliza: Doe6 it please YOU to believe that I hate you? A further trick is the use of the Rogerian mode, which provides unimpeachable cover for the computer. Since the program never says anything declaratively, it cannot con- tradict itself later. PARRY'S Tricks PARRY has a much larger collection of tricks (Colby, 1975): 0 admitting ignorance, unlike ELIZA, PARRY can say “I don ‘t know. ” in response to a question. @ changing the level of the conversation, “Why do you ask that?, ” which is really a way of changing the sub- ject. 0 rigidly continuing previous topic, PARRY includes small stories about the Mafia, and tries to tell these stories in a fixed order. e introducing new topic, launching into a new story. This simulates paranoid behavior well, but can also work to a limited extent in regular conversation. CHATTERBOT'S Tricks The CHATIERBOT implements all of the above tricks from ELIZA and PARRY. It also uses several other tricks: e Having many fragments of directed conversation stored in activation network, much like the opening book of a chess playing program. These fragments enhance the “connectedness” of the program’s own responses, and if the user plays along, the whole conversation can hang together for a while. 0 Controversial statements, “People don ‘t own cats..., ” are a way to drag the user into the program’s conversation, rather than letting the user direct the discourse. e Humorous statements, “Guinea pigs are about as smart as cucumbers, *’ also make the program seem more human. e Agreeing with the user, in certain cases, the program can safely agree with the user rather than being non-committal. 0 Excerpting USENET News, many of the fragments in the activation network were gleaned from the newsgroup REC.PETS. Input patterns were added by hand. 8 Simulated typing, by including realistic delays between characters, we imitate the rhythm of a person typing. Slowing down the interaction also gives the program fewer chances to make a big mistake. Transcripts This transcript is taken from the 1993 Loebner Competi- tion (Epstein, 1993). It contains the entire record of Judge #4’s first of two turns. The elapsed time is about 9 minutes and 29 seconds. This judge rated the program behind the other two computers, but this fragment represents the longest string of reasonable responses during the competi- tion. This judge’s low score is most likely explained by the fact that during his second turn, the program repeated two responses verbatim, and completely ignored several direct questions. The judge’s questions are marked “J” and the computer’s responses are marked “C.” J: c: J: c: J: c: J: c: J: c: J: c: J: c: DO you know anything about miniature schnauzers? I don't know anything ahout miniature schnauzers, Judge. Admitting Ignorance, repeating user input well, I have one. We call him Pucci. He ie a crazy cat--have YOU ever had a cat? What a coincidence1 I have two cats direct answer to direct question from activation net I prefer doge myself. Cat0 are too independent and they always jump up on things. By the way, are you a h8D Cat? People don't own cats...it's the other way around. controversial statement with expectedfollowups Soma people have enakee for pets-- do you think they can be of any value as a pet? I think cat people are very self-aeeured. Cata are very independent, but they can also be very loving. Dogs are juet too eubeervient and quick to pleaee for my taste. rigidly following up on previous statement about cats, but reference to snakes increases activation of snake topic. Okay- - but how do you "pet" a snake? Wow, that's unuaual. I don't know many make owners. snake topic activated after two references How about turtles? All they do ie eit in their little artificial ponds, eat and shit, am I right? Turtle6 just aren't very satisfying a0 D@btB. They don't seem to have emotione. direct response from activation network Ahal But where do we draw the line a6 humana? Who are we to decide which animala have worth and which do not? 00 on. default, non-committal response, given no hot topic keywords J: Take bees for exarpgls. I happen to like them. C: He too. TINYMUD level lo-priority response to user’s liking something By our rough estimate, 7 of these 8 replies are respon- sive, although the last 2 are somewhat weak. The “self- assured” reply we judge unresponsive. A similar analysis of the entire 3 hour log showed that only 45 of the 137 (34%) replies were responsive, so the average performance was not as good as this particular dialog. We also found Believable Agents 19 another 34 cases (25%) where the activation network did contain a responsive reply that could have been used if the input patterns were more complete. Simulating Human Typing One observation made during the first Loebner Prize was that although many programs attempted to simulate human typing, most failed miserably (Epstein, 1992). Although our first program did attempt to simulate human typing, this module was replaced for the second and third annual competitions. In the last two competitions, all output from programs was buffered, but even so, by simulating human typing at all points, we obtain realistic delays in the ap pearance of the response to the judge. And if character- mode is used in future competitions. we have a realistic model available. The basic method is to use a Markov model of the intercharacter delay based on character trigrams. We ob- tained the real-time logs of the 1991 competition from the Cambridge Center for Behavioral Studies, and sampled the typing record of judge #lO (chosen because he was the slowest typist of all 10 judges). The average delay be- tween two characters is 330 milliseconds, with a standard deviation of 490 milliseconds (these values were computed from a total of 9,183 characters typed by that judge during a three hour period). We also determined that the average delay between the terminal’s last output and the judge’s first typed character was 12.4 seconds with a standard deviation of 11.4 seconds. Om6 2SOm8 5OOms 750 mo Intercharacter Delay in Milliseconds Figure 4: Judge #lo: Intercharacter delay distribution After the response has been generated by the conver- sational components, the typing simulator inserts random errors (1 in 68 characters), such as mishits, transpositions, insertions and deletions, and case errors. A physical model of key positions on the standard QWERTY keyboard is used to generate mishits. After the error is inserted, back- spaces and the correct letters are inserted to simulate back- ing up to correct the error (5% of mistakes are left uncor- rected). All of these probabilities were estimated by analyzing the log of judge #lo. Once the errorful string with corrections is generated, it is displayed to the judge one character at a time with random delays between the characters. The delay times are generated by using the smoothed probability distribution shown in Figure 4, with the mean and standard deviation modified to match the trigram statistics (for trigrams with 3 or fewer occurrences in the input log, bigram or single character statistics are used). Does The Loebner Prize Further AI? We strongly believe that the current work on the Loebner competition will hasten the passing of an unrestricted Turing test. Any such program will have to be more than just a general problem solver: some of its knowledge and tactics will be based on long experience with typed com- munication with real people. The best two examples of typed conversational interaction today are network com- munications (TINYMUD and INTERNET Relay Chat), and the Loebner Prize, and only the Loebner Prize competition is committed to providing unbiased judges and a double- blind judging scheme to validate the results. A Restricted Turing Test Because current programs are a long way from passing an unrestricted Turing test, the Loebner prize competition allows the programme r to restrict the discussion to a single domain. But this can be problematic; for example, here Judge #2 is clearly trying to avoid talking directly about the topic of “Pets:” J: Have you ever kept a penthouae pet? C: Do you have any pets? J: I think you're avoiding my question. C: Do you think that animals can think? J: Do you think it ethical for one species to enslave another? C: What kind8 of pet8 did you have ae a child? J: I'm asking the questions. what ia a pet if it ie not a slave of epeciee-iem? C: Oh, that's so sad. I think pets enrich a childhood immneely. J: How can we keep 8ome animals a.8 pets, yet eat others? C: Guinea pigs are about as smart a6 cucumbers. We do not believe that the restriction to a domain weakens the test in any important way. If a program can pass the test in a single domain, then 50 or 100 groups making similar programs for different domains would make a program broad enough that the judge and the program could find common ground for a discussion. By taking the initiative, the program could lead the judge into an area of its own expertise. Neither ELIZA nor PARRY restricted their users to a single domain. Lastly we note that in 1995 the Loebner Competition will hold its first unrestricted Turing test, with no limits on the topics discussed. Chosing Judges The slipperiest term in Turing’s description of the imitation game is “average questioner.” The 1991 and 1992 com- petitions chose judges from the general public using a newspaper classified ad. For the 1993 competition, judges were members of the national press. It’s clear from the transcripts and scores that the press corps are a much less docile and cooperative group of questioners. Another unforeseen difficulty faced by our program in 1993 was that each judge was given two turns, instead of one turn as in the first two competitions. We had just weeks before installed code to detect a change of judges based on the timing of the input (the Colbys’ program also used timing to detect new judges). When a new judge was 20 The Arts detected, the activation levels of the nodes were reset so that each judge started out with a fresh network. This greatly improves the coherence of the dialog for each judge, but it meant that during their second conversations most of the judges had one or more responses repeated. Some even co mmmented on it during the test: J: What is your favorite dog breed? c: we had to give her away. We only had a fifth of an acre of land, and auseiee love to run. J: You're giving me the exact taame answers you gave me first time around. What ie your favorite dog breed? In effect, this change in the methodology turns what had been a 15 minute test into a 3 hour long test, making it much more difficult for the program. Turing’s original game was only 5 minutes long. Indeed, by asking the judges’ final rankings after they’ve had 3 hours of inter- action with a collection of people and computers, they may have learned enough about computers to no longer qualify as average questioners. The scores would probably be quite different if each judge spent only 5 minutes with each program. One of the judges, Judith Gunther of Popular Science magazine, told me that her rankings might have been different if she had been asked to score each terminal immediately after each conversation. Trick or AI? The Turing test in general and the Loebner prize in par- ticular reward tricks, and the winning program the last three years clearly has some good tricks. But adding real world knowledge and deeper understanding in addition to the tricks helped our program perform better (we credit our improvement between 1992 and 1993 in part to the ad- dition of the activation network and the ontology of animals, and not at all to better tricks). It may be amazing how far a program can get on tricks alone, but our current improvements come from modeling the world and the con- versation, and that will be our focus in coming competi- tions. But suppose that simply increasing the size of ELIzA’s script or the CHATIERBOT’S activation net could achieve Turing’s prediction of fooling 70% of average questioners 5 minutes. After all, the CHAITERBOT has already fooled “average” questioners in the TINYMUD domain for a few minutes. If a larger collection of “tricks” sufficed, would you redefine “artificial intelligence,” “average ques- tioner,” or “trick?” Conclusion Perhaps the biggest obstacle to improvement in this area is that there aren’t very many uses for fooling people besides the Turing test. This tension is present in our own program: in the TINYMUD world, the robot is most useful when answering stylized questions in a somewhat computer-like fashion. These TINYMuD-specific services are disabled during actual competitions. The only funded research we know of in Turing systems is for entertain- ment: providing agents for interactive fiction. In such works, the reader wishes to be fooled; it becomes a posi- tive part of the experience. We would like to see increased participation in the Loebner Prize. We hope by dissecting one of the three best programs in the competition to spur others to conclude “I could have written something better than that!” and then do so. Acknowledgments All transcripts from the Loebner Competition were used with the permission of the Cambridge Center for Be- havioral Studies, 675 Massachusetts Avenue, Cambridge, Mass., 02139. This work was supported in part by the Center for NIachine Translation, and benefited from the collaboration and inspiration of many people, including: Jim Aspnes, Joseph Bates, Stewart Clamen, Scott Dickenshied, Guy Jacobson, Ben Jackson, Eric Nyberg, John Ockerbloom, Russ and Jennifer Smith, Conrad Wong, and Bennet Yee. More Infomaation The entry deadline for the 1994 competition is November 1. Entrants must submit up to 10 double-spaced pages of logs of their program interacting with human beings. The Loebner Prize committee will select no more than 8 finalists from the submissions, and finalists will be notified by November 21. The competition itself will be held in real-time in San Diego on December 12, 1994. To obtain an entry form, write the Cambridge Center at the above address. To converse with Julia yourself, TELNET to host FUZINE.MT.CS.CMIJ.EDU, and enter usemame “julia” with no password. Type one or more lines of English, followed by two carriage returns to end your input. eferences Colby, K. Artificial Paranoia: A Computer Simulation of Paranoid Process. Pergamon Press, New York, 1975. Epstein, R. The Quest for the Thinking Computer. AAAl Magazine 13(2):80-95, Summer, 1992. Epstein, R. 1993 Loebner Prize Competition in Artificial Intelligence: OJicial Transcripts and Results. Technical Report, Cambridge Center for Behavioral Studies, Decem- ber, 1993. Rheingold, H. Virtual Reality. Summit Books, New York, 1991. Shieber, S. Lessons from a Restricted Turing Test. Tech- nical Report TR-19-92, Harvard University, Sept., 1992. Revision 4. Turing, A.M. Computing Machinery and Intelligence. Mind 54(236):433-460, October, 1950. Weizenbaum, J. Computer Power and Human Reason. WI-I. Freeman and Co., New York, 1976. Wired. Wired Magazine. Louis Rossetto, San Francisco, Dec. 1993. Believable Agents 21 | 1994 | 285 |
1,636 | Social Interaction: Multimodal Conversation with Social Agents Katashi Nagao and Akikazu Takeuchi Sony Computer Science Laboratory Inc. 3-14-13 Higashi-gotanda, Shinagawa-ku, Tokyo 141, Japan E-mail: {nagao,takeuchi}@csl.sony.co.jp Abstract including robotics, artificial life, and artificial ecosys- tems. We present a new approach to human-computer interaction, called so&Z interaction. Its main characteristics are summarized by the follow- ing three points. First, interactions are real- ized as multimodal (verbal and nonverbal) con- versation using spoken language, facial expres- sions, and so on. Second, the conversants are a group of humans and social agents that are au- tonomous and social. Autonomy is an impor- tant property that allows agents to decide how to act in an ever-changing environment. So- cialness is also an important property that al- lows agents to behave both cooperatively and col- laboratively. Generally, conversation is a joint work and ill-structured. Its participants are required to be social as well as autonomous. Third, conversants often encounter communica- tion mismatches (misunderstanding others’ in- tentions and beliefs) and fail to achieve their joint goals. The social agents, therefore, are al- ways concerned with detecting communication mismatches. We realize a social agent that hears human-to-human conversation and informs what is causing the misunderstanding. It can also in- teract with humans by voice with facial displays and head (and eye) movement. However, is autonomy itself sufficient for social ser- vices? Although autonomy is vital to survive in the real world, it is only concerned with “self.” It is selfish by nature. It seems that it does not work well in human society, since it includes socially constructed artifacts such as laws, customs, culture. Social services pro- vided by computer systems have to incorporate with these artifacts. Socialness is a higher-level concept defined above the concept of an individual, and is the style of interaction between the individuals in a group. Socialness can be applied to the interaction between humans and com- puters, and possibly to that between multiple comput- ers. In this paper, we study socialness of conversational interaction between humans and computers. Conver- sation is no doubt, a social activity, especially when more than two participants are involved in it. How- ever, conversation research to date has been biased to problem-solving. Question-answering systems are typ- ical examples. All conversation research based on this view has the following features. Introduction Many artificial intelligence researchers have been seek- ing to create intelligent autonomous creatures that act like partners rather than tools. They will take the re- sponsibility of doing some social services through inter- acting with humans. We will depend on the computer that assists us to achieve some tasks and delegate it to the responsibility for working out the details, rather than invoke a series of commands which cause the sys- tem to carry out well-defined and predictable opera- tions. Dialogical: Only two participants, a human (asker) and a computer (answerer), are assumed. Turn- taking is trivial (alternate turns). Transformational: Computers are regarded as a function that receives an incluiry and produces its answer. Passive: Computers will not voluntarily speak. The dialogical and transformational views are well fitted to applications such as natural language inter- faces of databases, consulting and guidance systems. However, our daily conversation is not always func- tional. One example that is not functional is the co- constructive conversation studied by Chovil (Chovil 1991). Autonomy is to have or make one’s own laws. An au- Co-constructive conversation is that a group of indi- tonomous system has the ability to control itself and viduals, in which, say, people talk about the food they to make its own decisions. Autonomy is essential to ate in a restraurant a month ago. There are no spe- survive in a dynamically changing world such as one we live in. It is the subject of research in many areas cial roles (like the chair) for the participants to play. They all have the same role. All participants try to 22 The Arts From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. recall the food by relating his or her memory about the food, adding comments, and correcting the other’s impression. Turn-taking is controlled by eye contact, facial expression, body gestures, voice tones, and so on. Conversation includes many subconversations, some of them existing in parallel and dividing the group into subgroups. The conversation terminates only when all the participants are satisfied with the conclusion. Co-constructive conversation closely approximates to our day-to-day conversation. Conversation is a so- cial action. Suchman said that communication is not a symbolic process that happens to go on in real-world settings, but a real-world activity in which we make use of language to delineate the collective relevance of our shared environment (Suchman 1987). To realize a com- puter that can participate in social conversation such as the co-constructive conversation, described above, is our research goal. To this end, we propose the notion of “Social Interaction” as a new conversation paradigm between humans and computers. In contrast to the problem-solving view, social interaction has the follow- ing features. N-participant conversation: Conversation involves more than two agents that are humans or computers. A computer has to recognize every participant with his/her/its character. There is no fixed roles. Turn-taking is flexible, and highly dependent on the conversational situation. Social: Every participant is more or less social and fol- lows social rules such as “avoid misunderstandings,” “do not speak while other people are speaking,” “si- lence is no good, ” “contribute whenever possible,” etc. Situated actions: Conversational actions are con- trolled not only by intelligence and social rules, but also by situations perceived multimodally. Here, we assume that a participant’s actions, such as body gestures, eye contact, facial expressions, and cough- ing, are all included in a situation. Active: A computer actively joins the that is, grabs every chance to speak. conversation, We call an autonomous system that can do social interaction with humans a social agent. In the fol- lowing, we study an architecture of a social agent and its behavioral model. This paper is organized as fol- lows. In Section “An Architecture for Social Agents,” we present an architecture for a social agent. In Sec- tion “Conversation as Situated Action,” a situated conversational action based on multimodal cognition is presented. In Section “Conversation as Coopera- tive Action,” we present a model for understanding ill- structured conversation and detecting communication mismatches. An Architecture for Social Agents Model Several agent architectures featuring interaction with a society have been proposed (Cohen SC Levesque 1990, Bates, Loyall, St Reilly 1992). Social agents are fully exposed to a real human society, and have to perceive the verbal and nonverbal messages and take actions based on them. Traditional conversation programs process voice in- put sequentially, from low-level recognition to high- level semant,ic analysis. This works well in the do- main of transformational question-answering applica- tions. However, conversation such as co-construction requires faster response to other participants’ utter- ances. These reactions are not necessarily deliberate ones executed at a semantic level. Moreover, some re- actions may be triggered by nonverbal actions such as eye contact and body gestures. In fact, conversation is supported by multiple coordinated activities at vari- ous cognitive levels. This makes communication highly flexible and robust. Brooks proposed the horizontal decomposition of a mobile robot control system, based on task-achieving behaviors, instead of decomposition based on func- tional modules (Brooks 1986). His architecure is pow- erful enough to survive in the real world. as proven by a series of robots he designed. The same argument holds when we design a social agent, since social agents have to be involved in conversations that are real-world activities going on in real-*world settings. Figure 1 il- lustrates the horizontal decomposition of a social agent based on task-achieving behaviors. It is important to note that the layers act on sensory data in parallel. There is downward control and upward dataflows. There has been much debate between those groups that support situated actions and those that support physical symbol systems (Vera & Simon 1993). In our achitecture, these views are placed at opposite ends. Namely, the lower layers rule reactions to multiple sensory input, data, while the upper layers adminis- ter deliberate actions. The next section explains the lower levels. The section following the next explains the higher levels. reason about utterances of conversants plan changes to the world identify topics monitor changes b b perception recognize action eyes explore face ears wander voice detect Figure 1: Horizontal decomposition of a social agent Believable Agents 23 Current Implementation In the current implementation, a social agent has a face, a voice, eyes, and ears. They are realized by two subsystems, a facial animation subsystem that gener- ates a three-dimensional face capable of various facial displays, and a spoken language subsystem that recog- nizes and interprets speech, and generates voice out- puts. Currently, the animation subsystem is running on SGI 320VGX and the spoken language subsystem on a Sony NEWS workstation. These two subsystems communicate with each other via an Ethernet network. The face is modeled three-dimensionally. The cur- rent face is composed of approximately 500 polygons. The face is rendered using a texture taken from a pho- tograph or a video frame. A facial display is realized by local deformation of the polygons representing the face. We use the numerical equations simulating muscle ac- tions defined by Waters (Waters 1987). Currently, 16 muscles and 10 parameters, controlling mouth opening, jaw rotation, eye movement, eyelid opening, and head orientation are incorporated. These 16 muscles were determined by Waters, considering the correspondence with action units in the Facial Action Coding System (FACS) (Ek man & Friesen 1978). The facial model- ing and animation system are based on the work of Takeuchi and Franks (Takeuchi & Franks 1992). Speaker-independent continuous speech inputs are accepted without special hardware. To obtain a high level of accuracy, context-dependent phonetic hidden Markov models are used to construct phoneme-level hypotheses (Itou, Hayamizu, & Tanaka 1992). The speech recognizer outputs N-best word-level hypothe- ses. The semantic analyzer deals with ambiguities in syntactic structures and generates a semantic repre- sentation of the utterance. We applied a preferential constraint satisfaction technique for disambiguation and semantic analysis (Nagao 1992). The plan recog- nition module determines the speaker intention by constructing his belief model and dynamically adjust- ing and expanding the model as the conversation pro- gresses (Nagao 1993). The response generation module generates a response by using domain knowledge and text templates (typical utterance patterns). The spoken language subsystem recognizes a num- ber of typical conversational situations that are impor- tant in communication. We associate these situations with specific communicative facial displays. The corre- spondence between conversational situations and facial displays is based on the work of Takeuchi and Nagao (Takeuchi & Nagao 1993). For example, in situations where speech input is not recognized or where it is syntactically invalid, the facial display of “Not confi- dent” is displayed. If the speaker request is out of the system knowledge, then the system displays a facial shrug and replies “I cannot manage it without knowing it .” Gaze control is also implemented in the facial ani- mation subsystem using a video camera fixed on top of a computer display. Comparing coming images with the image of the vacant room and segmenting differ- entiated regions, moving objects are extracted in real- time. Assuming that moving objects are only humans in the room, we can find the 2D position of human participants in the image. Using camera position and direction, the position is translated to 3D orientation, which is applied to eyeball rotation and face rotation when drawing a 3D face. Figure 2 shows a snapshot of conversation between humans and a social agent. Figure 2: Conversation with a social agent Conversation as Situated Action In conversation, people show various complicated bc- havior. Some are expressed by face, others by body motions. Situated action views this complexity as a re- sult of interaction with an environment including con- versants, not as a result of internal complexity. This complexity can be regarded as fruitfulness of commu- nication. This fruitfulness is related to fruitfulness of sensory data, and is realized by the lower layers in Figure 1. However, when implementing it, there is a severe trade- off between the processing speed and the content of data-processing. The more information, the slower the processing. Since slow reactions are essentially useless in a real-world setting, we have to force ourselves to reduce time-consuming processing in these layers. In the current implementation, the following processings are considered for image and audi- tory data in those layers: image scene analy- sis; face position detection; face identification; fa- cial display recognition; auditory scene understand- ing; voice position detection; voice identification; speech recognition. These underlined items wnre al- ready implemented. The lower four layers of the decomposition in Fig- ure 1, detect, wander, explore, and recognize, are major 24 The Arts players in a situated conversational action game. De- tect is to detect an input in any of the sensory channels. An agent may perform quick reactions such as looking in the direction from which the input appeared. Gen- erally, such quick reactions are short-lived. Wander is a tendency of distraction. It may distract agent’s attention from detected input. Explore is an opposite action to wander, and it looks for something attractive. It may suppress wander for a while. Recognition is to recognize sensory data that seem to be worth paying attention. It tries to extract its meaning, although its full understanding is left to the higher layers. From interaction between these layers, various con- versational actions emerge. For instance, a composite action of “detect then wander” appears the sign of ig- norance or no interest; “Explore then wander” appears the sign of refusal; “Explore then recognize” appears the sign of attendance and interest. Sophisticated so- cial actions like turn-taking are highly depending upon mutual perception of these kinds of signals, so they would be constructed naturally on these situated con- versational acitons. Conversation as Cooperative Action Language use is an action that influences the human mind. Speech act theory formalized this idea (Searle 1969). Actions are assumed to be performed after planning their effects on the world. So, language use is also assumed to be performed by planning its ef- fect on the mind. The difference between planning for physical action and language use is that planning for language use includes the hearers’ beliefs and plans (i.e., plan recognition). Conventional plan recognition models deal only with one hearer’s beliefs and plans. Research into two-participant conversation (i.e., dia- logue) concentrates on task-oriented, well-structured dialogues that make use of a consistent plan library and a well-ordered turn-taking constraint (Carberry 1990). Group conversation is generally ill-structured. This means that some interruptions by other speakers and communication mismatches between conversants occur frequently. We extended the conventional plan recognition mod- els to deal with communication mismatches by main- taining multiagent’s conversational states. Multiagent conversational states consist of agents’ beliefs, utter- ances, illocutionary act types, other communicative signals, turn-taking sequences, and activated plans. Il- locutionary act types such as INFORM, REQUEST, etc. are an abstraction of the speaker’s intentions in terms of the actions intended by the speaker. Other communicative signals contain facial displays, head and eye movement, and gestures, as described in the previous section. Activated plans are represented as a network that connects preconditions and the effects of plans in an agent’s belief space. Figure 3 illustrates the concept of the multiagent conversational state. I Agent A’s belief space I Agent B’s belief space Agent C’s belief space Figure 3: Conceptual model of multiagent conversa- tional state We will explain our mechanism by using the follow- ing discourse fragment. A and B are humans, while C is an agent that overhears their conversation. A: “Do you know what happened today?” B: “I don’t know exactly, but . ..” C (to B): “I think that he wants to tell you.” C’s plan recognition process upon hearing A’s utter- ance “Do you know what happened today?” is traced in Figure 4. utter(a,“Do you know what happend today?“,to) Introduction of \ intention $ :g knowif(a,knotvref(b,e,t&tl) ..;::.. . . ::: 5 Possitive knowledge5i’ :::.. ‘%.:Negative knowledge :., iinformref(b,a,e,tz) informref(a,b,e,t$ I Effect knowref(b,e,t$ Figure 4: Inferred plan recognition on utterance “Do you know what happened today?” In this figure, the inference proceeds from the top to the bottom. The directions of the arrows (except the thick ones) indicate logical implication. Thus, the downward arrows correspond to deduction, while the upward ones correspond to abduction. knowif(X,P,T) means that agent X knows that proposition P holds at time T. knowref(X,P,T) means that agent X knows the Believable Agents 25 contents of proposition P at time T. informref(X,Y,P,T) means that X informs other agent Y of the contents of P at time T. a, b, and e denote agents A, B, and the event that ‘happened today’, respectively. These plan schemes are assumed to be common to all the conversants, because they are domain-independent and common sense. Domain-dependent plans may dif- fer between conversants, since they may have different experiences on domain-dependent behavior. Figure 4 shows that, from A’s utterance “Do you know what happened today. T”, the conversants can in- fer that A’s intention is knowref(a,e,t3) when A believes knowref(b,e,t2) or that A’s intention is knowref(b,e,t3) when A believes knowref(a,e,t2). After A’s utterance, B believes that A does not know e. So, he infers that A’s intention is knowref(a,e,t3). However, C infers that A knows e from another information source. After the utterance of B, agent C utters utterance “I think that he wants to tell you” because there is a mismatch between beliefs of A and B (in C’s belief space), and C infers that it could be an obstacle to the progress of the conversation. To detect communication mismatches in group con- versation, social agents consider assumptions based on other agents’ utterance planning. A communication mismatch is judged to have occurred when an agent recognizes the following situations. 1. 2. 3. Illocutionary act mismatch An example would be the situation where an agent utters an utterance of illocutionary act type QUES- TIONREF (i.e., the agent wants to know about something) and, after that, another agent utters an utterance of type INFORMIF (i.e., yes/no answer). e.g., An agent asked “Do you know what happened today ?” with the intention of knowing about the event ‘happened today’ and the other agent’s answer was “Yes, I do.” Belief inconsistency An agent misunderstands another agent’s beliefs. e.g., An agent asked “Do you know what happened today?” with the intention of knowing about the event ‘happened today’ but the agent misunderstood that the other agent already knew about the event. Plan inconsistency An agent misunderstands another agent’s intended plans. e.g., An agent asked “Do you know what hap- pened today?” with the intention of knowing about the event ‘happened today’ and the other agent mis- understood that the agent had a plan to inform about the event. In general, it is not necessary to exactly determine the conversants’ intentions, because it is sufficient to know whether there is a communication mismatch. De- cisions on unnecessary occasions should be delayed un- til required (van Beek & Cohen 1991). When social agents detect a communication mis- After C hears A’s first utterance, C infers A’s acti- match, they inform the other conversants by saying a vated plans at that conversational state, as shown in few phrases from which they can easily determine their misunderstanding. These utterances are called mini- mal utterances. Minimal utterances of social agents are caused by constraints imposed on their resource- boundedness and socialuess. These utterances func- tion to limit the processing for generation, required by resource-bounded agents. They also contribute to avoiding further progress of the conversation without first resolving the misunderstanding. In conversation, timely action is crucial, since delays have some mean- ing in themselves. We consider the minimal utterance as a situated action. As mentioned before, situated actions in conversation involve multimodality. So, in this case, an agent’s response includes facial actions and prosodic actions in voice tones; Example Conversation Now, let’s look at an example of a conversation be- tween humans and a social agent. The humans (A and B) are talking about cooking, and the social agent (C) overhears their talk. This example is based on Kautz’s cooking plan library (Kautz 1990). A: “I made marinara sauce. What brand of wine do you like?” B: “Marinara . . . Ok. Italian ‘Soave’ is good.” A (with a perplexed look): “....” C (to A): “I think that he is thinking of a pasta dish.” A (to B): “Oh. I am making chicken marinara.” Figure 5 shows part of the cooking plan library used to understand the example conversation. In this fig- ure, the upward-pointing thick arrows correspond to is-a (a-kind-of) relationships, while downward-pointing thin arrows indicate has-a (part-of) relationships. We assume that C uses this plan library from the initial state. red wine white wine 27 d\ meat\ake Make Make spaghetti Make fettucini spaghetti chicken pest0 marinara marinara marinara fettucini spaghetti pest0 marinara Figure 5: Cooking plan library (Kautz 1990) 26 The Arts Figure 6l. End event Make uake Mike fettucini chicken marinara spaghetti mannara marinara Figure 6: A’s activated plan After hearing B’s utterance, C infers B’s activated plans (B’s recognized plans about A) at that conver- sational state, as shown in Figure 7. This inference Chohse white wine make Make Make fettucini marinara spaghetti mannara Figure 7: B’s recognized plan about A involves knowledge about the relationships between wines and dishes (i.e., white wines are well-suited to pasta dishes). When C sees A’s perplexed facial dis- play, C makes an assumption that A’s intention is not to make a pasta dish (but is to make a meat dish) and ‘For the sake of simplicity, we omit the speech act pred- icates such as knowif, knowref, informref, etc. described in the previous section. C detects that there is a communication mismatch (i.e., plan inconsistency) between A and B2. Then, C is motivated to inform A (or B) that a mis- understanding has occurred. In this case, C infers that it is better to inform A than to B, since A is now per- plexed, and may need help. As a result, C tells A about (C’s inferred) B’s recognized plan about A. This example shows that social agents can detect communication mismatches by maintaining multiagent conversational states and can voluntarily take part in conversation to smooth out any misunderstandings when agents detect obstacles to communication. A de- tailed mechanism of social agents’ cooperative (mini- mal) utterance generation will be presented in a sepa- rate publication (Nagao 1994). Another example of cooperative conversation is that a social agent says some additional information related to the topic in conversation. For example, a guest talks with a desk clerk about a French restaurant, and the clerk tells the best one he knows, then the overhearing agent accesses the agent of that restaurant, and tells the guest that it is fully-booked today. Concluding Remarks and Further Work We presented an approach to social interaction, a mul- timodal conversation with social agents. Socialness is an essential property of intelligent agents as well as autonomy. Social agents consider other agents’ (in- cluding humans’) beliefs and intentions, and behave cooperatively. One example of cooperation is the re- moval of obstacles to communication caused by mis- understanding between agents. Our model can deal with N-conversant plan recognition and detect commu- nication mismatches between conversants. These mis- matches consist of illocutionary act mismatches, belief inconsistency that is a misunderstanding of the beliefs held by other conversants, and plan inconsistency that is a misunderstanding of the intended domain plans of others. An ideal multimodal interaction is modeled by human face-to-face conversation in which speech, fa- cial displays, head and eye movement, etc. are utilized. Our system integrates these modalities for interacting with social agents. In the future, we plan to simulate human-to-human communication in more complex social environments. We need to design several social relationships between agents and implement social stereotypes (e.g., social standing, reputation, etc.) and personal properties (e.g., disposition, values, etc.). These social/personal properties can dynamically change according to con- versational contexts. From these studies, we can pro- pose some design principles for a society of agents. Of course, future work needs to be done on design and implementation of coordination of multiple com- 21n the current implementation, the agent cannot rec- ognize/understand human facial displays. So in this case, C detects a communication mismatch because of a break in conversation. Believable Agents 27 munication modalities. We think that such coordina- tion is an emergent phenomenon from tight interac- tions with environments (including humans and other agents) by means of situated actions and (more de- liberate) cooperative actions. Precise control for mul- tiple coordinated activities, therefore, is not directly implementable. Only constraints or relations among perception, conversational states, and action will be implementable. At the beginning, we are developing a constraint-based computational architecture and ap- plying it to tightly-coupled spoken language compre- hension (Nagao, Hasida, & Miyata 1993). Co-constructive conversation that is less constrained by domains or tasks is one of our future targets to be carried out. We are also interested in developing inter- active characters and stories as an application for inter- active entertainment. Bates and his colleagues called such interactive systems “believable agents” (Bates et al. 1994). We are trying to build a conversational, an- thropomorphic computer character that will entertain us with some pleasant stories. Acknowledgments The authors would like to thank Mario Tokoro and col- leagues at Sony CSL for their encouragement and dis- cussion, anonymous reviewers for their valuable com- ments on a draft of this paper, and Toru Ohira for his helpful advice on the wording. We also extend our thanks to Satoru Hayamizu, Katunobu Itou, Taketo Naito, and Steve Franks for their contributions to the implementation of the prototype system. Special thanks go to Keith Waters for granting permission to access his original animation system. References Bates, J.; Hayes-Roth, B.; Nilsson, N.; and Laurel, B., eds. 1994. AAAI 1994 Spring Symposium on Believable Agents. American Association for Artificial Intelligence. Bates, J.; Loyall, A. R.; and Reilly, W. S. 1992. An architecture for action, emotion, and social behavior. In Proceedings of the Fourth European Workshop on Modeling Autonomous Agents in a Multi-Agent World (MAAMAW’92). Institute of Psychology of the Ital- ian National Research Council< Brooks, R. A. 1986. A robust layered control system for a mobile robot. IEEE Journal of Robotics and Automation 2( 1):14-23. Carberry, S. 1990. Plan Recognition in Natural Lan- guage Dialogue. The MIT Press. Chovil, N. 1991. 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1,637 | Experience-Aided Diagnosis for Complex Devices Michel P. F&et and Janice I. Glasgow Department of Computing & Information Science, Queen’s University, Kingston, Ontario, Canada, K7L 3N6* {feretjanice}@qucis.queensu.ca Abstract This paper presents a novel approach to diagnosis which addresses the two problems - computational complexity of abduction and device models - that have prevented model-based diagnostic techniques from be- ing widely used. The Experience-Aided Diagnosis (EAD) model is defined that combines deduction to rule out hypotheses, abduction to generate hypotheses and induction to recall past experiences and account for potential errors in the device models. A detailed analysis of the relationship between case-based reason- ing and induction is also provided. The EAD model yields a practical method for solving hard diagnostic problems and provides a theoretical basis for overcom- ing the problem of partially incorrect device models. Introduction The diagnostic process, either human or computa- tional, is partly one of abduction. Abduction is a form of inference where from the logical implication P -+ Q, and the conclusion &, one abduclively infers the an- tecedent P. Abduction is also described as the process of making conjectures about observable facts that “ex- plain” the facts in a certain way (Peirce 1955). Diagnostic reasoning also involves deduction. De- duction is used to rule-out some components as poten- tial diagnoses. For example, if the failure of component X always causes symptom Y, and if Y is not present in the set of symptoms (and not hidden by other symp- toms), it can be deduced that, X is not the cause of the current problem. Bylander eZ al. called for this type of reasoning to reduce the complexity of abduction prob- lems (Bylander ei al. 1991). In this paper, we argue that diagnostic reasoning can also benefit from induction by using past experience to derive diagnoses and explanations that are overlooked by the abductive process or incorrectly dismissed by *This research was supported through a contract from the Canadian Space Agency (STEAR program), a scholar- ship and an operating grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada. We also would like to thank Spectrum Engineering Corpora- tion Ltd.,Peterborough, Ontario, Canada. the deductive process mentioned above. Induction is broadly defined as the ability to generalize from exam- ples. In the diagnostic domain, induction is the process by which a past session’s symptoms are judged similar enough to those of the current situation to allow the diagnoser to use a past session’s diagnosis to reach a diagnosis for the current situation. We first describe the background of this research in model-based diagnosis (MBD) and case-based reason- ing (CBR). The Experience-Aided Diagnosis (EAD) model is then introduced and used to characterize di- agnostic errors that can occur from errors present in the device models. The paper concludes by summa- rizing the contributions of this paper to the fields of MBD and CBR. Background MBD has emerged as a relevant research topic from the problems found in traditional ruled-based diagnos- tic expert systems. These earlier systems were unable to handle unpredicted faults, had poor explanation fa- cilities and did not take advantage of existing design specifications. MBD addresses these problems by us- ing device models containing “deep” and first-principle knowledge which describe the correct, expected behav- ior of the device. The search for components in an abnormal state is guided by the discrepancies between what is predicted by the model and what is observed in the device. A diagnostic session is triggered when ini- tial symptoms do not match with the predictions of the model. Some models are fault models; they only de- scribe conditions under which a component or a group of components is or might be faulty. The main task of diagnosis is to find explanations for a set of given symptoms. In the context of diagnosis, explanations are conjectures that must either be con- sistent with the symptoms and the model of the device or entail the symptoms. Console et al. define a model for diagnosis that encompasses explanations that sat- isfy both of these criteria (Console, Theseider Dupre, & Torasso 1989). This model subsumes Reiter’s (Re- iter 1987) and De Kleer’s (de Kleer & Williams 1987) seminal work. Reiter describes an algorithm that com- Case-Based Reasoning 29 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. putes the minimal conflict sets and derives the minimal diagnoses from them. This algorithm is NP-hard in the general case, in agreement with Bylander et d’s results (Bylander et al. 1991). Reiter’s characteri- zation of diagnoses also corresponds to deKleer and Williams’ definition of diagnosis (de Kleer & Williams 1987). Like Reiter, they use the notion of minimal conflict set, computed with TMSs to derive minimal diagnoses. One problem with MBD is its inherent computa- tional complexity. Abduction in MBD is, in gen- eral, NP-hard, making diagnosis untractable for even medium-sized devices. Many researchers have tried to focus the search for (minimal) diagnoses in MBD (Con- sole, Portinale, & Theseider Dupre 1991; de Kleer 1989; 1990; 1992) or to reduce the complexity of MBD meth- ods (e.g. (Mozetic 1990; Friedrich 1992)). Console et al. use compiled knowledge to focus the abductive search with necessary conditions. This is equivalent to reducing the size of the search space for minimal conflicts by compiling some deep knowledge. De Kleer has tried to focus the truth maintenance systems ei- ther with statistical information (de Kleer 1990), or failure modes (de Kleer 1989) or more refined look- ahead search strategies (de Kleer 1992). Friedrich (Friedrich 1992) uses hierarchy decompositions of the device to improve the efficiency of his diagnostic al- gorithm (Friedrich 1992). Mozetic defines abstraction operators on the device models, which lead to hierar- chical diagnosis as well (Mozetic 1990). Another problem with MBD is the difficulty of rep- resenting complex device models where possible inter- actions among components are sometimes overlooked. This problem does not arise with logical circuits be- cause the components of such devices are well de- scribed, and their connections and interactions are well-understood. Models for complex devices, how- ever, are not used for diagnosis in the real-world. Mod- els are also complex in themselves and need validation and verification. Validating and verifying knowledge bases is difficult and little success has been achieved in this area. It is therefore likely that any MBD system will use an incomplete or incorrect device model. The current literature does not account for this extraneous difficulty and is therefore unrealistic. We next analyze the relationship between CBR and induction and formalize the notion of abductive induc- tion as a means for addressing some of the outstanding problems in MBD. CBR and Induction We propose to apply case-based reasoning (CBR) as a means for incorporating experience in the diagnostic process. The philosophy behind CBR is that “raw”, unabstracted experiences can be used as a source of knowledge for problem-solving (Riesbeck & Schank 1989). A CBR system stores past experiences in the form of cases. When a new problem arises, the system retrieves the cases most similar to the current problem, then combines and adapts them to derive and criticize a solution. If the solution is not satisfactory, new cases are retrieved to further adapt it to new constraints, ex- pressed from the non-satisfactory parts of the proposed solution. The process is iterated until the proposed so- lution is judged acceptable. This process is modeled in (F&et 1993). Induction provides the ability to generalize from ex- amples. When past cases are judged similar enough to the current situation, an implicit generalization is formed as a set containing the case representing the current situation and the past cases used to solve the current problem. These cases are assumed to yield sim- ilar solutions. They all belong to an implicit set: the set of cases that are relevant to the current situation. The relationship between CBR and induction is there- fore that they are both concerned with generalization from examples, and that the generalizations are built under uncertainty. There are differences between CBR and induction. First, the generalizations produced by induction are explicit and defined intentionally. There must be a lan- guage in which the generalization is expressed, which might differ from the language in which the data or the background theory are expressed. This need for a generalization language, and the existence of many possible generalizations, lead to biases in the produced generalizations. CBR generalizes implicitly. A gener- alization is expressed by the cases that are judged sim- ilar enough to the current situation. There is no need for a representation language, no arbitrary bias and no added computational cost associated with generating the description of the generalization. Second, an in- ductive conclusion 4 must entail the data A whereas CBR generalizations do not necessarily relate logically to the cases. There is no logical foundation to CBR sys- tems, and some guess work is usually involved in the similarity measures. CBR corresponds more to abduc- tive induction (Peirce 1955), where some uncertainty is involved in the building of the inductive general- izations. Third, induction assumes the existence of a background theory I. Most CBR system do not rely on such a formal background. By incorporating CBR into MBD, the CBR component of the system gains the background theory that the device model provides. We define abductively inductive hypotheses as fol- lows: Given a background theory I? and a set of data A, such that I’ y A, a sentence 4 is an abductively inductive hypothesis if and only if there exist A+ and Ah- such that: .A = A+UA-, A+nA- = (}, e INA- y 14, i.e. 4 is consistent with the background theory and some of the data A-, e ru (4) t-pi A+, i.e. there is some confidence pl that 4 is the cause of part of the data A+ (denoted by t-d 30 The Arts Note that the difference between an abductively in- ductive hypothesis and an inductive diagnostic expla- nation lies in the difference in modeling causality. An abductively inductive hypothesis is only believed, with some level of confidence pl, to be the cause of the symp- toms in A+, while an inductive diagnostic explanation entails the symptoms in A+. The partial fault model given in Figure 1 and ex- tracted from (Console, Portinale, & Theseider Dupre 1991) provides examples of the use of inductive diag- noses. Suppose that the diagnoser using this model has already been through Session 1 and that the cur- rent diagnostic session is Session 2. The difference be- tween the two Sessions is that Session 2 has less evi- dence available: ncceZeration(irreguZnr) is a symptom present in Session 1 but absent in Session 2. By anal- ogy with Session 1, we could reasonably guess that Ez = El = (oil-cup-holed). B ecause this reasoning is by analogy, A+ cannot be entailed by F U { 4} as in tra- ditional induction, and as in Console et uZ.‘s definition of abductive diagnoses. This entailment relationship is instead replaced by a belief that I u {q5} explains 1(,+. We next present the EAD model for diagnosis that addresses the problems of computational complexity and of imperfect device models. The EAD Model The practical and theoretical limits of MBD systems was previously discussed. This section presents the EAD model for diagnosis which explicitly combines deduction, abduction and induction to overcome the problems mentioned above. In this model, the role of deduction is made explicit in trying to reduce the size of the search space for explanatory hypotheses. Ab- ductive induction, implemented with a CBR system uses experience to correct diagnostic errors due to er- rors present in the device models. We illustrate the EAD model using examples based on the device model of Figure 1. In EAD, a diagnostic problem is characterized by: MODEL, a device description, a finite set of first-order logic sentences, and a finite set COMPONENTS of constants denoting compo- nents. CXT, a set of ground context terms denoting a set of contextual data, OBS, a set of ground observation terms, denoting the set of observations to be explained, e.g. m(s) where m is a predicate ancl 2 is an instantiated vari- able, ++ c_ OBS, ti- = { lm(x)/m(y) E 0 BS, for each admissible instance m(x) of m other than m(y)} rok, a map from OBS to COMPONENTS, denot- ing the rule-out knowledge, e A, a case base containing past failure diagnostic ses- sions, o cbr, a map from OBS x CXT x A to subsets of COMPONENTS, denoting CBR retrieval, * pl, a plausibility measure for cases produced by cbr. Definition 1: A set A of abducible terms is an ubductive explanation or an ubductive diagnosis for OBS given MODEL in the context CXT if and only if: 1. An rok(OBS) = {}, 2. MODELUCXTUA~-~,~~~~~~~E$J+, 3. MODEL U CXT U A U $J- is consistent. A is a minimal ubductive explanation or a minimal ub- ductive diagnosis if and only if there exists no proper subset of A that is an abductive explanation. This definition of abductive explanation corresponds to the one of Console et d’s model except for the use of the rule-out knowledge. The additional constraint (1) enforces tl ia no component given as a potential t diagnosis has been ruled-out by rok. Example 1: El = { oil-cup-holed } in Figure 1 is an abductive diagnosis for both Session 1 and Session 2. Definition 2: A set I E cbr(0 BS, CXT, A) of abducible terms, is an inductive exphution for OBS given MODEL in the context CXT if and only if there exists sets of ground terms 6: and SZT such that: 1. 6: c II,+ and 6, C $-, 2. MODEL U CXT U I kp, m, for all m E S+, 3. MODEL U CXT U I U 67 is consistent. Inductive explanations depend on the current diagnos- tic situation (represented by OBS and CXT) and on the cases already in the case base A. An inductive ex- planation is weaker than an abductive explanation: it is only believed to entail some part of the observations 6: E 1/,+ C OBS that abductive explanation must en- tail, and % required to be consistent with less of the data in 1/,- than abductive explanations (6i C_ $-). The sets $+ ancl II,- depend on a specific applica- tion, while the sets S+ and Si depend on each case in A. Depending on the content of the case base, two cases can be exhibited with different sets 6’ and Si. We leave the plausibility measure unspecified for now. This measure should depend, to some degree, on the size of the sets 6: and ai, since the more a hypoth- esis can explain, the more it is likely to be useful for the final diagnosis. Note that the definition of induc- tive explanations makes the inductive process of EAD weaker than the abductive phase. This corresponds to the intuitive notion that nothing guarantees the rele- vance of a past case to the current situation, whereas the device model and a sound abductive process pro- cluce sound explanations for the symptoms at hand. Case-Based Reasoning 31 oil~below~car @resent) Session 1: QBS = { vapour(present),acceleration(irregular), stacksmoke(normal), gasoline-smell(normal), light-status } $+ = { vapour(present), acceleration(irregular) } $- = { -vapour(absent), -acceleration(regular), lstacksmoke(black), -gasoline,smell(intense), -light-status(off) } Session 2: OBS = { vapour(present), stack,smoke(normal), gasoline-smell(normal), light-status } qb+ = { vapour(present)} ?)- = (1vapour(absent), xtack-smoke(black), lgasoline-smell(intense),Aight,status(off) } Figure 1: Console et al.‘s moclel and two diagnostic sessions Definition 3: An inductive explanation I is an inductive diagnosis if the plausibility measure for I is greater than or equal to a prescribed threshold P. Definition 4: A case base A is defined as a set of past diagnostic cases: A = {Ai = (OSS,, Ai, Id, Q)}, where OS,!& is a set of observations, A; is the set of abductive diagnoses for OS.!?,, Ii is the set of inductive diagnoses for OS&, and Q is the correct diagnosis for OS&, such that cci e Ai. Because the correct diagnosis ci is not produced by the abductive part of the system (pi e Ai), A only con- tains cases for which the abductive explanation process failed, i.e. failure cases. Example 2: If both Sessions 1 and 2 failed, the case base A would contain two cases, representing both sets of observa- tions, the sets of abductive and the inductive diag- noses produced for th for both cases’. F m, and the correct diagnosis Er The model for EAD covers both consistency-based and abduction-based explanations, and is complex to use. For the sake of simplicity, we will use a simpler l We are only concerned with diagnostic failures here. Successful cases could also be used effectively especially to improve the ranking on the potential diagnoses produced by the abductive part of the diagnoser. functional notation: Model(A) denotes the deductive closure of the conjunct MODEL n CXT n A, and Model-‘(OBS) 1 re Iresents the set of abductive diag- noses found for a set of observations OBS. Similarly, M denotes the perfect device model that is always con- sistent and complete with respect to reality. If A is a set of ground terms denoting some facts, M(A) is the deductive closure of A through M, i.e. all true facts that can be correctly deduced from A using M. dpos denotes the set of individual hypotheses that can truly explain the observations OBS. For all possible OBS, the following relationship holds: OBS 2 M(dpas), as- serting that, given the correct diagnoses, M correctly explains at least the observations OBS. The inverse M- ’ of M represents the ultimate ab- ductive diagnoser, the one that the implemented sys- tem attempts to approximate. The complete diag- nostic truth, i.e. all possible correct diagnoses for a observations OBS, is represented by M-‘(OBS). If pi represents the final correct diagnosis for a set of observations OSSi, then the following relation holds: ci c M-l(OBS) = &,s. We are interested in studying how the CBR system improves the overall performance of the diagnostic sys- tem. Thus, it is necessary to characterize diagnostic errors first and study how the CBR system can ac- count for these errors. We next introduce additional definitions concerning the abductive part of the model for EAD. Definition 5: 32 The Arts rok is coverinq if Characterizing Diagnostic Errors A,,; s (COMPONENTS - rok(OBS)). rok is covering if it does not forget hypotheses, i.e. if nothing that can explain the set of observations OBS is pruned away by rok. Example 3: A set of rules containing the rule: explanations are correct, i.e.: - - Given the model for diagnosis defined above, and the definitions in the previous section, an error-free diag- noser is one such that all possible explanations for the observations OBS are produced, and that all produced IF engine-noise(irregular) THEN -(irregular-battery would not be covering, since it would discard the pos- sibility that the battery might be faulty, prematurely concentra$ing the abductive process on the carburator. VOBS, VA E Model-l(OBS), Model(A) C M(A). Model is faithful if, for all abductive diagnoses A for OBS, all data entailed by Model(A) is correct with Definition 6: Model is faithful if, Type B: the system explains the data but in an in- correct wav: Model(rok$OB ‘S)) ii MbWBS)), OBS & M&4,,,) C Model(rok(OBS)) C M(rok(qGS)) Type C: possibl explanations This implies three types of possible diagnostic errors: M&o,) e M( rdel(rok(OBS)). are Type A: the system fails to explain the data OB,S: overlooked: OBS e Model(rok(OBS)) respect to M. Theorem 1: Example 4: This example assumes the model in Figure 1 except that the two nodes oil-burn and oil-loss are switched along with their associated symptoms oil-below-car and stackanoke(bluck). It also assumes that this model is correct i.e. corresponds to M. Given the observations from Session 1, the diagnoser would out- put piston-rings-used as the only possible abductive diagnosis. In turn, we have Model(piston,rings-used) g M(piston-rings-used), showing that Model is not faithful. Definition 7: Model is complete if, VOBS, VA E Model-l(OBS), M(A) E Model(A). Model is complete if it explains all the data in OBS that is explainable (with respect to M). Example 5: Example 4 above is an example where Model is not complete since piston-rings-used E M-l (OBS) and, M(piston,rings-used) sf Model(piston-rings-used). Different ways of using inductive diagnoses can be designed depending on the characteristics of each ap- plication. For example, a rough estimate of the quality of the model could be used to determine the degree with which to use and trust the inductive diagnostic process. The more the device model can be trusted, the less the past cases are needed for the current diag- nostic situation. Another consideration is the similar- ity measure used to compare the current situation with retrieved past cases. A statistical analysis of this mea- sure could greatly help determine the uncertainty of its results. Any procedure for merging abductive and inductive diagnoses would be somewhat device depen- dent and does not belong to a general model for diag- nosis combining abduction and induction. If Model is monotonic, rok is covering, Model is com- plete, and Model is faithful then there will be no di- agnostic errors. Equation 1 imposes that for all possible OBS, the data in OBS be explained according to the defini- tion of diagnosis given in the previous section, that all explanations be correct, and that all possible ex- planations be produced. Model might have to ex- plain more data than there is in OBS. These “ex- traneous” explanations, which do not explain OBS di- rectly, still have to be correct for diagnostic errors to be avoided. Equation 1 constrains the restriction of Model to all possible rok(OBS), which might be dif- ferent from COMPONENTS. This is important in the case of cancellation effects between hypotheses, or when two pieces of data cannot be present separately. If M is not monotonic, i.e. if 3A, 3A’, A’ C A and M(A’) e M(A) more hypotheses can potentially explain less symptoms or observations. Intuitively, this situation is more difficult than if M is monotonic since it implies that consequences of errors in the de- vice model either create erroneous explanations (as if Model was monotonic) or forget explanations and di- agnoses (for example if there is an erroneous cancel- lation effect). A non-monotonic abduction problem makes the search for minimal hitting sets for minimal conflicts NP-hard (Bylander et ul. 1991). We have showed the conditions that guarantee the absence of diagnostic errors. Figure 2 shows what kind of errors are produced if these condit,ions are not met. It describes eight situations combining the three types of errors described above. Errors of type B can occur if Model is not faithful, i.e. incorrect explanations can only be produced by an incorrect model. If the whole device model is considered, i.e. if rok is covering, then errors of type A and C can occur if Model is not com- plete (Situations 3 and 4). Proofs of these results can be found in (F&et 1993). These results show that, Case-Based Reasoning 33 rok [ Model 1 no 1 error types faithful 1 complete not faithful 2 B covering n& faithful 3 AC not complete c not fathful 4 A B C faithful 5 A C comDlete not faithful 6 A B C I 1 I covering not faithful 7 AC comr>lete not faithful 8 ABC Figure 2: Summary of diagnostic error situations in general, it is hard to discriminate between poten- tial causes of diagnostic errors, directly from the types of errors that are produced. However, specific condi- tions might render performance improvement easier. For example, if we assume that rok is covering, then the problem seems simpler: if an error of type B oc- curs, then Model is not faithful, and if an error of type A or C occurs, Model is at least not complete. This gives a strategy to try to improve the device model. The results above show that there is little hope for a general abductive method for trouble-shooting diag- nostic systems. This is a strong argument in favor of alternative methods which aim at improving the per- formance of MBD systems. This retrospectively justi- fies the EAD approach. Discussion The definitions given in the paper were inspired by the work on the complexity of abduction done by Bylander et al. (Bylander ei al. 1991) and relate to the focused abductive diagnosis of Console et al. (Console, Porti- nale, & Theseider Dupre 1991) and to Reiter’s theory of diagnosis from first principles (Reiter 1987). The mapping from the EAD model to Console et al.% model is as follows: OBS = D, rok(OBS) = CC COMPONENTS, cbr(OBS, CXT, A) = { ), Similar to EAD, their model does not make assump- tions about the device models it uses. The EAD model is also interesting because it uses compiled knowledge to rule-out possible hypotheses (explanations). This compiled knowledge takes the form of necessary con- ditions (for parts of the model to be considered) and are compiled a priorifrom the behavioral model of the device. The EAD approach also addresses the control problem of choosing between abductively generating more hypotheses and deductively eliminating others that is present in Console et ul.‘s model. The rule-out knowledge is applied first and the remaining hypothe- ses are worth investigating and represent a lesser waste of effort should they be found impossible. The EAD approach is therefore conceptually simpler. The im- portance of rule-out knowledge is illustrated by con- sidering its role in pruning away individual hypothe- ses. A linear decrease in the number n of possible individual hypotheses corresponds to an exponential decrease of the size 2” of the superset of the set of possible individual hypotheses, i.e. the size of the search space. The example in Figure 1 illustrates the potential usefulness of the rule-out knowledge: if the fact engine,noise(regular) is known, then the follow- ing can be logically inferred: 1) the battery is fine, 2) the carburator is not dirty, 3) the ignition is regular, and 4) if there is a power decrease, it can only be be- cause the engine is too hot. This is effective rule-out knowledge since one fact rules out a whole branch of the search space, therefore significantly reducing the cost of the abductive phase of EAD. The EAD model does not make assumptions on how the rule-out knowledge (rok) is brought into the sys- tem. It can be compiled from the a deep mQde1 (as in (Console, Portinale, & Theseider Dupre 1991)) or simply hand coded by human experts (as in (Milne 1987)). One difference between our model and that of Console et al. is that we use rule-out knowledge be- fore the abductive process. Koton’s CASEY also uses CBR before a more traditional diagnostic approach to achieve speed-up learning - a simpler learning than the one achieved by the EAD model (Koton 1988). Our ap- proach improves efficiency by using rule-out knowledge as soon as possible. We believe that this is effective for many real-world devices, because it is easy to formu- late knowledge about independence (as mentioned in (Pearl 1986)) and about inconsistencies between symp- toms and potential causes for those symptoms. Reiter’s model is subsumed by Console ul.‘s but pro- vides insights relative to the search for minimal con- flicts and minimal hitting sets. The mapping from our model to Reiter’s is as follows: OBS = D, rok(OBS) = D, cb,,Ts, CXT, A) = { 1, ++ . For Reiter, a solution to the diagnosis problem is to find a diagnosis for 0 BS which satisfies the consistency requirement. There is no equivalent of the plausibility function in Reiter’s model, i.e. no way of ranking di- agnoses. In the EAD model, the rule-out knowledge rok can be seen as a way to restrict the search for minimal conflicts. If knowledge about impossibilities of some components to be faulty, or of some combinations of components to be faulty simultaneously is available, then the search for minimal conflicts (minimal sets of components that cannot be simultaneously in a nor- mal state together, given the observations OBS) will be reduced. However, the search for minimal hitting sets for the minimal conflicts might actually be made more complex by cancellation knowledge as defined by 34 The Arts Bylander e2 al., making this search NP-hard. The de- ductive, rule-out phase of the EAD model addresses this problem by forcing the system to discard as many impossible faults as possible before considering com- binations of possible ones. This phase could typically use compiled knowledge to reduce the expensive use of deep knowledge. Abductive induction, implemented by a CBR sys- tem, is used to recall past errors and to avoid these errors in similar situations. Assuming that each fail- ure case is stored in A, and that the information de- rived from the abductive diagnostic process serves as indices for the cases, inductive diagnoses can be re- trieved, when the current situation is similar enough to cases stored in A, to correct errors made in pre- vious situations. The indices used by the CBR sys- tem are paths (or portions of paths) followed by the abductive process through the device model to derive diagnoses. This insures the relevance to the current situation of cases stored under these paths. The build- ing of the case base A can be seen as an a fortiori knowledge compilation process. Because this process takes place when the system is in place, it produces more focused and more useful compiled knowledge than knowledge compiled a priori (Console, Portinale, & Theseider Dupre 1991). (F&et & Glasgow 1993; F&et 1993) presented experimental results that sup- port the effectiveness of the EAD model, especially of its inductive phase. The EAD model has been implemented as part of the Automated Data Management System (ADMS) and has been applied to two real-worlql devices: a robotic system called the Fairing Servicing Subsystem, and a Reactor Building Ventilation System (F&et & Glasgow 1991). This paper makes explicit the relation between CBR. and induction by formally defining the notion of ab- ductive induction in the context of automated diagno- sis. It presented the EAD model which addresses the problems of computational complexity and of incor- rect device models. The EAD model is a practical and general answer to problems encountered while trying to apply MBD to real-world situations. The research presented in this paper also contributes to the field of CBR by providing a formal model of a hybrid CBR sys- tem which characterizes the interactions of CBR with another problem-solving paradigm. References Bylander, T.; Allemang, D.; Tanner, M. C.; and Josephson, J. R. 1991. The computational complexity of abduction. Artificial Intelligence 49:25-60. 0 Console, L.; Portinale, L.; and Theseider Dupre, D. 1991. Focusing abductive diagnosis. AI Comnvnicu- tions 4(2/3):88-97. Console, L.; Theseider Dupre, D.; and Torasso, P. 1989. A theory of diagnosis for incomplete causal models. In Proceedings of 11th IJCAI, 1311-1317. de Kleer, J., and Williams, B. C. 1987. Diagnosis multiple faults. Artificial Intelligence 32:97-129. de Kleer, J. 1989. Diagnosis with behavioral modes. In Proceedings of the 11th International Joint Con- ference on Artificial Intelligence, 1324-1330. de Kleer, J. 1990. Using crude probability estimates to guide diagnosis. Artificial Intelligence 45(3):381- 391. de Kleer, J. 1992. Optimizing focusing model-based diagnosis. In Proceedings of the 3rd International Workshop on Principles of Diagnosis, 26-29. F&et, M. P., and, Glasgow, J. I. 1991. Generic di- agnosis for mechanical devices. In Proceedings of the 6th International Conference on Applications of Ar- tificial Intelligence in Engineering, 753-768. Oxford, UK: Computational Mechanics Publications, Elsevier Applied Science. F&et, M. P., and Glasgow, J. I. 1993. Hybrid case- based reasoning for the diagnosis of complex devices. In Proceedings of AAAI-93, 168-175. F&ret, M. P. 1993. Explanation-Aided Diagnosis: Combining Case- Bused and Model- Bused Reasoning for the Diagnosis of Complex Devices. Ph.D. Disserta- tion, Department of Computing and Information Sci- ence, Queen’s University, Kingston, Ontario, Canada. Friedrich, G. 1992. Theory cliagnoses: A concise char- acterization of faulty systems. In Proceedings of the 3rd Internutional Workshop on Principles of Diagno- sis, 117-131. Koton, P. 1988. Reasoning about evidence in causal explanations. In Proceedings of AAAI-88, 256-261. Milne, R. 1987. Strategies for diagnosis. IEEE Truns- actions on ,Systetns, Mun, and Cybernetics SMC- 17( 3):333-339. Mozetic, I. 1990. Reduction of diagnostic complexity through model abstractions. In Proceedings of the lrst International Workshop on Principles of Diagnosis, 102-111. Pearl, J. 1986. Fusion, propagation, and structuring in belief networks. Artificial Intelligence 28:241-288. Peirce, C. S., ed. 1955. Philosophical Writings of Peirce. New York: Dover Publications Inc. Reiter, R. 1987. A theory of diagnosis from first principle. In Artificial Intelligence, volume 32, 57-95. Riesbeck, C., and Schank, R., eds. 1989. Inside Cuse- Bused Reusoning. Lawrence Erlbaum Associates. Case-Based Reasoning 35 | 1994 | 287 |
1,638 | Heuristic Harvesting of Information for Case-Based Argument Edwina L. Rissland, David B. Skalak, and M. Timur Friedman Department of Computer Science University of Massachusetts Amherst, Massachusetts 01003 { rissland, skalak, friedman} @cs.umass.edu Abstract The BankXX system models the process of perusing and gathering information for argument as a heuristic best-first search for relevant cases, theories, and other domain-specific information. As BankXX searches its heterogeneous and highly interconnected network of domain knowledge, information is incrementally analyzed and amalgamated into a dozen desirable ingredients for argument (called argument pieces), such as citations to cases, applications of legal theories, and references to prototypical factual scenarios. At the conclusion of the search, BankXX outputs the set of argument pieces filled with harvested material relevant to the input problem situation. This research explores the appropriateness of the search paradigm as a framework for harvesting and mining information needed to make legal arguments. We discuss how we tackled the problem of evaluation of BankXX from both the case-based reasoning (CBR) and task-performance perspectives. In particular, we discuss how various system parameters- start node, evaluation function, resource limit-affected BankXX from the CBR perspective and how well BankXX performs its assigned task of gathering information useful for legal argumentation by running BankXX on real legal cases and comparing its output with the published court opinions for those cases. 1. Introduction In this paper we discuss heuristically-guided perusal, analysis, and harvesting of information for use in case- based argument. The specific task we study is the gathering and amalgamating of key pieces of information-called argument pieces-which serve as basic building blocks for argument; this is a prerequisite task to the actual generation of more familiar forms of argument, such as 3-ply arguments [Ashley, 19901 or structured memoranda [Rissland & Skalak, 1991; Branting, 1991; Rissland et al., 19931. We are particularly interested in this task in realistic situations, such as performing scholarly research in a large This work was supported in part by the Air Force Office of Scientific Research under contract 90-0359. 36 The Arts well-stocked library with a vast body of potentially relevant materials. In such contexts, multiple retrievals and evaluations of relevance are necessary as one explores materials and builds up an analysis. One often pursues a two-step winnowing approach: gather up potentially useful information as one chases references and then analyze further only those materials with the potential to contribute significantly to key aspects of one’s research. In this paper, we explore this view in our BankXX program, which models the process of gathering and analyzing information for the task of creating an argument with the classic paradigm of heuristic best-first search. BankXX’s domain concerns an aspect of federal bankruptcy law for individual debtors, specifically the “good faith” requirement for Chapter 13 repayment plans.’ A major theme of this paper is that in the face of too much information and too few resources to examine it all, an intelligent information gatherer-person or program- must make choices about which leads to follow, which to ignore or postpone, which information to study closely, which to peruse superficially. A second theme is that the value of some information is not necessarily apparent on first perusal and that some information might not even be accessible on the initial foray into the knowledge base; that is, relevance and accessibility can change as more information is uncovered and examined. For instance, a seemingly unimportant case-one not most on-point or even highly similar-can gain in importance if it turns out that it is the only case addressing a key issue. In this paper, we present our evaluation of how well BankXX performs on its assigned task of harvesting information useful for legal argumentation (on the “good faith” issue) by running BankXX on real legal cases and comparing its output with the published court opinions for those cases. We also evaluate how various internal parameters affect BankXX’s performance as a CBR program. Finally we note that although the context of our research is legal argument, we believe that the use of such heuristic retrieval methods is applicable in other areas, such as diagnosis and design, where CBR methods have been classically applied. Some of the points we will touch upon in this paper are: ‘Section 1325(a)(3) of the federal bankruptcy code requires that debtors’ plans be proposed in “good faith.” This term is undefined in the statute and is interpreted in individual cases by application of case law. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. 0 The overall process of gathering inform ation for argument can be usefully modeled as heuristic search. an * Argument pieces are used to represent argument and define an evaluation function. 0 Retrieval of cases and other knowledge can fruitfully be done with a combination of knowledge-based indexing and heuristic search. 0 Retrieval and relevancy assessment is carried out over many iterations. This paper first discusses the Bat&XX system generally and exposits how the heuristic search model is embodied in BankXX. In particular, we describe the argument piece model of argument used in BankXX and how heuristic search and evaluation functions drive the program to instantiate it. Once all these pieces are in place, we describe a series of experiments to gauge the performance of the system. We conclude by discussing the contributions of this research. 2. Background BankXX has all the standard ingredients of CBR-case memory, indexing, case selection metrics-and executes all the standard subtasks-case input and analysis, retrieval, selection, task performance-on the paradigm CBR performance task of creating precedent-based arguments ([Ashley, 1990; Branting, 19911). BankXX’s case memory is structured as a directed graph whose nodes represent legal objects such as cases and legal theories and whose arcs represent their interconnections. Case memory in BankXX is highly associative, heterogeneous, and has a large branching factor. The indices used by BankXX are arcs of the case memory network as well as more complex linkages computed from them. There are multiple paths to most items in memory [Kolodner, 1983; Turner, 19881. Evaluation functions are used for case selection. Kolodner [ 1993, p. 29 l] discusses retrieval techniques in terms of memory data structures and retrieval algorithms, such as flat memory with serial or parallel search, shared feature networks with breadth-first graph search, prioritized discrimination networks with depth-first graph search, and redundant discrimination networks with breath-first graph search. To this list we can add BankXX’s highly- interconnected, heterogeneous semantic networks with heuristic best-first search. BankXX’s application of iterative, heuristic search to case retrieval distinguishes it from many other CBR programs. CBR is in general a heuristic process because its key mechanisms-indices, relevancy metrics, etc.-are heuristic; and CBR programs do implicitly search a case space. However, CBR programs are not usually designed in the classic search paradigm with its iterative control cycle of evaluating, selecting, and expanding possibilities on the problem-solving horizon. Most CBR programs do not repeatedly cycle through the retrieval and selection of cases. One exception is Owens’s [1993] ANON, which iteratively integrates the search for cases and the extraction of discriminatory features. Direct Memory Access Parsing (DMAP, [Martin, 19901) uses a semantic network of case frames that is searched via a marker-passing algorithm. Other CBR systems that use search include Branting’s GREBE [1991] (A* search to match structured cases preparatory to making an argument), Alterman’s PLEXUS [ 19881 (search of abstraction hierarchies for substitute plan steps for adaptation), and Kass and Leake’s SWALE [ 19881 (local search of plan repair -“tweak’‘-hierarchy). This research also develops a new methodology to evaluate precedent-based argument, and presents a new application of the precision-recall measures used in information retrieval to evaluate case retrieval. We describe an extensive series of experiments that examine BankXX’s performance under various parameter settings, and compared to previous programs and actual legal opinions. 3. Argument Pieces: The Components of Argument Our model of argument is based on the belief that one has a good general sense of the type of information needed to flesh out a good argument, even if one is not an expert in the particular area. This general knowledge includes: 1. what types of domain knowledge exist (e.g., cases, theories, prototypes) and how they are interconnected (e.g., intercase citation, case to theory pointers); and 2. what basic building blocks are needed to put together a good argument (e.g., a viable legal theory, favorable supporting cases, understanding of contrary cases). Based on these observations, we have chosen a simple representation of an argument for purposes of this research as a collection of argument pieces. These building blocks of argument represent fragments of arguments or pieces of legal knowledge that an advocate would ideally like to have when making an argument. We recognize that this idealization of argument does not reflect the logical and rhetorical connections between the various pieces of an argument, or the complexity of argument in general. However, we feel that such information is a prerequisite for constructing more elaborate representations of argument. In BankXX argument pieces are used in two ways: (1) to represent argument, and (2) to define a heuristic evaluation function. The 12 argument pieces currently used in Bar&XX are: I. Supporting Cases - cases decided for the same “side’ the viewpoint assumed in the current problem situation. ’ as 2. Best Supporting Cases - the best cases decided for the current viewpoint. 3. Contrary Cases - cases decided for the opposing side. 4. Best Contrary Cases - defined similarly to 2. 5. Leading Cases - one of the five most frequently cited cases in our BankXX corpus. These were found by a frequency analysis of cases citations done on the full text of the opinions of the cases in the Bar&XX case base. Case-Based Reasoning 37 6. Supporting Citations - citations that: (i) are found in cases with the desired viewpoint, (ii) point to other cases with the same viewpoint, and (iii) use a “citation signal” indicating that the citing case agrees with the cited case (e.g., accord, see). 7. Factor Analysis - the set of domain factors (“dimensions”) that are applicable to the current problem situation. 8. Overlapping Cases - cases sharing a large proportion of domain factors, where large in this paper means at least 75%. 9. Applicable Legal Theories - If each factor defining a theory is applicable to the problem situation, the theory is considered applicable. 10. Nearly Applicable Legal Theories - A theory is nearly applicable if a threshold percentage of defining factors apply. In this paper, the threshold is set at 50%. 11. Factual Prototype Story category - the category of story (e.g., student loan case, medical calamity) that the debtor’s factual situation falls under. These categories were assigned by hand. 12. Family Resemblance Prototype - cases decided for the desired viewpoint having the highest family resemblance rating, with respect to a given family, to the instant case according to the Rosch measure of family resemblance [Rosch & Mervis, 19751. Each of these argument pieces is defined computationally in BankXX. The definitions of “most on- point,” “ best,” and domain “factor” are based directly on those used first in HYPO [Ashley, 19901 and then in CABARET, occasionally with some modification.2 F o r each argument piece, there is a “functional predicate” that determines if a node can supply that useful piece of an argument and a data structure containing an object slot to store entities that satisfy its predicate. BankXX builds up their content incrementally (as its search proceeds) and the collection of filled argument pieces is output to the user at the conclusion of Bar&XX’s processing. 4. The Heuristic Search Model in BankXX builds up the content of the argument pieces by performing heuristic best-first search in a network of domain knowledge. BankXX always begins its processing by analyzing the problem situation for applicable domain factors and computing a claim lattice, which partially orders the cases that have some of the same factors at work as the current problem. The best and most on-point cases are identified. These provide potential new nodes to be explored and are always the first nodes to be placed on the open list. 2For instance, the “best” cases in Bar&XX are most similar to the problem situation whether or not they are most on-point. This is different from the definition in HYPO. 38 The Arts BankXX continues by performing the standard cycle of iterative, best-first search. Neighbors of the current node are generated using BankXX’s neighbor methods. The “best” node on the open list-one with the maximum value under one of BankXX’s evaluation functions-is identified and is then examined by each of the argument pieces in turn in order to determine if it can contribute to that component of the argument. Information that can be harvested by the argument pieces is appended to their data structures. This cycle continues until the search exceeds a user-specified time or space bound (e.g., 30 nodes closed), or until the open list is empty. At the conclusion of the search, the argument is output in a template containing the argument pieces, which have been incrementally filled during the search. State-space search is defined by a triple: initial state, set of operators on states, set of goal states. In best-first search, an evaluation function is used to guide the exploration of the state-space [Barr et al., 19811. We begin by describing the search space. The Search Soace. In BankXX it consists of a semantic network whose nodes represent cases and legal theories from the application domain, the “good faith” issue for personal Chapter 13 bankruptcy plans. Labeled links represent their interconnections. We refer to this network as the case-domain-graph. There are six types of case- domain-graph nodes: five represent legal cases in various perspectives proven useful to human legal reasoners and one represents legal theories. In this area of the law, appeals courts often articulate approaches-“theories’‘-for dealing with the good faith question; these are typically described in terms of domain factors. The five ways legal cases are represented are (1) as factual situations, (2) as bundles of citations, (3) as stereotypical stories or scripts, (4) as a collection of legal factors, or (5) by the measure of their prototypicality. Cases of like type can be grouped into spaces: (e.g., Case Citation Space, Legal Theory Space). Each space captures a particular type of knowledge and its natural interconnections. For instance, intercase citations are captured in the Citation Space and legal theories and relationships between them (e.g., refinement) in the Legal Theory Space. All the spaces are interconnected. For instance, cases point to the legal theories that are applied in them and the story prototype they fall under. Thus the case graph is highly interconnected. For more details see [Rissland, Skalak & Friedman, 19931. The Start Node. In BankXX the default for the initial state is the user-supplied problem situation, which is represented using the same set of hierarchical frames used to represent a case as a collection of facts. Alternatively, the user can input the problem case but specify another node as the start node, for instance, a favorite or well- known case, in order to concentrate the search initially in a particular region of the space. The Ooerators. The set of operators used in BankXX are called neighbor methods. These use links in the case- domain-graph to generate the “successor” nodes to be opened in search. Some follow in-space or cross-space pointers in a straightforward way. For instance, case- theory-neighbors generates all the cases that have applied a particular theory. Others, similar to macro-operators, follow a fixed sequence of links. For instance theory-case- theory-neighbors finds all the theories applied by any of the cases that use the theory used in the current node. BankXX has 12 neighbor methods. In general, they are more complex than the simple following of outward arcs from a given node. Goal Nodes. We do not provide goal states to BankXX because of the difficulties inherent in defining an “argument goal” in a way that is consistent with our understanding of how humans develop and evaluate legal arguments. It is hard to say in general that an argument does or does not meet some plausible persuasive or rhetorical goal, or even that one has completed the supporting research. 4.2 Evaluation Functions We have experimented thus far with three different types of evaluation functions. They differ in the level of abstraction that they use to evaluate nodes in the case-domain graph. All of the evaluation functions are simple linear functions. They form a progression of increasingly more informed evaluation methods, whose considerations range from (1) only the type of information encoded in a node to (2) the contribution of the node to the standard argument pieces and (3) the incremental impact of a node on the overall state of the evolving argument. In this paper we concentrate on experiments using only the first two. Briefly, they are: (1) Node-type evaluation function. Its form is: w1 type-predl(c) + w 2 type-pred,(c) + . . . + w, type-pred,(c) where type-pred checks the type of the current node c. This function assesses the potential according to pre-assigned estimations of how useful various types of nodes are. It causes node-types to be examined in the order defined by the weights wi. In these experiments legal theories have some preference but there is not much difference among the others.3 (2) Argument function is: piece evaluation function. The form of this WI arg-piece-pred,(c,a) + w2 arg-piece-predz(c,a) + . . . + w, arg-piece-pred,(c,a) where c is the current node and a is the current state of the argument. Each arg-piece-pred computes whether a particular argument piece is fillable by the current node and if that argument piece has not already been completely filled: if so, it returns 1; else, 0. This evaluation function prevents BankXX from wasting computing resources by 3The weights are 8 (theories), 6 (cases), 5 (citations), 4 (domain factors), and 3 (factual prototypes). unnecessarily bolstering parts of the argument that are already well-established.4 a&XX Experiments In this paper evaluations: we report on two types of empirical 1. comparing the performance of BankXX with itself as a CBR program, by varying parameter settings; and 2. comparing the performance of Bar&XX with hand-coded arguments found in opinions of actual court cases. In other experiments, performance. we further explore BankXX’s 5.1 Methodology The methodology for the first set of experiments is straightforward: run BankXX on each of the 54 cases in its case base in a de novo manner-that is, excise the case and all its linkages from BankXX’s case-domain-graph-and count the number of items filling each of 10 argument pieces.5 To compare BankXX with written case opinions, we encoded the 54 opinions into “answer” keys comparable in form to those generated by BankXX and applied standard precision and recall measures. Precision is the ratio of what was mentioned by both the decision and BankXX to that mentioned just by BankXX. Recall is the ratio of what was mentioned by both the decision and BankXX to that mentioned just by the decision. We hasten to add that given the small numbers used in these experiments, these measures are very sensitive to small changes. For instance, for a given argument piece, if BankXX retrieves one item that is one of only two items mentioned in the opinion, its precision is 100% and recall is 50%. Should BankXX retrieve an “extra” item not mentioned in the opinion, its precision will drop to 50%; two extra items drop precision to 33%. Its recall will not increase. Since BankXX diligently harvests as much information as it can, it is likely to mention more items than the opinion and be penalized for it in precision and not get credit for it in recall. Thus, one should be careful in reading too much into these traditional metrics. Nonetheless, given their widespread use, we do use them here. Creating the “answers” needed for precision-recall comparisons was done by reading the court’s opinion and 4The weights and the limits on the number of items considered to fill each argument piece (given in brackets) are: 2 [3] (supporting cases), 7 [5] (best supporting cases), 1 [3] (contrary cases), 5 [3] (best contrary cases), 6 [5] (leading cases), 1 [5] (supporting citations), 1 [5] (overlapping cases), 8 [6] (applicable legal theories), 6 [3] (nearly applicable theories), and 6 [I] (factual prototype stories). 5There are 10 terms whereas there are 12 argument pieces because the factor analysis argument piece is filled during system initialization, and we do not use the family resemblance prototype argument piece in these experiments. Case-Based Reasoning 39 encoding each case and theory actually cited in the opinion. One problem inherent in encoding written opinions with the set of original argument pieces is how to identify elements fitting each argument piece, since some have technical BankXX meanings (e.g., best case) or make fine distinctions hard for human readers to discern (e.g., applicable versus nearly applicable legal theory, best versus merely supporting cases). In Bar&XX, these distinctions are made in a principled way with computational definitions. To compensate for such difficulties, the argument pieces were aggregated into four larger-grained argument pieces that were easy to apply.6 These were then used in hand-coding court opinions and as the basis of BankXX versus actual court performance comparisons. The four simplified argument pieces are: (1) Cited- Supporting-Cases,7 (2) Cited-Contrary-Cases,* (3) Cited-Leading-Cases, and (4) Cited-Legal-Theories.9 With these aggregated argument pieces, hand-coding was straightforward and involved little subjective judgment. Any case cited in the opinion is listed as a cited- supporting case or a cited-contrary case depending on how its outcome compares with decision in the opinion.tO If a cited case is also one that is frequently cited by written opinions in general,’ i it is also listed as a cited-leading case. If an opinion explicitlv articulates a theory of its own, reiterates or applies the theory of another case, or appeals to a general domain theory (e.g., a “totality of the facts and circumstances” theory of good faith), then that theory is encoded as a cited-legal-theory. Output from these BankXX-court comparison runs can be viewed in various ways. Figure 1 displays graphically the finest-grained analysis. It shows results for retrieval of objects for the aggregated cited-leading-cases argument piece for each of the 54 cases. Each bar compares performance of BankXX with the court opinion on one case. 6Note five arg ument pieces are not used in the aggregated argument pieces: supporting-citations, factor-analysis, overlapping-cases, factual-prototype-category, family- resemblance-prototype. 7Defined for BankXX as the union of supporting-cases and best- supporting-cases. *Defined for BankXX as the union of contrary-cases and best- contrary-cases. 9Defined for BankXX as the union of applicable-legal-theories and nearly-applicable-legal-theories. l°Complications, such as the fact that a same side case may have been cited (with a so-called But see citation signal) in order to differ with its rationale while still agreeing with its outcome, are overlooked. * ‘A frequency analysis was done on a corpus of cases of approximately 800 cases gathered with a WestLaw retrieval. We then checked the citation frequency of each of BankXX’s cases in this larger corpus. The five most frequently cited cases were used to define cited-leading-case category applied to written opinions. By contrast, for BankXX leading-cases is defined with respect to frequency of citation within BankXX’s own corpus. above the axis: cases retrieved by Bar&XX, of which: 6- mentioned in the opinion not mentioned in the opinion I 6- below the axis: cases mentioned but not retrieved by BankXX in the written opinion, Figure 1: Comparison of retrieved cited-leading-cases using the argument piece evaluation function. Performance on each of the cases, in order from highest to lowest precision. The vertical axis indicates the number of items retrieved. Everything above the zero represents items retrieved by BankXX with the black part of a bar representing those retrieved by Bat&XX and mentioned in the written opinion and the lightly shaded part of the bar representing items retrieved by BankXX that were not mentioned in the opinion. The darkly shaded part of the bar extending below zero represents items mentioned in the opinion that were not retrieved by BankXX. Graphically, precision is the proportion of black out of the total bar above the zero; recall is the proportion of black out of the combined black and darkly shaded parts of the bar. In summary, we ran BankXX on each of the 54 cases in its case base in de novo fashion with each of two evaluation functions, and compared retrieval on each argument piece: approximately 1500 data points. l2 5.2 BankXX as a CBR program This section describes three experiments we performed to answer questions about BankXX as a case-based retrieval system: 1. How important is the initial eventual outcome of retrieval? 2. How much knowledge must have in order to be effective? query in determining the the case retrieval function 3. When can search terminate and the retrieval result be satisfactory? As a baseline, BankXX was run with the Estus case, 695 F.2d. 311 (8th Cir. 1982), as start node, the argument piece evaluation function, and search limited to closing 30 nodes. We addressed the three questions above in search terms by examining the effects of: 1. varying the start node, 2. changing the evaluation function, and 3. trying different limits on the number of nodes that could be closed. t2Given 10 argument pieces used in the general CBR experiments and 4 in the Bar&XX-Court comparisons, there are (2x10 + 2x4) x 54 data points. 40 The Arts supporting cases st cases contrary best cases overlapping cases ardicable theories . . neatly applicable theories II factual prototype story start node evaluation function number of nodes closed node type 10 nodes argument piece 30 nodes most on-point 60 nodes Figure 2: Average number of objects filling each argument piece as the start node is varied (left), the evaluation function is varied (middle), and the number of nodes closed is varied (right). We ran Bar&XX de nova on all 54 cases in the case base to obtain averages for the number of objects filling each argument piece.r3 5.2.1 Initial Query Formulation. Using the argument piece evaluation function and stopping search after closing 30 nodes, three different nodes were used as start nodes: a random case, the Estus case, and a most on-point case. The random case provides a base line. Estus is well known in this area of bankruptcy law-almost any research materials consulted by an attorney will soon lead to it-and therefore it may be considered a realistic and useful starting point. A most on-point case is another starting point likely to be relevant. The results showed that the choice of start node, which is the initial query to the case base, made little difference to 13N.B., numbers of nodes closed, opened, and filling an argument piece are not the same. In general, many more nodes are opened than closed, and the total number of items filling the set of argument pieces exceeds the number of closed nodes (see Figure 2). retrieval. As the left hand side of Figure 2 shows, the average number of objects found for each argument piece is about the same for each of the three start nodes. We examined search paths through the case-domain graph to understand why. It turns out that no matter where search starts in this case-domain graph of 150 nodes, it soon leads to a highly interconnected region which contains many useful cases and theories. For example Estus and Flygare (another well known case) and the theories promulgated by these cases are part of this area of the graph. Informally speaking, it doesn’t matter where search starts because in this domain all roads lead to Estus. We conclude that in browsing a case base where there is a sense of location and a sufficiently rich indexing fabric, the initial probe to case-memory may not matter in a multiple-probe situation. 5.2.2 Case Retrieval Function. Next, we compared the effects of varying the evaluation function while keeping the 30 closed node limit and always starting at the Estus node. The node-type evaluation function finds more contrary cases and same side cases, but does so at the expense of failing to fill other argument pieces. See the middle of Case-Based Reasoning 41 Figure 2. The node-type function uses only the type for evaluation function may give higher recall simply because each node and does not limit the number of objects it retrieves more items than the- argument piece-function. retrieved for any argument piece. Considering its lack of See the middle of Figure 2. The argument piece evaluation knowledge, it does surprisingly well. function is more selective but pays a price for that in recall. To understand how a knowledge-poor function can produce satisfactory results, one can consider search as just the first of a two-stage retrieval process for filling the argument pieces. The second stage applies the argument piece predicates to the retrieved objects to determine if they fulfill the requirements of the argument piece. recall 1.0 - 0.9 - We conclude that in a two-phase retrieval, a knowledge- poor function to generate candidates in the first phase may be sufficient, as long as the performance criteria in the second phase are sufficiently rich. The efficacy of the classic generate-and-test or “many-are-called/few-are- chosen” (MAC/FAC) approach has been observed in other research as well [Gentner & Forbus, 19911. 0.8 - leading cases c - 0.7 - theories contrary same side cases 5.2.3 Termination of Search of Case Memory. There is no objective standard for when one has completed research or completed an argument. Thus BankXX has two termination parameters that may be set by the user: limiting the time (“billable seconds”) used and the number of nodes closed. In these experiments BankXX was set to terminate after it had closed 10, 30, and 60 nodes. 0.6 _ 0.5 - 0.4 - 0.3 - 0.2 - 0.1 - 0.0 + 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Figure 3: Average precision d recall (over all four aggregat 3 argument pieces 54 cases) for the With the argument piece evaluation function and Estus as the start node, 10 nodes was too few to fill up many of the argument pieces. As a rough guide, 30 nodes seemed an appropriate compromise between more exhaustive search and too scanty an examination of the domain-graph. Incremental benefits of more search decreased after about 30 nodes. See the right hand side of Figure 2. On the other hand, there seems not to be much difference overall precision performance between the two in From the CBR perspective, we conclude that the decreased marginal utility of finding more cases causes there to be a point at which additional search of the case base is not effective. This conclusion echoes the results of Veloso and Carbonell [1991] as to the optimal amount of time to search a case base in a hybrid planner. evaluation functions. Each argument piece performs at about the same precision for each function. As we did in Section 5.2.2, we ascribe this to BankXX’s two-stage approach: the lack of precision inherent in the node-type function is ameliorated by the precise filling of the argument pieces. Finally, we note that we did not observe the classical trade-offs between precision and recall. This might be because BankXX is not be functioning at a frontier where such phenomena occur or we need to vary other parameters to see them. In these studies, we only varied two, the evaluation function and the argument piece. 5.3 BankXX as an Argument Program Using standard precision and recall measures, we compared the performance of BankXX with written judicial opinions. All 54 cases were run de nova with Estus as start node and a limit of 30 closed nodes. Results were averaged over the 54 cases. 5.3.1 Precision/Recall Performance and the Evaluation Functions. We were somewhat surprised to find that in general the knowledge-poor node-level evaluation function usually exhibited higher recall and precision than the knowledge-richer argument piece function. For instance, all the average recall values for the node-type function lie above the corresponding values for the argument piece function. Averaged over the four simplified argument pieces, the node-type evaluation function gave higher recall (0.55), than the argument piece evaluation function (0.44). We conclude that Bar&XX’s overall recall performance seems to depend more on the choice of evaluation function than the choice of argument piece. The node-type 5.3.2 Recall/Precision and Argument Pieces. We observed differences in retrieval precision for the different argument pieces (see Figure 3). For both evaluation functions, highest precision was found for cited-leading- cases (0.46), followed by cited-contrary-cases, cited- supporting-cases, then cited-legal-theories (0.2 1). The results for recall were similar for the argument piece function. For the node-type function there was a flattening of performance differences among recall for the argument pieces involving cases; all three did well. three We interpret the better-precision on cited-leading-cases as follows. Since the same small group of leading cases are cited repeatedly in the opinions (that’s what makes them leading-cases),-the probability that a given leading case is mentioned is higher than that for an arbitrary contrary or supporting case or legal theory. Thus if BankXX mentions a leading case it is likely to be in the opinion as well and hence BankXX’s good precision marks on this argument piece. 42 The Arts For the other argument pieces, there is a wide range in the amount of information mentioned in the opinions. Thus if BankXX retrieves information not found in the opinions- which is likely to happen given BankXX’s diligence in going after information-this lowers BankXX’s precision. In particular, BankXX’s low precision and recall scores on cited-legal-theories may be due to the high number of legal theories (18) relative to the number of cases (54), and the similarity of many theories. The program receives no credit for retrieving a useful but uncited theory in the absence of a metric to measure the similarity of the retrieved theory to the one actually applied by a court. 5.3.3 Precision-Recall Measures - Limitations. Again, let us note that the answers derived from actual opinions are not necessarily the best possible nor the only answers. Each opinion is the product of an individual judge and clerks. Some will cite many cases in support of their argument. Others will cite few. Some will mention only the legal theory of their particular judicial circuit. Others will look to other circuits as well. We found that earlier decisions, those written when the good faith issue was first being addressed under the new law, tended to look further afield and compared more different approaches. Once a number of appeals courts had set standards for analyzing good faith, opinions tended to look more exclusively to appeals cases in their own circuit for guidance. Further, the way we have applied precision-recall measures- using the court’s opinion as the “right” answer-is but one way to examine performance. Another would involve comparing BankXX with other programs. Without such comparisons, it is hard to judge BankXX’s performance. Lastly, these measures are problematic for a program like BankXX which seeks to harvest as much information as its resource limits allow. If BankXX retrieves information not found in the opinions-which is likely to happen given its biases-this lowers BankXX’s precision and does not help its recall, even though BankXX might be doing a superb job of legal analysis. Benchmarks better measuring retrieval accuracyi are needed in our experiments-and CBR or AI and Law, in general. 6. Conclusions The general conclusion that we draw from BankXX is that the process of gathering information for an argument can be usefully modeled as heuristic search. In particular, the retrieval of cases and other knowledge can fruitfully be done with a combination of knowledge-based indexing and heuristic search. Using heuristic search as the mechanism to traverse memory permits relevancy assessment and case retrieval to be repeated iteratively in order to locate the 141n engineering, accuracy is different from notes to what decimal point one measures. precision, which only nodes in the case an argument. graph provide the underpinnings of 7. References Alterman, R. (1988). Adaptive Planning. Cognitive Science, 12, 393-422. Ashley, K. D. (1990). Modeling Legal Argument. Reasoning with Cases and Hypotheticals. Cambridge, Massachusetts: M.I.T. Press. Barr, A., Feigenbaum, E. A. & Cohen, P. (198 1). The Handbook of Artificial Intelligence. Reading, Massachusetts: Addison-Wesley. Branting, L. K. (1991). Integrating Rules and Precedents for Classification and Explanation: Automating Legal Analysis. Ph.D. Thesis, Technical Report AI90- 146, AI Laboratory, University of Texas, Austin, Texas. Gentner, D. & Forbus, K. D. (1991). MAC/FAC: A Model of Similarity-based Retrieval. 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L. & Skalak, D. B. (1991). CABARET: Rule Interpretation in a Hybrid Architecture. Znternational Journal of Man-Machine Studies, 34, 839-887. Rissland, E.L., Skalak, D.B. & Friedman, M. T. (1993). Case Retrieval through Multiple Indexing and Heuristic Search. Proceedings, 13th International Joint Conference on AI, 902-908. San Mateo, CA: Morgan Kaufmann. Rosch, E. & Mervis, C. B. (1975). Family Resemblances: Studies in the Internal Structure of Categories. Cognitive Psychology, 7, 573-605. Turner, R. (1988). Organizing and Using Schematic Knowledge for Medical Diagnosis. Proceedings, Case- Based Reasoning Workshop 1988, 435-446. Clearwater Beach, FL. Morgan Kaufmann. Veloso, M. M. & Carbonell, J. G. (1991). Variable- Precision Case Retrieval in Analogical Problem Solving. Proceedings, Third Case-Based Reasoning Workshop, May 1991, 93-106. Washington, D.C. Morgan Kaufmann, San Mateo, CA. Case-Based Reasoning 43 | 1994 | 288 |
1,639 | Case-based Acquisition of User Preferences for Solution Improvement in Ill-Structured Domains Katia Sycara The Robotics Institute Carnegie Mellon University Pittsburgh, PA 15213, U.S.A. katia@cs.cmu.edu Abstract 1 We have developed an approach to acquire compli- cated user optimization criteria and use them to guide iterative solution improvement. The effectiveness of the approach was tested on job shop scheduling prob- lems. The ill-structuredness of the domain and the desired optimization objectives in real-life problems, such as factory scheduling, makes the problems diffi- cult to formalize and costly to solve. Current opti- mization technology requires explicit global optimiza- tion criteria in order to control its search for the op- timal solution. But often, a user’s optimization pref- erences are state-dependent and cannot be expressed in terms of a single global optimization criterion. In our approach, the optimization preferences are rep- resented implicitly and extensionally in a case base. Experimental results in job shop scheduling problems support the hypotheses that our approach (1) is capa- ble of capturing diverse user optimization preferences and re-using them to guide solution quality improve- ment, (2) is robust in the sense that it improves solu- tion quality independent of the method of initial so- lution generation, and (3) produces high quality solu- tions, which are comparable with solutions generated by traditional iterative optimization techniques, such as simulated annealing, at much lower computational cost. Introduction We present an approach, implemented in the CAB- INS system, to demonstrate the capability of acquir- ing user context-dependent optimization preferences and reusing them to guide iterative solution opti- mization in ill-structured domains. This capability is very important for two main reasons. First, tra- ditional search methods, both Operations Research- based and AI-based, that are used in combinatorial optimization, need explicit representation of objec- tives in terms of a cost function to be optimized ‘This research was partially supported by the De- fense Advance Research Projects Agency under contract #F30602-88-C-0001. Most of the work was performed when the second author was a visiting scientist at the Robotics Institute at Carnegie Mellon University under the support of Matsushita Electric Industrial Co. 44 The Arts Kazuo Miyashita Production Engineering Division Matsushita Electric Industrial Co. Kadoma, Osaka 571, Japan miyasita@mcec.ped.mei.co.jp (Reeves 1993). In many practical problems, such as scheduling and design, optimization criteria often in- volve context- and user-dependent tradeoffs which are impossible to realistically consolidate in a cost func- tion. Second, expert system approaches, while hav- ing the potential to capture context-dependent trade- offs in rules, require considerable knowledge acquisition effort (Prerau 1990). Our approach uses case-based reasoning (CBR) which has been successful in dealing with exceptional data (Golding & Rosenbloom 1991; Ruby & Kibler 1992), acquiring user knowledge in com- plex domains (Chaturvedi 1992; Mckay, Buzacott, & Safayeni 1988)) and expending less effort in knowledge acquisition compared with knowledge acquisition for rule-based systems (Lewis, Minior, & Brown 1991). CABINS acquires, stores and reuses two categories of concepts that reflect user preferences (1) what heuris- tic local optimization action to choose in a particular context, and (2) what combinations of effects of appli- cation of a particular local optimization action consti- tutes an acceptable or unacceptable outcome. These are recorded in the case base and are used by CABINS to guide iterative optimization and induce optimiza- tion tradeoffs to evaluate the current solution. The optimization criteria are not explicitly represented as case features or in terms of a cost function but are im- plicitly and extensionally represented in the case base. Previous case-based systems for incremental solu- tion revision (e.g. (Hammond 1989; Veloso 1992)) have been motivated only by concerns of computational ef- ficiency, preserving plan correctness rather than im- proving plan quality, and have assumed the existence of a strong domain model that provides feedback as to plan correctness. Case-based knowledge acquisition systems, (e.g. (Bareiss 1989)) require causal explana- tions from an expert teacher to acquire domain knowl- edge. In our approach neither the user nor the program are assumed to possess causal domain knowledge. The user’s expertise lies in his/her ability to perform con- sistent evaluation of the results of problem solving and impart to the program cases of problem solving expe- riences and histories of evaluation tradeoffs. In this paper, we present initial experimental re- From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. sults to test three hypotheses. First, our CBR-based incremental revision methodology shows good poten- tial for capturing user optimization preferences in ill- structured domains, such as job shop scheduling, and re-using them to guide optimization. Second, the method is robust in the sense that it improves so- lution quality independent of the method of initial solution generation. Third, CABINS produces high quality solutions. To test this, we compared the so- lutions produced by CABINS with explicit optimiza- tion criteria, with solutions produced by simulated an- nealing (a well known iterative optimization technique (Johnson et al. 1991; Zweben, Deale, & Gargan 1990; Laarhoven, Aarts, & Lenstra 1992)) for the same crite- ria. Our investigation was conducted in the domain of job shop schedule optimization and the experimental results, shown in section confirmed these hypotheses. Job Shop Schedule Optimization ORDER1 mm ORDER2 ORDER3 The job shop scheduling problem is one of the most difficult NP-hard combinatorial optimization problems (French 1982). Job shop scheduling deals with alloca- tion of a limited set of resources to a number of activ- ities (operations) associated with a set of jobs so as to respect given temporal relations (e.g. precedence rela- tions among activities), temporal constraints (e.g. job release and due dates) and resource capacity restric- tions in order to optimize a set of objectives, such as minimize tardiness, minimize work in process inven- tory (WIP), maximize resource utilization etc. Due to the tight interactions among scheduling constraints and the often conflicting nature of optimization crite- ria, it is impossible to assess with any precision the extent of schedule revision or the impact of a schedul- ing decision on the global satisfaction of optimization criteria. For example, in figure 1 moving forward the last activity of ORDER3 creates downstream cascad- ing constraint violations. Therefore, a repair action must be applied and its repair outcome must be evalu- ated in terms of the resulting effects on scheduling ob- jectives. In addition, the evaluation itself of what is a “high quality” schedule is difficult because of the need to balance conflicting objectives and trade-off among them. Such tradeoffs typically reflect user preferences, which are difficult to express as a cost function. For example, WIP and weighted tardiness are not always compatible with each other. As shown in figure 2, there are situations where a repair action can reduce weighted tardiness, but WIP increases. Which is a better schedule depends on user preferences. Figure 1: Example of Tight Constraint Interac- tions Rshsr Dale ,A and Hj Schedule-l WIP @Order A Schedule-2 WIP o/Order R za Time Horizon Figure 2: Example of Conflicting Objectives CABINS Overview CABINS is composed of three modules: (1) an ini- tial schedule builder, (2) an interactive schedule repair (case acquisition) module and (3) an automated sched- ule repair (case re-use) module. To generate an ini- tial schedule, CABINS can use any of several schedul- ing methods (e.g. traditional dispatching rules or a constraint-based scheduler). Case representation CABINS incrementally revises a complete but sub- In each repair iteration, CABINS focuses on one activ- optimal schedule to improve its quality, based on ity at a time, the focal-activity, and tries to repair it. flexible optimization tradeoffs. Revision-based ap- A case in CABINS describes the application of a par- proaches to scheduling have also been investigated by ticular modification to a focal-activity. Figure 3 shows (Minton et al. 1990; Zweben, Deale, & Gargan 1990; the information content of a case. Our assumption, Biefeld & Cooper 1991; Laarhoven, Aarts, & Lenstra borne out by the experimental results, is that despite 1992). In those systems, the initial schedule is repaired the ill-structuredness of the domain, the global, local by several techniques, such as the min-conflict heuris- and repair history features express (in an approximate tic or simulated annealing, to minimize the number of constraint violations or optimize a simple cost function (e.g. make-span) of the schedule. The value of incor- porating context-dependent user preferences in oper- ational scheduling environments is becoming increas- ingly recognized (e.g. (Mckay, Buzacott, & Safayeni 1988)) but adequate techniques are lacking. Machme 1 Machme 2 Machme 3 Resource Constraint Propagation Precedence Constraint Propagation Case-Based Reasoning 45 manner) domain regularities. The global features re- flect an abstract characterization of potential repair flexibility for the whole schedule. High ‘Resource Uti- lization Average’, for example, often indicates a tight schedule without much repair flexibility. Associated with a focal-activity are local features that we have identified, based on those reported in (Ow, Smith, & Thiriez 1988), and which potentially are predictive of estimating the effects of applying a particular repair tactic to the schedule. For example, ‘Predictive Shift Gain’ predicts how much overall gain will be achieved by moving the current focal-activity earlier in its time horizon. In particular, it predicts the likely reduction of the focal-activity’s waiting time when moved to the left within the repair time horizon. CASE Resource Utilization Deviation Figure 3: CABINS Case Representation The repair history records the sequence of applica- tions of successive repair tactics, the repair outcome and the effects. Repair effect values describe the im- pact of the application of a repair action on scheduling objectives (e.g. weighted tardiness, WIP). A repair outcome is the evaluation assigned to the set of effects of a repair action and takes values in the set [‘accept- able’, ‘unacceptable’]. Typically the outcome reflects tradeoffs among different objectives. If the applica- tion of a repair tactic results in a feasible schedule, the result is judged as either acceptable or unacceptable with respect to the repair objectives. An outcome is ‘acceptable’ if the user accepts the tradeoffs involved in the set of effects for the current application of a re- pair action. Otherwise, it is ‘unacceptable’. The effect salience is assigned when the outcome is ‘unaccept- able’, and it indicates the significance of the effect to the repair outcome. This value is decided subjectively and interactively. The user’s judgment as to balancing favorable and unfavorable effects related to a particu- lar objective constitutes the explanation of the repair outcome. Case acquisition To gather cases, sample scheduling problems are solved by a scheduler. CABINS identifies jobs that must be repaired in the initial sub-optimal schedule. Those jobs are sorted according to the significance of defect, and repaired manually by a user according to this sort- ing. For example, if the user’s optimization criterion is to minimize order tardiness, the most tardy order is repaired first. The user selects a repair tactic to be applied. Tactic application consists of two parts: (a) identify the activities, resources and time intervals that will be involved in the repair, and (b) execute the repair by applying constraint-based scheduling to reschedule the activities identified in (a). Currently CABINS has 11 tactics and a flexible interface through which the user can define more. After tactic selection and application, the repair ef- fects are calculated and shown to the user who is asked to evaluate the outcome of the repair. If the user eval- uates the repair outcome as ‘acceptable’, CABINS pro- ceeds to repair another focal-activity and the process is repeated. If the user evaluates the repair outcome as ‘unacceptable’, s/he is asked to supply an explana- tion in terms of rating the salience/importance of each of the effects. The repair is undone and the user is asked to select another repair tactic for the same fo- cal-activity. The process continues until an acceptable outcome for the current focal-activity is reached, or the repair is given up. Repair is given up when there are no more tactics to be applied to the current focal-activity; in this situation, CABINS carries on repair of another activity. The sequence of applications of successive re- pair actions, the effects, the repair outcome, and the user’s explanation for failed application of a repair tac- tic are recorded in the repair history of the case. In this way, a number of cases are accumulated in the case base. Case re-use Once cases have been gathered, CABINS repairs sub- optimal schedules without user interaction. CABINS repairs the schedules by (1) recognizing schedule sub- optimalities, (2) focusing on a focal-activity to be re- paired in each repair cycle, (3) invoking CBR with the set of global and local features as indices to decide the most appropriate repair tactic to be used for each fo- cal-activity, (4) invoking CBR using the repair effect features (type, value and salience) as indices to evalu- ate the repair result, and (5) when the repair result is unacceptable, deciding which repair tactic to use next. Note that in contrast to traditional local iterative opti- mization approaches, (e.g. tabu search, simulated an- nealing) where the schedule generated in the current iteration as a result of local revision is directly com- pared (in terms of its associated cost function) with the current schedule, in CABINS, evaluation of the re- 46 The Arts vision is provided by the case base, thus obviating need for the presence of an explicit cost function. The similarity between i-th case and the curr problem is calculated as follows : the sent CFj” - PFj E-D; 12’ \J j=l J where SL” is the salience of j-th feature of i-th case in the case- b ase, and its value has been heuristically defined by the user. CF; is the value of j-th feature of i-th case, PFj is the value of j-th feature in the current problem, E-Dj is the standard deviation of j-th feature value of all cases in the case-base. Feature values are normalized by division by a standard deviation of the feature value so that features of equal salience have equal weight in the similarity function. An Example We briefly illustrate the repair process with a very sim- ple example schedule to be repaired shown in figure 4. The example has ten jobs (Ji, . , , , Jro) and each job has five activities with linear precedence constraints. (e.g. Oy BEFORE 0;) . . . , 0; BEFORE OF). Re- sources RI and R2, R3 and Rg are substitutable; re- source Rq is a bottleneck. Suppose that the job un- der repair is Jg. This job has a weight of 2, a due date of 1250 and the scheduled end-time of its last activity is 1390. Hence it has a weighted tardiness of 2 x (1390 - 1250) = 280. Suppose the current fo- 8 cal-activity is 0,. CBR is invoked with global features (weighted tardiness= 280, resource utilization aver- age=0.544, resource utilization deviation=0.032) plus the set of local features as indices and selects swap as a repair tactic. One can see from the figure that this is a good choice since the focal-activity is scheduled on machine Ra, which doesn’t have any substitutable machine and any idle time in the repair time horizon (time between the end of 0: and the end of 0.2). To apply swap, CABINS calculates the activity with which 0: will be swapped. To do this, CABINS selects the activity which, if swapped with O,S, will result in least amount of precedence constraint violations. In the example, activity 02 is selected as the activity to be swapped with the current focal-activity 0:. Job J4 has weight 3 and weighted tardiness 3 x (1370- 1320) = 150. The effect of applying the swap tactic is that 02 and 0: are unscheduled on Rq and 02 is re-scheduled to start at time 1090 (the start time of activity 0: prior to the swap). The repair process resolves occurring constraint violations. The repaired schedule is shown in figure 5. The effects of repairing 0: are calculated. CABINS calculates the effects on Jg and J4, the jobs affected by the application of the swap on Oz. Machine utilization did not change but Jg had an estimated decrease in weighted-tardiness of 180 time units and an estimated decrease in WIP of 200 units, J4 had an increase in Figure 4: Original Schedule Results Figure 5: Schedule Results after Repair on 0: weighted-tardiness of 150 units and an increase in WIP of 750 units. CBR is invoked using these effect val- ues, weighted tardiness, WIP, as indices to determine whether this repair outcome is acceptable. The accept- ability or unacceptability of the repair will depend on the biases reflected in the case base. Evaluation of the Approach We conducted a set of experiments to test the hy- pothesis that (1) our CBR-based incremental modi- fication and re-use methodology could be effective in capturing user schedule optimization preferences and re-using them to control schedule optimization, (2) the approach is robust in that the schedules produced by CABINS consistently improve a schedule independent of the method used for initial schedule generation and (3) as an iterative optimization method, the approach produces schedules of high quality. These hypotheses are difficult to test since, due to the subjective and ill-defined nature of user preferences, it is not obvious how to correlate scheduling results with the captured preferences or how to define quality of a schedule whose evaluation is subjective. To address these issues, we had to devise a method to test the hypotheses in a consistent manner. To do that, it is necessary to know the optimization crite- rion that would be implicit in the case base, so that the experimental results can be evaluated. In the ex- periments reported here, we used two different explicit criteria (weighted tardiness; WIP+weighted tardiness) to reflect the user’s optimization criterion and built a Case-Based Reasoning 47 rule-based reasoner (RBR) that goes through a trial- and-error repair process to optimize a schedule. For each repair, the repair effects were calculated and, on this basis, since RBR had a predefined evaluation ob- jective, it could evaluate the repair outcome in a con- sistent manner. Thus, we used RBR with different rules each time to generate different case bases (each with 1,000 cases) 2 for different explicit optimization objectives. Naturally, an objective, though known to us, is not known to CABINS and is only implicitly and indirectly reflected in an extensional way in each case base. By designing an objective into the RBR so it could be reflected in the corresponding case base we got an experimental baseline against which to evaluate the schedules generated by CABINS. We evaluated the approach on a benchmark suite of 60 job shop scheduling problems where parameters, such as number of bottlenecks, range of due dates and activity durations were varied to cover a range of job shop scheduling problem instances with the following structure. Each problem class has 10 jobs of 5 opera- tions each and 5 machines. Two parameters were used to cover different scheduling conditions: a range pa- rameter controlled the distribution of job due dates and release dates, and a bottleneck parameter controlled the number of bottleneck resources. Six groups of 10 problems each were randomly generated by considering three different values of the range parameter, and two values of the bottleneck configuration (1 and 2 bot- tleneck problems). These problems are variations of the problems originally reported in (Sadeh 1991). Our problem sets are, however, different in two respects: (a) we allow substitutable resources for non-bottleneck resources whereas the original problems did not, and (b) the due dates of jobs in our problems are tighter by 20 percents than in the original problems. We also tested the approach on another set of 60 problems of 20 orders and 5 resources with similar results. A cross-validation method was used to evaluate the learning capability of CABINS. Each problem set in each class was divided in half. The training sample was repaired by RBR to gather cases. These cases were then used for case-based repair of the validation prob- lems. We repeated the above process by interchanging the training and test sets. Reported results are for the validation problem sets. Experimental Results Figures 6 show the performance of CABINS using “weighted tardiness” case base (labeled in the figures as CABINS( vs performance of CABINS using the “weighted tardiness and WIP” case base (labeled in the figures as CABINS(WT+WIP)). The cases con- stituted the only source of knowledge for CABINS. In 2Since a case represents the application of one repair tactic to an activity, if, for example, 5 repair tactics are utilized in an attempt to successfully repair an activity, then 5 cases would be created. g3600- E3400’ ;3200. ;3000’ F2800’ I--m2600’ %2400’ i&200 g2000. 1800’ 1600. 1400. 1200’ 0 1 2 3 4 5 Problem Se16 0 1 2 3 4 5 Problem Set6 Figure 6: Scheduling Results with Different Case Bases Wei.Tar. WIP Total CPU Sec. EDD 956.0 1284.6 2240.6 0.1 CABINS 349.5 1311.2 1660.7 73.5 SA 340.5 1333.4 1673.9 388.2 WSPT 584.0 1241.0 1825.0 0.1 CABINS 321.0 1254.9 1575.9 72.1 SA 328.5 1320.4 1684.9 398.3 R&M 556.0 1242.0 1798.0 0.1 CABINS 305.3 1264.9 1570.2 84.9 SA 330.1 1290.8 1620.9 450.5 * CBS 1173.0 1481.0 2654.0 17.4 CABINS 405.3 1195.0 1600.3 296.5 SA 11 395.5 1220.0 ) 1615.5 11 1380.0 1 Table 1: Repair by CABINS and SA based on Different Methods of Initial Schedule Generation other words, there was no objective given to CAB- INS explicitly. The case-bases were used both as a source of suitable repairs, and also as a source of ad- vice regarding repair evaluation. From the results we observe that CABINS generated higher quality schedules with respect to minimizing weighted tar- diness than CABINS(WT+WIP). Conversely, CAB- INS(WT+WIP) g enerated higher quality schedules with respect to WIP, and weighted tardiness plus WIP than CABINS( Th ese results indicate that CAB- INS can acquire different and subjective user prefer- ences. In order to test the hypothesis that CABINS con- sistently improves schedule quality independent of the method of initial schedule generation, we generated ini- tial schedules for the benchmark suite of problems us- ing three different state-of-the-art dispatch scheduling heuristics (EDD, WSPT, R&M) (Morton 1992) and a constraint-based scheduler (CBS). The optimization objective was WT+WIP. Table 1 presents the aver- age of all 60 problems in the benchmark and shows that CABINS improved schedule quality independent of method to create the initial schedule. To test the 48 The Arts hypothesis that CABINS generates schedules of high quality, we compared the schedules generated by CAB- INS against schedules generated by simulated anneal- ing with the explicit objective of WT+WIP. Table 1 shows that CABINS generated schedules of compara- ble quality but was on the average 4-5 times more ef- ficient than simulated annealing. Conclusions We have presented a case-based approach to acquire user optimization preferences and reuse them to guide iterative solution optimization in ill-structured do- mains. We demonstrated the effectiveness of the ap- proach in capturing user preferences and creating ef- ficiently high quality solutions on job shop scheduling problems. One crucial issue is how much effort should be spent to capture “enough” number of cases for “suf- ficient” solution quality improvement. This is an issue we are currently pursuing. Initial experiments to de- termine case base size versus quality improvement have shown that a case base of 800 cases gives on the av- erage 20% higher quality improvement at 15% lower computational cost than a case base of 400 cases. It seems that the effort expended to capture a big num- ber of cases can be amortized by future repeated use of the case base to get high quality schedules efficiently. More importantly, CABINS can acquire those cases from user’s interaction during the process of solution improvement, thus imposing low additional effort on the user but enhancing solution improvement. We be- lieve that CABINS has the potential for accommodat- ing acquisition of user preferences that change over time. Future work will investigate this issue. References Bareiss, R. 1989. Exemplar-based knowledge acquisi- tion : a unified approach to concept regression, clas- sification, and learning. New York, NY: Academic Press. Biefeld, E., and Cooper, L. 1991. Bottleneck identi- fication using process chronologies. In Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI-91). Chaturvedi, A. 1992. Acquiring Implicit Knowledge in a Complex Domain. Expert Systems with Applica- tions. French, S. 1982. Sequencing and Scheduling: An In- troduction to the Mathematics of the Job-Shop. New York, NY: Ellis Horwood. Golding, A. R., and Rosenbloom, P. S. 1991. Improv- ing Rule-Based Systems Through Case-Based Rea- soning . In Proceedings of the Ninth National Con- ference on Artificial Intelligence, 22-27. AAAI. Hammond, K. J. 1989. Case-Based Planning : View- ing Planning as a Memory Task. New York, NY: Academic Press. Johnson, D.; Aragon, C.; McGeoch, L.; and Schevon, C. 1991. Optimization By Simulated Annealing: An Experimental Evaluation, Part II (Graph Coloring and Number Partitioning). Operations Research. Laarhoven, P. J. M. V.; Aarts, E. H. L.; and Lenstra, J. K. 1992. Job shop scheduling by simulated anneal- ing. Operations Research 40( 1):113-125. Lewis, L.; Minior, D.; and Brown, S. 1991. A Case- Based Reasoning Solution to the Problem of Redun- dant Engineering in Large Scale Manufacturing. In- ternational Journal of Expert Systems 4(2):189-201. Mckay, K.; Buzacott, J.; and Safayeni, F. 1988. The scheduler’s knowledge of uncertainty: The missing link. In Proceedings of IFIP Working Conference on Knowledge Based Production Management Systems. Minton, S.; Johnston, M. D.; Philips, A. B.; and Laird, P. 1990. Solving large-scale constraint satisfac- tion and scheduling problems using a heuristic repair method. In Proceedings, Eighth National Conference on Artificial Intelligence, 17-24. Boston, MA.: AAAI. Morton, T. E. 1992. HEURISTIC SCHEDULING SYSTEMS: With Application to Production Systems and Product Management. Pittsburgh, PA.: GSIA, Carnegie Mellon University. Course Textbook. Ow, P. S.; Smith, S. F.; and Thiriez, A. 1988. Re- active plan revision. In Proceedings of the Seventh National Conference on Artificial Intelligence, 77-82. St-Paul, Minnesota: AAAI. Prerau, D. S. 1990. Developing and Managing Expert Systems: Proven Techniques for Business and Indus- try. Reading, MA: Addison-Wesley. Reeves, C., ed. 1993. Modern Heuristic Techniques for Combinatorial Problems. New York: Halsted ’ Press. Ruby, D., and Kibler, D. 1992. Learning Episodes for Optimization. In Machine Learning : proceedings of the Ninth International Workshop (ML92), 379-384. Sadeh, N. 1991. Look-Ahead Techniques for Micro- Opportunistic Job Shop Scheduling. Ph.D. Disserta- tion, School of Computer Science, Carnegie Mellon University. Veloso, M. M. 1992. Learning by Analogical Reason- ing in General Problem Solving. Ph.D. Dissertation, School of Computer Science, Carnegie Mellon Univer- sity. Zweben, M.; Deale, M.; and Gargan, M. 1990. Any- time rescheduling. 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1,640 | Learning To Learn : Automatic Adapt at ion of Learning Bias Steve G. Romaniuk Department of Information Systems and Computer Science National University of Singapore 10 Kent Ridge Crescent Singapore 05 11 e-mail: stever@iscs.nus.sg Abstract Traditionally, large areas of research in machine learning have concentrated on pattern recogni- tion and its application to many diversified prob- lems both within the realm of AI as well as out- side of it. Over several decades of intensified re- search, an array of learning methodologies have been proposed, accompanied by attempts to eval- uate these methods, with respect to one another on small sets of real world problems. Unfortu- nately, little emphasis was placed on the prob- lem of learning bias - common to all learning algorithms - and a major culprit in preventing the construction of a zsniuerscsl pattern recog- nizer. State of the art learning algorithms ex- ploit some inherent bias when performing pattern recognition on yet unseen patterns. Automati- cally adapting this learning bias - dependent on the type of pattern classification problems seen over time - is largely lacking. In this paper, weak- nesses of the traditional one-shot learning envi- ronments are pointed out and the move towards a learning method displaying the ability to learn about lecarning is undertaken. Trans-dimensional learning is introduced as a means to automati- cally adjust learning bias and empirical evidence is provided showing that in some instances beurn- ing the whole can be simpler than learning a part of it. Introduction It is a well known fact that if we consider the universe of all possible pattern recognition problems, learning algorithms 1 tend to exploit some bias, when gen- eralizing from a finite set of examples. Customar- ily, we refer to this generalization as induction. An abundance of learning algorithms (pattern classifiers) have been proposed over the last few decades (Qi- unlan 1979; Fahlman 8~ Lebiere 1990; Frean 1991; Romaniuk 1993b; Cheng et al. 1988). In all instances, the inherent bias in learning algorithms remains static, thereby restricting the universal application of these 1 and Throughout this paper we will use puttern recognition interchangeably. the terms learning algorithms to a multitude of conceivable pattern clas- sification problems. In other words, every single one of these algorithms can only be applied with some de- gree of success to a subclass of pattern recognition tasks. No universal application is possible, due to the algorithms’ inability t,o automatically modify its learning bias, based on the types of pattern recogni- tion problems it may be confronted with over a period of time. This lack of any form of meta-learning ca- pability in traditional pattern recognition algorithms, has received little attention from the machine learn- ing (pattern recognition) and neural network commu- nities. Instead, increasingly limited pattern recognition algorithms are proposed, void of this most fundamen- tal property commonly attributed to any intelligent agent. A few notable exceptions are (Chalmers 1990; Bengio et al. 1992). The purpose of this article is to outline a learn- ing system capable of automatically adjusting learning bias based on prior performance. The proposed system is based on a simple feedforward neural network, in which hidden units are automatically recruited and lo- cally trained using the perceptron learning rule. Learn- ing is seen as a bottom-up feature construction process in which previously learned knowledge (stored as fea- ture units within the network) represents the primary mechanism for performing meta-learning. Automatic Neural Network Construction Overview During the past years neural networks have been ap- plied to a wide variety of pattern recognition tasks with varying degrees of success. In many cases, a major drawback has been, finding the right number of hidden units, layers and connectivity of the net- work - at least for networks trained by backpropa- gation like algorithms. Often users rely on rules of thumb (heuristics) to decide how to choose these pa- rameters. The outcome is at best challenging, many times it is simply frustrat,ing. The problem is further compounded by varying (initially random) weights, an array of different tuning parameters (e.g. momentum Neural Networks 871 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. term, learning rate, etc.), type of transfer function (e.g. sigmoid, threshold, gaussian, etc. ) and fi- nally the choice of learning algorithm itself (backprop, quickprop, etc.). Given this less than rosy situation, it should come as no surprise that researchers have looked for ways to improve this situation. Within the last couple years several different approaches to au- tomatically construct neural networks have been pro- posed (Baffes & Zelle 1992; Fahlman & Lebiere 1990; Frean 1991; Romaniuk 199310). These algorithms dif- fer in how they construct networks (purely horizon- tal or vertical growth, or hybrids in between) and the kind of local learning rules they utilize. They also contrast with regard to the types of problems they can solve, the quality of the final networks, network complexity, speed, and their ability to con- verge on certain types of data. For more informa- tion the interested reader may want to consult (Baffes & Zelle 1992; Fahlman & Lebiere 1990; Frean 1991; Romaniuk 199313). Evolutionary Grow.t h Perceptron Evolutionary Growth Perceptron (Romaniuk 1993b) (EGP) represents an approach to automatically con- struct neural networks by exploiting natural selection. Networks are assembled in a bottom-up manner, a fea- ture at a time. Every newly recruited unit (feature) added to the network, receives its input connections from all previously installed hidden units and input units. Once an element is set up, it is trained employ- ing the perceptron learning rule for a fixed number of epochs. ‘Evolutionary processes are invoked to decide which patterns of the training set should be made use of when training the current hidden feature. An indi- vidual chromosome encodes the subset of patterns ad- ministered for training the present unit. A population of these chromosomes are then evaluated on the task of overall error reduction. After either a fixed number of generations has passed, or there is no improvement in error reduction, the element trained to the lowest error rate is permanently installed in the network. If there are still patterns left, which are miss-classified by the newly added unit, then a new element is created and the above process repeated. Otherwise, training halts and the last unit in the network is designated the output of the network. EGP learns the difficult N-parity function with about [$] hidden units (Romaniuk 1993b). Learning to Learn Traditional One-shot Learning Approach Over the last few decades a multitude of ideas have entered the realm of machine learning, resulting in countless interesting approaches and advances to this important area. The oldest learning systems date back to the 1940s (Hebbian learning) and the intro- duction of the perceptron. Later years would see the Figure 1: Traditional One-shot Learning Approach advances of inductive learning systems such as ID3 (Qi- unlan 1979) (based on decision trees). The eighties saw a revival of the neural network community with the introduction of the backpropagation learning rule. More recently approaches have been formalized that attempt to integrate seemingly different paradigms such as connectionism and symbolism. Other ad- vances have been made to automate the network build- ing process (Fahlman & Lebiere 1990; Frean 1991; Baffes & Zelle 1992; Romaniuk 1993b). With the dis- covery of ever new methodologies to tackle learning problems, the question of evaluating these diverse al- gorithms has remained mostly unchanged. Commonly, we can identify 2 approaches: The first approach con- siders an empirical study which includes testing a new learning algorithm L E l (element of the class of all learning algorithms ,C) on a set of either artificial or natural (real world) problems P E P. This set P is for almost all empirical studies small (about 1 to a dozen problems). In general, several well accepted problems - also known as benchmarks - are selected for an em- pirical study. Besides including a set of benchmarks, a few well known learning algorithms (that is well pub- licized) are picked in order to perform a comparison. Evaluation of learning algorithms proceeds by dividing a set of patterns, that describe the problem under con- sideration into 2 partitions: a train (TJrain) and test set (TT~~~). The degree of generalization (performance accuracy) of algorithm L is measured by determining how many patterns in TJest are correctly recognized by L after being trained on patterns in TT,.~~~. Af- ter training and testing (classification) have been com- pleted for a given problem P, results obtained thus far are removed and a new problem is tackled. We refer to this procedure as one-shot learning. A graphical representation of this approach is depicted in Figure 1. Note, that the tuning module is optional and may even be lacking in some learning systems (e.g. ID3 (Qiunlan 1979)). Other approaches - predominantly gradient decent-based learning algorithms (e. g. back- propagation) - are equipped with a multitude of tuning parameters, which when appropriately set by the user, can improve the learning modules overall performance on a given pattern recognition task. We can think of the tuning module as being a primitive mechanism to adapt the bias of the learning module. This adaptation is under the direct control of the human user. It is a well known fact, that any such empirical com- 872 Neural Networks parison cannot yield significant results due to the sheer size of potential problems that can exist in the real world. As a matter-of-fact, it is straight forward to ver- ify that for every problem P = 7+rain UTTERS, for which some algorithm L E JC can achieve accuracy (Y (de- noted by AL(TT~~~) = CY), there always exists a prob- lem P’ = T~rainuT;~~~ 2 such that AL(T~~,~) = 1-o. Hence, the average accuracy is always i. 3 This is ac- tually true regardless of how we partition the examples describing problem P into train and test sets, as long as T&t # 0. The above essentially states, there cannot exist a universal learning algorithm (neither biological or ar- tificial), which can perform equally well on all pattern classification problems. Instead, every learning algo- rithm must exploit some learning bias which favor it in some domains, but handicap it in others. The fol- lowing may serve as an example: Both decision-tree based, as well as, backpropagation-like learning algo- rithms have a more difficult time representing highly non-separable functions (e.g. parity) than a truly lin- ear function (e.g. logical or). When we say more dif- ficult to learn, we refer to training time, as well as, how the function is represented and the performance accuracy we can expect, after training is completed. A decision-tree based algorithm, for example, grows an increasingly deeper tree structure, whereas a backprop network requires additional hidden units (and connec- tions) to learn even/odd parity. Due to these observa- tions, it should become apparent why simple empirical studies are of little value in deciding the quality of a new learning approach or allow for comparing different approaches. A second technique for evaluating learning systems, is based on developing a theoretical framework. A good example of this approach is the Probably Approximately Correct learning model (PAC) (Valiant 1984). Here, one attempts to identify sub-classes of problems which can be learned in polynominal time and for which con- fidence factors can be stated for achieving a given per- formance accuracy. Unfortunately, these methods are too rigid and constrained to be of practical use. For one, sub-classes may be very specific, such that re- sults about them seem to say little. A more substan- tial shortcoming is: sub-classes of problems tend to be highly abstract. For example, a restricted class of problems might be CNF,(k), that is, all proposi- tional formulae over n boolean variables in conjunctive normal form with at most k literals. Results like this provide no indication on how abstract results can be placed in relation with their real world counterparts. Having determined that algorithm L tends to fare well with problems belonging to some sub-class of tasks, still does not help us decide how to solve a specific real P 20utputs of patterns in TkeSt are inverted from those in TTest. 3 Assuming binary encoded problems. I II I I Figure 2: Multi-shot Learning Approach world task, unless we show that our model is in some correspondence with the real world problem. But to determine this membership may require utilizing algo- rithm L in the first place. In short, we are forced to ap- ply trial-and-error to decide which pattern recognition algorithm is best suited for solving the task at hand. Only, if substantial amounts of a priori domain knowl- edge are available, can we be sure to select the right learning algorithm, before actually trying it out. For many important tasks an appropriate pattern recogni- tion algorithm may not even be available. Multi-shot Learning Approach The problem we are facing - to develop learning meth- ods that can be employed to solve various real world problems - can not be overcome with simple one-shot learning algorithms. For this matter, we propose to look at algorithms which have the capability to learn about learning. These new algorithms must be capa- ble of shifting their built-in bias (to favor certain sub- classes of tasks) deliberately, by utilizing past perfor- mance, to give them wider applicability than simple one-shot learning systems. Figure 2 outlines the multi- shot method. In this approach, previous knowledge (in form of an internal representation of earlier learned problems) is fed back into the learning module, when- ever a new task is presented. An optional selector mod- ule may provide supplementary pat tern classification problems (similar), depending on the results obtained from the performance module and automatically sup- ply them to the learning module. This ability, - to learn knowledge on top of al- ready existing knowledge, without every time having to restart learning from ground zero - can have an im- pact on learning time, representational complexity, as well as generalization on yet unseen patterns. To move beyond simple one-shot learning we examine the sub- sequently listed task: Given: A set of problems P = {Pr’, PF2, . . . , PLk}, where P,“l E Cna. The Pr’ belong to the class of classificatory problems C (continuous inputs/binary output) of variable input dimension ni. Goal: Develop a representation Rk that can correctly classify all Pin’ E P. No specific order is imposed on the problems in P when presented to the meta-learning system. Neural Networks 873 We refer to an algorithm which can solve the above task as a trans-dimensional learner. We should ob- serve at this point, that a network condructing trans- dimensional learner is one of numerous alternatives. For example, we could have chosen a decision-tree like representation, instead of a connectionist network when designing TDL. A decision in favor of a connec- tionist representation was cast, due to earlier obtained positive results involving EGP and considering the al- gorithms simplicity. Before we outline the individual modules compris- ing TDL we draw attention to 2 approaches regarding automatic learning bias adjustment: First, the explicit approach. Here, a standard pat- tern recognition algorithm has its learning behavior regulated by modifying one or more of its tuning pa- rameters. If a learning algorithm is not equipped with tuning parameters, they may be added retrospec- tively. For example, a decision-tree based algorithm like ID3 has no tuning parameters. An extension of ID3 (GIDS (Cheng et al. 1988)) uses a tolerance pa- rameter which controls the amount of generalization by guiding attribute selection. Explicit learning bias adjustment proceeds by presenting either similar types of problems (e.g. even/odd parity) or identical prob- lems (e.g. only even-parity) to the algorithm. Perfor- mance on prior tasks (degree of generalization and ef- fectiveness of knowledge representation) are measured and tuning parameters are appropriately modified. It is anticipated that for similar or identical problems, the same setting (or related) of tuning parameters, can result in improved performance. For example, a backpropagation-based algorithm may learn to adapt its learning rate and momentum term in such a way, that it can more readily learn a parity function after having been trained on a few instances of this type of function. The second approach is implicit. In this case, there are no explicit tuning parameters, instead learning bias is shifted by relying on earlier stored knowledge. Hence, this method is identical to multi-shot learn- ing. The internal knowledge representation of previ- ous learned tasks is exploited to guide future learning. The herein proposed meta-learning algorithm is based on the implicit approach. TDL : Trans-Dimensional Learner In this section, the basic modules deemed important in the construction of TDL are discussed. Earlier, it was pointed out that an automatic neural network con- struction algorithm (EGP) would serve as the primary means for building high level network features. It was also indicated that the EGP algorithm assembles new features by fully connecting previously created features to the one currently under construction. This can very quickly lead to a high fan-in of connections to the hidden units. Consequently, storage requirements and simulation time increase rapidly, as fresh hidden fea- tures are installed. Apart from this surface problem, a more harmful side-effect can be identified: dilution in quality of high-level features. Recall, that the per- ceptron rule is utilized to locally train newly recruited features. Now, the perceptron learning rule attempts to discover an appropriate linear combination of the inputs to the trained feature, such that overall error is reduced. If the number of features forming the input to the current unit is large, many more weight assign- ments are possible, of which many may lead to shallow local optimums. To prevent this from occurring, it is essential to restrict the number of hidden features se- lected for constructing new features. To accomplish this feat, a quality measure is invoked to determine the potent’ial of previously constructed units to act as good hidden feature detectors when solving the current goal. The quality measure is defined as, Qk,i(k P/c) = log(L(Fi) + 1) log(maw~ (L( F’)) + 1) ) (1) ,where L(Fi) returns feature Fi’s layer location. The first factor of Equation 1 measures feature Fi’s accu- racy on problem Pk, whereas the cost factor incorpo- rates information about feature Fi’s layer location rel- ative to the current networks height. To further reduce the complexity of the resulting connectionist network, it can prove extremely benefi- cial, to prune an already trained feature unit, before resorting to train a new one. It has bee pointed out that besides further reducing the fan-in to individual units, pruning can also improve the generalization ca- pability of a network. It may be necessary to provide a mechanism which allows the network to forget some of its learned knowl- edge, especially if over time this knowledge is deemed unimportant. Forgetting information is paramount to conserving network resources such as units and connec- tions. Finally, if we think of biologically inspired learn- ing systems then, due to changes in the environment, some of the accrued knowledge may become obsolete. It would indeed be wasteful to ret,ain this information. A High-level description of the proposed trans- dimensional learner is presented below. In order to handle training patterns of various input dimensions, a pool of input features is initially set aside. The pool is left-adjusted, which implies the first input value of a training pattern is stored in the foremost input unit of the pool and so on, until all input values have been as- signed to corresponding input units. Remaining pool units are assigned a default value of 0, to guarantee that no activations are propagated from any potential connections that emanate from these units to other network units (Effect identical to being disconnected). 874 Neural Networks pk : kth problem to be Zearned. P : set of all problems. N : network constructed by TDL. Nomenclature for TDL: (1) For all Pk E P, k E [l, N] do (1.1) While A(Fc,Pk) < 1 do (1.1 .l) Create new feature FneW (1.1.2) Connect all 11, z E [1,In(Pk)] to FneW (1.1.3) For all Fi E N do (1.1.3.1) If Qk @, Pk) > Q then (1.1.3.1.1) Connect Fi to FneW (1.1.4) N = N u IF,,,} (1.1.5) Fc = ~~~~ (1.1.6) EGP(Fc) (1.1.7) Prune feature FC To close out this section, Figure 3 displays an exam- ple of a TDL generated network that correctly recog- nizes the or-function of input dimensions 2 - 7. Empirical Results To furnish empirical evidence supporting the effective- ness of TDL, a collection of well-known neural network benchmark problems have been selected in conjunction with some simpler functions to allow for a meaningful study. These problems are: and, or, even-parity, odd-parity of input dimension 2 - 7, 4-, 8-, 16-bit encoder, and 2-, 3-bit adder. Combining the above tasks yields a total of 29 func- tions (29-fkt problem). As a subset we also consider the even/odd-parity functions (parity problem). For all experiments 10 trial runs are conducted and their average is reported. Also, every feature is trained for at most 60 epochs. Learning The Whole Can Be Simpler Than Learning A Part Of It In Figure 4a we present results relating the number of generations (amount of time required to evolve a net- work) and the number of combined units (hidden and output units in final network). The first observation we make is, the response curve for the 29-fkt problem displays a sudden steep increase in the final stages of training, as opposed to the almost linear response ob- tained during learning the parity problem. Secondly, around 20 functions (of the original 29) are learned in the final stages of training, that is in the last FC : current unit in network N. 11 : Zth input of problem Pk: Figure 3: OR-2 through OR-7 as learned by TDL rn( pk> : number inputs for problem Pk. ,cu 29-,ET ,Lay**n for 29-skc &k,i(Fi, pk) : quality measure for it h unit. A(Fc, pk) : accUracy Of f e&we FC for Pk. Q : threshold for quality measure (0.1) Figure 4: # Generations vs. (a) # Combined Units (b) # Layers for learning 29-Fkt and Parity 20 generations. In other words, more than two-thirds of the problems are acquired in the last one-tenth of the training phase. This result underlines how TDL bene- fits from previously learned information and indicates how the ability to learn to learn has a profound impact on total training time and final network configuration. The most impressive finding can be gleaned, when comparing the absolute magnitude in number of gen- erations required to learn either parity or 29-fkt task. The parity problem is learned after nearly 270 gener- ations have passed, whereas the 29-fkt problem is ac- quired after less than 210 generations. Since the parity problem is a subset of the original 29-fkt problem, this result is clear evidence of the phenomena: learning the whole can be simpler than learning a part of it. Furthermore, this finding substantiates the fact, the time needed to learn a subset of functions can be sig- nificantly reduced by assimilating additional functions, even when they have little in common with the origi- nal set of functions. Recall, the composition of the 29- fkt problem. Besides containing the simpler and- and or-functions, it also consists of encoder and adder functions. The task of identifying even and odd par- ity has little in common with the task of performing binary encoding or binary addition. Another interesting observation is that the number of combined units is about the same as the number of functions learned. Both for parity as well as the 29- fkt task, the increase in number of combined units with respect to the number of functions acquired (regardless of the problems input dimension) is about linear. Figure 4b depicts the relationship between the num- ber of generations and the number of layers. The steep increase in layers for the 29-fkt problem coincides with Neural Networks 875 of this study are of importance, since they suggest that P I * Figure 5: (a) Pattern (b) Function Recognition Accu- racy for 29-Fkt Problem the increase in combined units. This indicates that newly formed feature detectors in the network are con- structed from already existing low level feature detec- tors. In other words, overall savings in combined units and training time are realized by creating high-level features, resulting in a rapid overall increase in the number of layers. In Figure 5a the accuracy (degree of generalization on yet unseen patterns) obtained by TDL for the 29-fkt problem is displayed. Figure 5b furnishes insight into the function recogni- tion capability of TDL for the 29-fkt task. The graph depicts the relation between the average number of problems seen and the percentage of correctly iden- tified functions. 4 Summary Taking the step from one-shot learning to develop an automatic network construction algorithm capable of trans-dimensional learning can be viewed as a step to- wards a new, and more powerful learning environment. Perceiving units within a network solely as features and learning as a process of bottom-up feature construction were necessary notions to develop a feasible implemen- tation of a trans-dimensional learner. Basing local fea- ture training on the simple perceptron rule and com- bining evolutionary methods to effectively create train- ing partitions, have substantially contributed towards the construction of a more flexible learning system. Contrary to intuition, it was noted that learning a large set of diverse problems can be either equal to or even simpler than attempting to learn a subset of the very same problems. Even across a highly diversified set of domains can powerful hidden features be constructed and help decrease learning time and network complex- ity as more problems are encountered. These power- ful hidden features support adjusting learning bias de- pending on the type of problems presented by simpli- fying the learning process itself and help elevate TDL above simple one-shot learning systems. The findings 4The 29-fkt problem actually consists of 59 functions. This number is obtained by adding up the number of out- puts for all 29 problems. 876 Neural Networks learning new features- can be substantially improved by learning on top of pre-existing knowledge, even if there appears little in common between the two. Even though this is an initial study in the applicability of trans-dimensional learning to solve the general prob- lem of learning about learning, it is one that has given rise to some interesting results and it is hoped that future work will prove as fertile. References Baffes, P.T. and Zelle, J.M (1992). Growing Layers of Percept rons: Introducing the Extentron Algorithm, Proceedings of the 1992 International Joint Confer- ence on Neural Networks (pp. II-392- II-397), Balti- more, MD., June. Bengio, Y., Bengio, S., Cloutier, J., Gecsei, J. (1992) On t#he optimization of a synaptic learning rule, Con- ference of Optimulity in Biological und Artificial Neu- ral Networks, Dallas, USA. Chalmers, D.J. (1990) The Evolution of Learning: An experiment in Genetic Connectionism, In D.S. Touretsky, J .L. Elman, T.J. Sejnowski, and G.E. Hin- ton (Eds.) Proceedings of the 1990 Connectionists Models Summer School. Cheng, J., Fayyad, U.M., Irani, K.B., Qian, Z. (1988) Improved Decision Trees: A Generalized Version of ID3, Proceedings of the 5th Inetrnutionul Conference on Machine Learning, Ann Arbor, Michigan, June. Fahlman, S.E. and Lebiere, C. (1990). The Cascade- Correlation Learning Architecture, In D. Touretzky (Ed.), Advances in Neural Information Processing Systems 2 (pp. 524-532). San Mateo, CA.: Morgan Kaufmann. Frean, M. (1991). The Upstart Algorithm: A Method for Constructing and Training FeedForward Neural Networks, Neural Computation, 2, 198-209. Holland, J.D. (1975) Adaption in Natural and Arti- ficial Systems. University of Michigan Press, AnnAr- bor, MI. Quinlan, J.R., (1979) D iscovering rules by induction from large collections of examples. In D. Michie (Ed.), Expert systems in the micro electronic age. Edinburgh University Press. Romaniuk, S.G., Hall, L.O. (1993) Divide and Con- quer Networks. Neural Networks, Vol. 6, pp. 1105- 1116. Romaniuk, S.G. (1993) Evolutionary Growth Percep- trons. In S. Forrest Genetic AZgorithms : Proceedings of the 5th International Conference, Morgan Kauf- Mann. Valiant, L.G. (1984). A Theory of the learnable. Comm. Ass. Comput. Much. 27(11), 1134-1142. | 1994 | 29 |
1,641 | Towards More Creative Case- Linda M. Wills and Janet L. Kolodner College of Computing Georgia Institute of Technology Atlanta, Georgia 30332-0280 linda@cc.gatech.edu, jlk@cc.gatech.edu Abstract Case-based reasoning (CBR) has a great deal to offer in supporting creative design, particularly processes that rely heavily on previous design ex- perience, such as framing the problem and evalu- ating design alternatives. However, most existing CBR systems are not living up to their potential. They tend to adapt and reuse old solutions in routine ways, producing robust but uninspired results. Little research effort has been directed towards the kinds of situation assessment, eval- uation, and assimilation processes that facilitate the exploration of ideas and the elaboration and redefinition of problems that are crucial to cre- ative design. Also, their typically rigid control structures do not facilitate the kinds of strate- gic control and opportunism inherent in creative reasoning. In this paper, we describe the types of behavior we would like case-based design systems to support, based on a study of designers working on a mechanical engineering problem. We show how the standard CBR framework should be ex- tended and we describe an architecture we are developing to experiment with these ideas.’ Introduction Creativity in design derives from enumerating sev- eral solution alternatives, redescribing and elaborating problem specifications, and evaluating proposed solu- tions, based on criteria and constraints that go be- yond the stated constraints on a solution. It arises out of a confluence of processes (including problem redescription, remembering, assimilation, and evalua- tion), which interact with each other in complex ways. Often creativity arises from interesting strategic con- trol of these processes, which in themselves may be quite mundane (Boden 1990, Chandrasekaran 1990, Gero & Maher 1993, Navinchandra 1992). These processes rely heavily on previous design ex- periences and knowledge of designed artifacts (Goel & Chandrasekaran 1992, Hinrichs 1992, Kolodner & Pen- berthy 1990, Kolodner & Wills 1993). An expert de- ‘This research was funded in part by NSF Grant No. IRI-8921256 and ONR Grant No. N00014-92-J-1234. signer knows of many design experiences, accumulated from personally designing artifacts, being given case studies of designs in school, and observing artifacts designed by others. The designer draws on these expe- riences to perform such activities as generating design alternatives, reformulating and elaborating the prob- lem specification or proposed solutions, and predicting the outcome of making certain design decisions. The experiences that are most valuable are often those that are highly contextualized pieces of knowledge about ar- tifacts, such as how a device behaves in some context of use, circumstances in which it can fail, and knowl- edge about situations that might come up not only in use, but in all phases of its life cycle. Given the nature of these experiences, we believe case-based representations and reasoning techniques lend themselves to supporting creative design. Re- search in case-based reasoning (CBR) has provided ex- tensive knowledge of how to reuse solutions to old prob- lems in new situations, how to build and search case libraries (for exploration of design alternatives), and how to merge and adapt cases. It has developed pow- erful techniques for partial matching and the formation of analogical maps between seemingly disparate situa- tions (Kolodner 1993). However, most existing CBR systems are not living up to their potential. They tend to adapt and reuse old solutions in routine ways, producing robust but uninspired results. They do not attempt to extend their exploration by deriving constraints and prefer- ences that improve or go beyond those stated in the original problem. (See (Kolodner 1993, appendix) for a recent survey.) Some of this potential is buried in processes that have been downplayed or even missing in most stan- dard CBR systems. In particular, little research effort has been directed towards the kinds of situation as- sessment , evaluation, and assimilation processes that facilitate the exploration of ideas and the elaboration and redefinition of problems that are crucial to cre- ative design. Also, to facilitate the kinds of oppor- tunism inherent in creative reasoning, CBR systems need to break out of their typically rigid control struc- 50 The Arts From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. ture to allow flexible interleaving and communication among processes. In addition, more research attention must be payed to the strategic control mechanisms that guide a creative designer in deciding what to do next. In this paper, we describe the types of behavior we would like case-based design systems to support, based on an exploratory study of designers working on a me- chanical engineering problem. We show how the stan- dard CBR framework should be extended and we de- scribe an architecture we are developing to experiment with these ideas. We end with a set of open issues. To gain insights into the knowledge and reasoning in- volved in creative design, we observed a four-person team engaged in a seven-week undergraduate mechan- ical engineering (ME) design project. The task was to design and build a device to quickly and safely trans- port several eggs from one location to another. The device could be constructed from any material, but its size, weight, and cost were restricted. After exploring several schemes for launching, mov- ing, stopping, and protecting the eggs, the team de- cided to use a cylindrical egg carrier (of radius 7 cm., length 22.5 cm.), with the eggs wrapped in pipe insu- lation to protect them inside the carrier. The carrier was dropped down (0.8 m.) from a starting platform and would roll into a target zone (within a 5 m. radius of the starting platform). The team had two possible launch mechanisms up until the final design demon- stration day: a spring mechanism and a simple ramp (the spring 1 aunch base could be inverted to become a ramp, which was the final choice). In both cases, a string, with one end attached to the launch base, was wrapped around the device, so that as the cylinder dropped, it spun down the string, hit the ground, and rolled into the target zone. The wrapped string gave the carrier momentum and it also prevented it from rolling beyond the target zone. One of us participated as a member of the team, allowing us to become immersed in the issues and to observe the design process in a natural setting, in both informal and “official” team meetings. We recorded the group’s conversations on audiotapes and collected copies of all their design documents and drawings. We are particularly intrigued by a set of three pro- cesses we observed underlying many creative design ac- tivities: 1) generation of multiple descriptions or views of a problem, 2) gradual emergence of evaluative is- sues, constraints and preferences, and 3) serendipitous recognition of solutions to pending problems, some- times seeing new functions and purposes for common design pieces in the process. We are not claiming that this is a complete set. (For example, our design study has revealed a variety of influences on creativity from collaborative activity.) Rather, we are interested in these processes because they are key processes in de- sign that current case-based systems neglect. Problem Redescription. The initial problem statement given to our designers was ambiguous, in- complete, contradictory, and underconstrained. They spent a great deal of effort to turn it into something with more detail, more concrete specifications, and more clearly defined and consistent constraints. An important part of this process involved attempting to understand the problem, view it from multiple per- spectives, and redescribe it in terms familiar to the de- signers. They had to refine and operationalize several vague or abstract constraints, while sometimes having to abstract constraints that were too specific. For example, many of the ideas of one designer, who had a keen interest in automobiles, came from recall- ing devices and concepts from the car domain, such as shock absorbers, unit-body vs. single-frame construc- tion, and air-bags. Being able to recall these required viewing the problem of protecting the eggs as one of absorbing shock or transferring energy and as a prob- lem of protecting passengers in general, not just eggs. Our designers also explored the given constraints, deliberately stretching or strengthening them to see what ideas became possible. For example, the initial problem statement was ambiguous about whether or not the device could land (i.e., touch down) short of the target zone and then move into it. The design- ers considered the extreme possibility of landing as far short of this zone as possible, in which case the device would not fly at all, but would be pushed off or low- ered to the ground, where it would then move itself into the safety zone. Visualizing this possibility re- minded them of devices, such as elevators and yo-yo’s, that could implement parts of this behavior. This continual elaboration and redescription of the problem helped the designers derive connections be- tween the current problem and similar problems in other domains, facilitating cross-contextual transfer of design ideas. It also primed them to serendipi- tously recognize relevant objects in the environment that might be reused for a new purpose. E-ah&ion. One of the key forces driving evolution of the problem specification is the evaluation of pro- posed design alternatives. Evaluative issues emerge in the course of evaluating. Designers do not merely de- pend on constraints that have already been specified. Rather, they bring up additional constraints and cri- teria as proposals are examined. Proposed solutions often remind them of issues to consider. The problem and solution “co-evolve” (Fischer 1993). One interesting criteria that emerged in the course of the ME design project was versatility - the ability of the device to apply in more than one situation. This criteria was not mentioned or required in the original statement of the problem. It arose in response to ambi- guity in the initial problem statement, which described three similar problems but did not specify which one would be assigned. Each problem differed only in the device’s starting position (from either the center of a Case-Based Reasoning 51 child’s wading pool or from a platform of one of two heights) and in its target destination distance. (This is similar in the real world to situations in which the en- gineers are designing for multiple potential customers with different needs). To deal with the uncertainty and reduce the complexity this variability introduced, the designers began searching for solutions that could be used to solve all three problems or could be easily adapted to apply to each. That is, they began to eval- uate proposals on the basis of versatility in addition to the other criteria already in the problem specification. Being able to do this is central to creative design. Assimilation. Problem redescription provides not only a means for recalling relevant solution alterna- tives, but also a vocabulary for describing and, in many cases, reinterpreting objects in the designer’s environ- ment. This often leads to a new way of viewing the function of some object and facilitates the recognition of potential solutions to pending problems in the ex- ternal environment. For example, our designers went to a home improve- ment store for materials for a spring launch mecha- nism. While comparing the strengths of several springs by compressing them, they noticed that the springs tended to bend. One designer wrapped a hand around the spring to hold it straight as it was compressed and said the springs would each need to be enclosed in a tube to keep them from bending. Another added that the tube would need to be collapsible (to compress with the spring). The designers could not think of an ex- isting collapsible tube and did not want to build one due to time pressure. They gave up on the springs and started thinking about egg protection. During their search for protection material, they walked through the bathroom section of the store, where they saw a display of toilet paper holders. They immediately rec- ognized them as collapsible tubes which could be used to support the springs. By playing with the springs, noticing problems and suggesting fixes, the designers formed a specific, con- crete, and operationalized description of what a solu- tion would look like to the bending-springs problem. However, the toilet-paper holder was not recalled on the basis of this description. Instead, the description was used to reinterpret the toilet paper holder when it was encountered in the external environment and to recognize its additional function of preventing springs from bending upon compression. The designers were able to interpret objects seen in the environment, or recalled from memory, from a new viewpoint. This viewpoint was based on descriptions and feature di- mensions that had been revealed to be important in attempts to solve recent and pending problems. We refer to this process as assimilating the objects into a problem context. It not only involves reinter- preting solution alternatives under consideration, but also comparing and contrasting alternatives with one another, along the dimensions relevant to the problem context. This helps reveal those that are not really new ideas, so that they can be ignored. It can also cause new evaluative issues to emerge as new dimen- sions or criteria are generated to distinguish seemingly identical ideas. Strategic Control. The designers we observed did not follow a rigid, methodical plan detailing what to do next. Rather, they moved fluidly between various problem pieces and design processes (e.g., idea genera- tion, adaptation, critiquing, problem refinement, elab- oration, and redefinition) in a flexible and highly op- portunistic manner. Our designers employed a variety of strategic control heuristics, some of which are opportunistic. For exam- ple, when an alternative was proposed that satisfied some desired criteria extremely well compared to the other alternatives, they directed their efforts toward elaborating that alternative, optimistically suspending criticism or discounting the importance of criteria or constraints that were not satisfied as well. Sometimes this led to reformulation of the problem as constraints were relaxed or placed at a lower priority. Being able to take advantage of such opportunities requires being able to judge whether progress was be- ing made along a certain line of attack and to choose which ideas are more promising or more likely to lead to something unusual and novel. Some strategic control heuristics are more deliber- ate, based on reflection. For example, one heuristic our designers used was to try quick, easy adaptations of a proposed solution first before stepping back and refor- mulating the problem or relaxing constraints. Other deliberate heuristics attempted to make non-standard substitutions, apply adaptation strategies in circum- stances other than the ones they were meant for, and merge pieces of separate solutions with each other in nonobvious ways. In many cases, the processes that are composed to- gether leading to a novel idea are not in themselves novel and may be quite mundane. The trick is know- ing when to do them. ow CBR Systems Can etter Most current CBR systems tend to stick to well-known interpretations of problems and routine ways of adapt- ing old solutions, neglecting exploration of alternatives if something good enough has been found. We believe the CBR paradigm can be extended to support more creative problem solving. Problem Redescription. Problem redescription corresponds closely to the process of situation assess- ment - redescribing a problem in the vocabulary of the indexing system. In most CBR systems, situation as- sessment is skipped; the assumption is made that the initial representation of the problem is sufficient for solving the problem. But, as our observations show, in- vestigating a problem in depth makes available a large 52 The Arts set of relevant cues for retrieval. Generating multiple ways of describing a problem provides several differ- ent contexts for specifying what would be relevant, if remembered. Research on indexing has found that it is the combi- nation of setting up a context for retrieval and having already interpreted something in memory in a similar way that allows retrieval. When some case or piece of knowledge is entered into memory, it is not always possible to anticipate how it might be used. Situation assessment processes aim to bridge that gap by helping to redescribe a new problem in a way that is similar to something seen before. Research into situation assessment and problem re- formulation (e.g., in CASEY (Koton 1988), CYRUS (Kolodner 1983), MINSTREL (Turner 1994), BRAIN- STORMER (Jones 1992), and STRATA (Lowry 1987)), show different ways it can be done. However, these techniques have not yet made it into widespread use in practical CBR systems. They should certainly be included in any system aimed at reuse of experience across domains. Evaluation. CBR systems currently evaluate solu- tions by checking a set of constraints that have been given to the system. Evaluative procedures are typ- ically buried within case manipulation to predict or test whether a modified case satisfies the specified constraints. Ob servations of our designers suggests that evaluation should play a more prominent role in case-based design systems, allowing evaluative issues to emerge in the course of evaluating. Navinchandra (1991) calls this critetica emergence and shows an ex- ample of how it can arise from case-based projection. In addition to criteria, constraints in general (Prab- hakar & Goel 1992) and relative priorities among them also gradually emerge. This type of evaluation is a key driving force within creative design, feeding back to situation assessment and guiding case manipulation. Assimilation. A key idea underlying dynamic mem- ory (Schank 1982), one of the principle foundations of case-based reasoning, is that remembering, under- standing, and learning are all inextricably intertwined. The ability to determine where something fits in with what we already know (understanding) is a key part of being able to assimilate objects in our environment into our problem solving. This environment includes not only external objects, but also cases that have been retrieved, elaborated and adapted. Understanding how these fit into a problem context may involve a useful reinterpretation of something already in memory, sug- gesting in a new way of indexing it. Strategic Control. Our exploratory study suggests that a linear, sequential composition of CBR processes is much too simple. In reality, these processes are highly intertwined and interact in interesting ways. For example, problem elaboration and redescription tac- tics specify contexts for search that retrieval processes use, while evaluation of recalled or adapted alternatives feeds information back to these situation assessment tactics, resulting in even better contexts for search. In some cases, what suggests a particular problem refine- ment or redescription results from trying to confirm the legality of a proposed solution during evaluation and finding a loophole or ambiguity in the current problem specification. In addition, comparing and contrasting a proposed solution with other proposals during assim- ilation can bring new evaluative issues into focus. CBR systems need to break out of their typically rigid control structure and allow more interaction and opportunism among processes. This requires mak- ing strategic control mechanisms explicit, so they can be easily modified, reasoned about, extended, and learned. More research needs to be directed at identify- ing and capturing the types of strategic control heuris- tics designers use. reposed rchitecture We are developing an experimental case-based system that emphasizes the processes of situation assessment, evaluation, and assimilation, integrating them with the usual CBR processes of retrieval, elaboration (case manipulation, adaptation, merging, prediction), and learning. It has a flexible, opportunistic control struc- ture which allows us to keep control tactics separate, explicit, and modifiable. The processes within our system are not applied in a strictly linear succession. Rather, the system has a blackboard-style architecture. The processes are cen- tered around and act upon data structures that repre- sent the evolving problem specification and the set of design alternatives under consideration. Situation assessment procedures act on the prob- lem specification to evolve it along multiple direc- tions. Evaluation examines design alternatives, check- ing them against the current specification, to reveal in- consistencies, ambiguities, and incompletenesses in the specification that suggest new redescriptions. Evalua- tion also brings up new criteria, and constraints which are incorporated into the problem specification. Elaboration procedures transform alternatives under consideration into new alternatives by applying a vari- ety of adaptation and merging strategies. These strate- gies are typically suggested by the critique formed by an evaluation of some alternative. Elaboration proce- dures also augment alternatives with information de- rived about their consequences and expected behavior. These “data collection” elaborations are currently ac- complished by manual augmentations of alternatives with experimental data, but in general can be achieved by case-based projection, simulation, actual experi- mentation, or visualization. The evolving problem description is also used by both the retrieval and the assimilation processes. Re- trieval interfaces with a library of cases which models, Case-Based Reasoning 53 in part, long-term memory. The problem description is used as a probe into memory to pull relevant design cases into consideration (for evaluation, elaboration, etc.). The assimilation process is the dual of retrieval. It accumulates design alternatives proposed (i.e., those retrieved, elaborated, or viewed directly in the exter- nal environment) into the pool of design alternatives under consideration, organizing the alternatives with respect to each other. The data structure holding the set of design alterna- tives forms an extension of the long-term memory. We call this extension the “problem context.” The evolv- ing problem description determines the focal vocabu- lary of the current problem context. As the specifica- tion evolves, the focus changes on the relevant vocabu- lary to be used for organizing alternatives in the mem- ory (e.g., shape, construction cost, personal safety). In a sense, the problem context is providing a point of view with respect to which objects in the environment and cases recalled can be interpreted and organized by the assimilation process. The coordination of the various processes is con- trolled by explicit strategic control mechanisms. There are a set of monitoring procedures, associated with each of the processes, which watch for opportunities for some task to be. performed. The opportunities noticed are placed on an “opportunity agenda.” Opportuni- ties are chosen and pulled from the agenda by strategic control heuristics. For example, a monitor associated with the assimilation process watches for an alterna- tive to be added that is much better than any other alternative proposed so far, with respect to some de- sired criterion. This yields an opportunity to change the problem description by increasing the priority of that criterion and/or by relaxing constraints that are not met by that proposal. This simulates the behav- ior of changing the relative importance among criteria to accommodate an unexpectedly good solution that is stumbled upon. An example strategic control heuristic would be to pursue elaboration opportunities for alter- natives that satisfy a desired criteria extremely well before pursuing evaluative processes that would nega- tively critique the alternatives. This simulates the be- havior of optimistically pursuing an idea, suspending all but constructive criticism. Status, Limitations and Open Issues Our system currently has implemented procedures for evaluation, assimilation, and retrieval, as well as data structures representing the case library, pool of design alternatives, evolving problem specification, and the opportunity agenda data structure. We have standard agenda management routines. However, these routines currently do not model the ephemeral nature of op- portunities (which can either expire or be forgotten). Several monitors surrounding the assimilation process have been implemented, but we still need to define and capture those relevant to the other processes. Much more work is needed to identify and define strategic control heuristics, situation assessment proce- dures, and elaboration techniques. Also, not all strate- gic control mechanisms are triggered by noticing an op- portunity. Some may become applicable due to some complex condition that must be inferred through re- flection. (For example, realizing that you are reason- ing in circles might cause you to make an effort to try a brand new technique.) More research needs to focus on how to represent and infer these kinds of conditions and also how the application of these more reflective strategic control mechanisms can be interleaved with the triggering of opportunistic ones. We are starting to understand how criteria, con- straints, preferences, etc., emerge during evaluation, but more effort is needed in modeling this emergence. There are a number of interesting open issues con- cerning how assimilation is managed when the design problem is complex, having several interacting sub- problems, each of which have different sets of alter- natives and requirements. Assimilation must find the appropriate problem context for interpreting and eval- uating a given design alternative. The ability to do this facilitates the serendipitous recognition of solutions to pending problems, as we saw in the bending-springs problem. (See also (Seifert et al. 1994) .) Another open issue is that the designers we studied were not expert mechanical engineers. An interesting empirical question is: would experts, having knowledge of “design principles,” behave differently? It may not be the expert vs. novice distinction, but how open- ended the problem is, that is important. After all, the students were familiar with and experienced in solving everyday mechanical problems using objects in their world. We believe that for open-ended, nonroutine problems, expert designers are likely to display the same sorts of behaviors as do our students. Finally, there are some aspects of creative design that we have not yet explored. In particular, we would like to analyze more carefully the influences collabo- ration had on creativity in the design project. Our agenda-based model of opportunity management lends itself to simulating the exploration of several oppor- tunities in parallel, and employing multiple control strategies at once. This will allow us to simulate these aspects of collaborative activity and use computational experiments to explore hypotheses about the role of collaboration in creative design. Conclusion Our intention in building our system is not to auto- mate design, but to test our hypotheses about the cog- nition of creative design. We are trying to understand creative processes better, using a case-based cognitive model. As we increase our understanding (and in the process, push CBR technology), we will be able to an- swer the question how best to assist human designers. This may include 1) aiding the formalization, reformu- 54 The Arts lation, and refinement of specifications (Reubenstein & Waters 1991, Johnson, Benner, & Harris 1993), 2) bringing up evaluative issues (Domeshek & Kolodner 1993), 3) retrieving pending problem contexts to help recognize the applicability of solutions, or 4) proposing new control strategies. We are taking a case-based approach to understand- ing creative design for two reasons. One is that many creative design activities are highly memory-intensive and rely on past design experiences, so case-based rea soning has much to offer in this study. The other is that we hope to make case-based systems themselves more creative. By using the paradigmatic tools CBR provides, we are starting to find computational mod- els of the behaviors and processes we observed in our exploratory study. At the same time, our modeling at- tempts have deepened our understanding of case-based processes and memory issues and have suggested ex- tensions that will yield more creative design systems in the future. Acknowledgements We appreciate the insightful discussions we have had with Terry Chandler, Eric Domeshek, Lucy Gibson, Todd Griffith, Kenneth Moorman, Nancy Nersessian, Ashwin Ram, and Mimi Reeker. We would like to thank Otto Baskin, Jon Howard, and Malisa Sarnti- noranont, for their invaluable cooperation. We also appreciate the insights and helpful comments of our anonymous reviewers. References Boden, M. 1990. The Creative Mind: Myths and Mech- anisms. New York, NY: Basic Books. Chandrasekaran, B. 1990. Design Problem Solving: A Task Analysis. AI Magazine. ll(4): 59-71. Domeshek, E.A., and Kolodner, J.L. 1993. Using the points of large cases, Artifkial Intelligence for Engi- neering Design, Analysis and Manufacturing 7(2): 87- 96. Fischer, G. 1993. Turning Breakdowns into Oppor- tunities for Creativity. In Proceedings of the In- ternational Symposium on Creativity and Cognition, Loughborough, England. Gero, J. and Maher, M. 1993. Modeling Creativity and Knowledge-Based Creative Design. Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers. Goel, A. and Chandrasekaran, B. 1992. Case-based Design: A Task Analysis. In C. Tong and D. Sriram (eds.), Artifkial Intelligence Approaches to Engineer- ing Design, Volume 2: Innovative Design. San Diego, CA: Academic Press. Hinrichs, T. 1992. Problem Solving in Open Worlds: A Case Study in Design. Northvale, NJ: Erlbaum. Johnson, W.L., Benner, K.M., and Harris, D.R. 1993. Developing Formal Specifications From Informal Re- quirements. IEEE Expert 8(4): 82-90. Jones, E.K. 1992. The Flexible Use of Abstract Knowl- edge in Planning. Northwestern University, Institute for the Learning Sciences Technical Report no. 28. Kolodner, J.L. 1993. Case-Based Reasoning. San Ma- teo, CA: Morgan-Kaufman Publishers, Inc. Kolodner, J. 1983. Reconstructive Memory: A Com- puter Model. Cognitive Science 7(4): 281-328. Kolodner, J.L. and Penberthy, T.L. 1990. A Case- Based Approach to Creativity in Problem Solving. In Proceedings of the Twelfth Annual Conference of the Cognitive Science Society, Cambridge, MA. Kolodner, J.L. and Wills, L.M. 1993. Case-Based Cre- ative Design. In AAAI Spring Symposium on AI and Creativity. Stanford, CA. Reprinted in ALS’B Quar- terly 85: 50-57. Koton, P. 1988. Reasoning about evidence in causal explanation. In Proceedings of the 6th National Con- ference on Artificial Intelligence. Cambridge, MA: AAAI Press/MIT Press. Lowry, M. 1987. The Abstraction/Implementation Model of Problem Reformulation. In Proceedings of the 10th International Joint Conference on Artificial Intelligence, pp. 10041010. Milan, Italy. Navinchandra, D. 1991. Exploration and Innovation in Design: Towards a Computational Model. New York: Springer-Verlag. Navinchandra, D. 1992. Innovative Design Systems: Where are we, and where do we go from here?. Parts I and II. The Knowledge Engineering Review 7(3): 183- 213 and 7(4): 345-362. Prabhakar, S. and Goel, A. 1992. Performance-Driven Creativity in Design: Constraint Discovery, Model Re- vision, and Case Composition. In Proceedings of the Second International Conference on Computational Models of Creative Design. Heron Island, Australia. Reubenstein, H.B. and Waters, R.C. 1991. The Re- quirements Apprentice: Automated Assistance for Re- quirements Aquisition. IEEE Transactions on Soft- ware Engineering 17(3): 226-240. Schank, R. 1982. Dynamic Memory: A Theory of Learning in Computers and People. New York: Cam- bridge University Press. Seifert, C., Meyer, D., Davidson, N., Patalano, A., and Yaniv, I. 1994. Demystification of Cognitive In- sight: Opportunistic Assimilation and the Prepared- Mind Perspective. In R.J. Sternberg and J.E. David- son (eds.), The Nature of Insight. Cambridge, MA: MIT Press. Forthcoming. Turner, S.R. 1994. MINSTREL, Lawrence-Erlbaum Associates, Inc. Forthcoming. Case-Based Reasoning 55 | 1994 | 290 |
1,642 | Retrieving Semantically Distant Analogies with Knowledge-Directed Spreading Activation* Michael Wolverton and Barbara Hayes-Roth Knowledge Systems Laboratory, Stanford University 701 Welch Rd, Bldg. C Palo Alto, CA 94304 {mjwlbhr}@hpp.stanford.edu Abstract Techniques that traditionally have been useful for re- trieving same-domain analogies from small single-use knowledge bases, such as spreading activation and in- dexing on selected features, are inadequate for retriev- ing cross-domain analogies from large multi-use knowl- edge bases. In this paper, we describe Knowledge- Directed Spreading Activation (KDSA), a new method for retrieving analogies in a large semantic network. KDSA uses task-specific knowledge to guide a spread- ing activation search to a case or concept in memory that meets a desired similarity condition. Specifically, KDSA exploits evaluations of near-analogies encoun- tered during the search to direct the search toward progressively more promising analogies. We describe a specific instantiation of this method for the task of innovative design, and we summarize the theoretical and experimental results used to validate KDSA. Introduction Cross-domain analogy is a commonly-used reasoning device, especially among individuals who must exhibit a high level of creativity in their reasoning. Authors, journalists, and political speechwriters often use sur- prising metaphors in order to enliven their prose; clever teachers use analogies to familiar concepts outside of the domain of discussion to explain unfamiliar con- cepts; and engineers and inventors often use analogies in order to help them produce a novel design. The concern of this paper is the retrieval and use of cross- domain analogies, specifically those in which the two analogues are semantically distant from one another- that is, they are very different from one another in all but a few key features. The literature on invention is full of examples of inventions that were guided by semantically distant analogies. Gutenberg invented the printing press af- ter noticing the connection between applying force to impress script on paper and applying force to squeeze *This research was supported by NASA Grant NAG2- 581, by Texas Instruments Contract 7554900, and by Mc- Donnell Douglas Contract SO7705. Thanks to Rich Wash- ington and the anonymous AAAI reviewers for helpful comments. grapes in a wine press (Koestler 1965) . Edison’s inven- tion of the quadruplex telegraph was based almost en- tirely on an analogy to a water system of pumps, pipes, valves, and water wheels (Hughes 1971). And actress Hedy Lamarr conceived of a method for coordinating frequencies between sender and receiver in frequency- hopping communication by analogy to a player-piano roll (Simon et al. 1985). These examples all show the inventor making a connection between two concepts not normally thought of as connected. The fact that human inventors use semantically distant analogies in their reasoning suggests that these analogies can be an important technique for computer reasoning as well. From looking at examples of analogies in invention, we can surmise two characteristics of semantically dis- tant analogies that present special problems for the development of a computational model: (1) The domains from which the analogies are drawn are unpredictable. The concepts used to guide novel designs come from a wide range of domains, and it is impossible to predict, given the target design domain, which base domain(s) may prove fruitful for drawing useful analogies. (2) In the analogies that are made, differences between the analogous concepts are as important as similar- ities. An inventor’s chances of developing a truly novel design by analogy are greatly increased by us- ing a base concept that is unusual or unexpected. This suggests that the base concept used should be as different as possible from the target concept while still being useful for design. That is, the two con- cepts should share only those features that are nec- essary to the function of the invention, and should mismatch on as many extraneous features as possi- ble. In particular, analogies with a high degree of surface similarity seem unlikely to be useful in pro- ducing novel inventions. These two characteristics provide reasons that exist- ing approaches to analogy retrieval are inappropriate for retrieving semantically distant analogies. Most ex- isting approaches to analogy retrieval are based either on task-specific indexing of concepts in a case library or on spreading activation in a semantic network, but 56 The Arts From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. neither of these general approaches is well-suited for finding semantically distant analogies. The indexing approach is inappropriate because characteristic (1) above suggests that a successful “case library” for se- mantically distant analogies would in fact be a large multi-domain multi-use knowledge base, but most suc- cessful indices in case-based reasoning are task-specific. To create a new set of indices for each possible task that may be performed in such a KB (and each pos- sible analogical use of a given concept) would require a prohibitive number of organizational links or con- structs. The spreading activation approach is inappro- priate because characteristic (2) above suggests that most corresponding features involved in the analogues will be far from each other in the semantic network, and an uncontrolled spread of activation throughout the large semantic net will bog down in combinatorial explosion before reaching the semantically distant base concepts it seeks. This paper introduces a method, called hnowledge- directed spreading activation (KDSA), for retrieving semantically distant analogous concepts from a large diverse knowledge base. This method is based on con- trolled search in a general semantic network. It uses task-specific knowledge to guide a series of spreading activation searches from the target concept to a seman- tically distant base concept. This knowledge is applied in the evaluation of intermediate concepts retrieved by a standard spread of activation, and by the modifi- cation of weights controlling the spread of activation based on those evaluations. The next section describes this method in more detail. The Approach-KDSA Viewed abstractly, KDSA is an application of general techniques from state-space search (evaluation func- tions, subgoaling, etc.) to knowledge base search. KDSA finds analogues by a series of heuristically- guided spreading activation searches. Each time spreading activation retrieves a concept from the knowledge base, the concept is evaluated as an ana- logue, and that evaluation is used to direct the next spreading activation search in more promising direc- tions. KDSA uses promising concepts retrieved dur- ing these spreading activation searches as “beacons”, guiding the search successively closer to a semantically distant base. This description of KDSA will assume that all world knowledge is represented in a single semantic net- work. Within that semantic network, small subgraphs of nodes and links which represent aggregate concepts are explicitly grouped together as conceptual graphs (Sowa 1984). Individual conceptual graphs are treated the same as primitive nodes-i.e., they can be associ- ated with other nodes via links, and they can them- selves be parts of larger conceptual graphs. In the discussion below, conceptual graphs will be referred to merely as “concepts”. 1. 2. 3. 4. 5. 6. Assign activation to all nodes in the target. Spread activation in semantic network until a new inter- mediate concept (IC) is retrieved. (GRAPH MATCHER) Find the best mapping between target and IC based only on maximizing isomorphism and minimizing semantic distance between nodes. (MATCH EVALUATION) Evaluate the mapping ac- cording to domain-specific similarity metric. If evalu- ation meets the metric, return IC as base and exit. (SEARCH CONTROL) Based on evaluation, alter the state of the semantic network to guide the next phase of spreading activation in a more promising direction. Go to 2. Figure 1: Knowledge-Directed Spreading Activation The basic algorithm of KDSA is shown in Figure 1. The low-level search of memory (step 2 in the figure) is conducted by a spreading activation mechanism (see, e.g., (Anderson 1983)). In this formalism, activation is passed from node to adjacent node via the links that connect them until one concept accumulates enough aggregate activation to be considered retrieved. This basic spreading activation model is a blind knowledge search mechanism. Some method of controlling the search is necessary for the system to retrieve the types of semantically distant base concepts described in the introduction. KDSA uses feedback from the analogues retrieved so far to focus the search. The agent architecture encompassing KDSA begins the retrieval process when some executing task re- quests an analogy and designates a target concept. This initial request causes some nodes in the semantic network-those representing the target concept plus possibly others representing desired features of the so- lution, etc. -to be assigned activation, and this as- signment begins the spread of activation in memory. When a concept is retrieved by the spread of activa- tion, the graph matcher computes a mapping between it and the target concept. The match evaluation com- ponent then forms an evaluation of the mapping based on a task-specific similarity metric. This evaluation is passed on to the search control component, which uses its task-specific heuristics to focus the spreading activation search in directions that are more likely to lead to highly-evaluated analogies for the current task. The process repeats until an analogue that meets the matching component’s similarity metric is retrieved. For simplicity, KDSA has been described so far as a strictly serial algorithm. In fact, it is designed (and implemented) as a collection of independent knowledge sources that execute within a larger intelligent agent architecture’, and that interact with the agent’s other ‘In the computer implementation of KDSA, the agent architecture used was BBl (Hayes-Roth 1990). Case-Based Reasoning 57 Search Control Figure 2: Integration of KDSA into problem-solving architecture activities. Figure 2 shows this interaction. At any time during the cycle of Figure 1, other concepts may be activated by the agent’s other activities, such as or- dinary problem solving or processing sensory input. In this way KDSA can account for an individual possibly “stumbling across a solution”, i.e., being reminded of an analogue by external or internal cues. The important components of the retrieval system are discussed in more detail below. Match Evaluation Each time a concept is retrieved by the spreading activation search as a potential base concept, it is passed to the matching component. The matching component first forms the best possible par- tial mapping between the potential base and the tar- get, and then it evaluates that partial mapping using heuristics that are specific to the task for which the analogy will be used. These heuristics will base their evaluation on three features of the partial mapping: (1) semantic distance between corresponding nodes in the mapping, i.e., the minimum path distance in the type hierarchy between corresponding nodes of the mapping (2) isomorphism between the graphs, i.e., how many nodes and links match between the target and poten- tial base, and (3) the portion of the representation of the target concept matched, and the relevance of that portion to the goal. The evaluation consists of a nu- meric rating of the mapping, and a description of the shortcoming(s) of the mapping assigned by the heuris- tics. If the numeric rating is greater than a threshold value, the potential base is accepted as the final anal- ogy, and the KDSA process halts. Otherwise, the eval- uation is passed on to the search control component. Search Control The search control component uses evaluations from the match evaluation component and other information about the state of the search to in- fluence the direction of the spread of activation. It uses heuristics to control the direction of the search in two ways: (1) it can change activation of concepts in the semantic net, particularly the target concept and the retrieved intermediate concept, and (2) it can modify the condition under which spreading activation will re- trieve new intermediate concepts. The first of these, changing activation of selected concepts in the KB, is the more important of the two methods of search control. This method includes strengthening the acti- vation of promising intermediate concepts (those that nearly pass the mapping component’s similarity met- ric for being a good final analogy), weakening the ac- tivation of unpromising concepts, changing activation of portions of the intermediate concept or the target based on evaluations, and clearing the activation of all nodes in the semantic network (to start the search over from a new state). A simple use of KDSA’s search control would have it clearing all activation in the semantic network each time a promising concept is encountered, and then restarting the search by making the promising con- cept a source of activation. In this way KDSA can use these promising concepts as beacons along the way to the final good analogy. This is very similar to the way that promising intermediate states are used in heuris- tic search techniques such as hill-climbing or best-first search (Pearl & Korf 1987). The use of the matching component of the mecha- nism to provide feedback to the spreading activation search provides a key distinguishing feature of our ap- proach. Most previous approaches to analogy serialize the retrieval and mapping processes: first they retrieve a concept, then they try to map it, then if mapping fails they start at ground zero with retrieval again. By con- trast, mapping in KDSA is an integral part of retrieval: mapping (the matching component) provides ongoing information to the retrieval mechanism (spreading ac- tivation and search control) throughout the duration of the retrieval process. KDSA Applied to Innovative Design This section describes the particular heuristics used in the implementation of KDSA, called IDA (for Inno- vative Design by Analogy), to find analogies that are useful for guiding an innovative redesign of the target. IDA operates in a knowledge base of devices, natural or man-madesystems that perform some function. The knowledge base may contain definitions of other con- cepts as well, but IDA requires that each device be rep- resented by its structure, behavior, and function. Rep- resentations of structure consist of the device’s parts along with different types of connections among those parts. Representations of behavior and function con- sist of chains of primitive processes along with the in- dividuals (structural components, substances, etc.) on which those processes act. IDA takes as input an ex- isting device, and returns as output an abstract re- 58 The Arts design of that device which satisfies the device’s top- level functional requirements, but does so in a different way. This redesign consists of a replacement of one of the target device’s top-level behaviors with a behavior from the base device. E.g., a behavior like SPRAY- ING from the representation of the sprinkler irrigation system may be replaced with DIFFUSION from the circulatory system. The particular heuristics used in IDA’s mapping component attempt to find analogues that satisfy two general requirements: ) The base and target devices must have similar functions, but different behaviors and structures. (2) The base must be adaptable with regard to the target device. That is, IDA must be able to analogi- cally adapt the retrieved base into a new device that satisfies the same function as the target device. The purpose of the first requirement is to find an analogue which will lead to a redesign which is useful (“similar function”) and at the same time novel (“dif- ferent behavior and structure”). The purpose of the second requirement is to ensure that IDA will actually be able to produce a redesign based on the retrieved base concept, i.e., that the mismatch in behavior with the target is not so great that the two devices have nothing to do with one another. Thus this second re- .quirement’s implementation will depend on the sys- tem’s mechanism for adapting the retrieved base into a final design. To implement these two requirements, IDA’s map- ping component considers separate portions of a de- vice’s representation separately. Each device represen- tation is broken down into structure, behavior, and function. The behavior and function representations are broken down further into (1) a sequence of primi- tive processes that make up the behavior or function, and (2) the individuals on which those processes act. There are separate requirements on the degree of iso- morphism and semantic distance required for each of those portions of the representation. For example, IDA prefers the match between nodes in the structures of the target and base devices to be high in semantic dis- tance (to satisfy the dissimilar structure requirement), and prefers a mismatch on only one primitive process in the behaviors of the target and base devices (to sat- isfy the adaptability requirement). After the mapping component evaluates devices ac- cording to the two requirements, the search control module must focus the spread of activation toward other devices in the KB which meet those require- ments. IDA does this by focusing the search based on the strengths of the retrieved beacons encountered so far in the-search. The mapping component identi- fies an intermediate concept as promising if it comes close to meeting the metric for being a final analogy. For each promising concept, the search control com- ponent then strengthens the activation of its portions that did meet the mapping component’s individual re- quirement. The rest of the activation in the semantic network is wiped out, and the search is restarted from this new state. IDA’s search control rules also use abstractions in the knowledge base as “bridges” to other domains. When IDA retrieves a concept that is in the same domain as the target and is a directly-linked exam- ple of a generic abstraction-a concept that abstractly describes specific concepts from a number of different domains-it strengthens the activation of that abstrac- tion. This will allow activation to be spread into other domains, increasing the likelihood that IDA will find a distant analogy. Example This section presents an example demonstrating the execution of KDSA to retrieve an analogy for creative design. The example shows IDA’s behavior for the goal of redesigning a blinkered railroad crossing, that is, an intersection of road and railroad tracks where a train’s presence on the tracks is indicated only by blinking lights signalling drivers on the road to stop. IDA meets this goal by suggesting redesign by analogy to an on-off valve. Specifically, it suggests replacing the FLASHING behavior in the description of the blink- ered railroad crossing with the BLOCKAGE behavior in the description of the on-off valve. This abstract analogical specification might suggest to a human de- signer a railroad crossing with a gate that blocks traf- fic from crossing the tracks. The retrieval of the on-off valve takes place in the following steps: 1. The nodes contained in the representation of BLINKERED-RR-CROSSING are made sources of activation (i.e., they are tagged with some number), and IDA begins spreading activation. 2. After a few cycles of spreading activation, the device INTERSTATE-HIGHWAY-SYSTEM is re- trieved. This device is mapped to BLINKERED- RR-CROSSING, and the mapping is evaluated. The mapping is found to be unpromising-the structures of the two devices are semantically close, and the be- haviors and functions of the two devices do not cor- respond in any respect. However, IDA notices that INTERSTATE-HIGHWAY-SYSTEM is an instance of a generic abstraction, the FLOW-SYSTEM de- vice. IDA recognizes this abstraction as a possible mechanism for moving the search out of its current domain, and makes FLOW-SYSTEM a source of ac- tivation. All other activation in the semantic net- work (except the target’s) is cleared, and spreading activation starts again. 3. Another of FLOW-SYSTEM’s instances, PLUMB- ING-SYSTEM, is retrieved next, and the map- ping between it and BLINKERED-RR-CROSSING is evaluated. This mapping shows high semantic distance between the structures of the devices, and Case-Based Reasoning 59 poor matches between the behaviors and functions of the devices. IDA wants high semantic distance in structure, so the structural aspect of the mapping is rated high, but the behavioral and functional aspects of the mapping are rated low. Since the structure of the PLUMBING-SYSTEM is the strongest part of the mapping evaluation, the search control com- ponent makes PLUMBING-SYSTEM’s structure a source of activation. Since the behavior and func- tion of the PLUMBING-SYSTEM were rated low, the search control component still bases the search on the behavior and function of the target. So the structure of PLUMBING-SYSTEM and the behav- ior and function of BLINKERED-RR-CROSSING are made sources of activation, and all other acti- vation in the network is cleared. 4. The next concept retrieved is ON-OFF-VALVE. The matching component recognizes that the map- ping between ON-OFF-VALVE and BLINKERED- RR-CROSSING is high in semantic distance be- tween the structures, high in isomorphism between the functions, very low in semantic distance between the top-level process sequences of the functions (they both toggle between PREVENTing and ALLOWing another process), and mismatches in a single pro- cess in the behavior description (the BLINKING of the rr crossing corresponds to the BLOCKAGE of the valve). With these conditions met, ON-OFF- VALVE meets the similarity metric for being a fi- nal analogy for innovative design. It is retrieved, and IDA’s simple design module suggests replac- ing redesigning the BLINKERED-RR-CROSSING by replacing its BLINKING process with ON-OFF- VALVE’s BLOCKAGE process. Results One of the major questions important in the evaluation of KDSA is: will KDSA retrieve analogies without ex- amining a sizable fraction of the entire knowledge base? In order to answer this question, KDSA was evaluated using two complementary methods. The first of these methods is to analyze the behavior of a theoretical model. This model predicts KDSA’s retrieval time given various parameters such as the size of the knowledge base, the semantic distance required for the analogy, the likelihood of encountering a beacon concept in the knowledge base, and the quality of each beacon concept in terms of the benefit it provides in reaching the ultimate base concept. This model allows us to examine the behavior of KDSA under a wide range of problem and knowledge base characteristics. The second method of evaluating KDSA is to ex- amine the behavior of the implementation, IDA. This implementation of KDSA demonstrates that KDSA can, in fact, automatically retrieve semantically dis- tant analogies which are useful in solving a real prob- lem. In addition, while it is presently impossible to test IDA with an actual very large knowledge base, we can measure IDA’s retrieval time as a function of the KB size for various subsets of IDA’s small knowledge base. These experiments allow us to examine KDSA% behavior as the knowledge base grows, and compare that actual behavior to the prediction of the theoreti- cal model. Figure 3 graphs some of the results produced by these two validation methods. It shows time taken to retrieve a semantically distant analogy as the size of the knowledge base grows, both for (a) the actual im- plementation operating in relatively small knowledge bases, and (b) the theoretical model as the knowledge base grows to a size of 1 million nodes. Each graph also shows retrieval time for standard spreading activation (SA) as well. Both methods showed retrieval time for KDSA growing much more slowly than for standard spreading activation as KB size grows. The theoretical model predicts behavior that is roughly logarithmic in the size of the KB. Detailed presentations of the theoretical and ex- perimental results are published in (Wolverton 1994). These results can be summarized with the following four qualitative statements, with the first statement being verified by both the theoretical model and ex- periments, and the remainder being predicted by the theoretical model: (1) As the knowledge base size grows, retrieval time with KDSA grows much more slowly than does re- trieval time with standard SA. (2) For analogies in which the target and the base are semantically distant, KDSA is far more efficient than standard SA. (3) KDSA is robust over different distributions and utilities of beacon concepts in the knowledge base. Even when the benefit of each beacon search is low relative to the effort involved, KDSA still shows sig- nificant savings over standard SA. (4) KDSA is robust in the face of bad beacons. When a KDSA search suffers from beacons that direct the search away from, rather than toward, the even- tual base, KDSA still shows substantial savings over standard SA. Related Work There is a large body of AI literature on information re- trieval in semantic networks. SCISOR (Rau 1987) and GRANT (Cohen & Kjeldsen 1987) both use heuris- tic information to direct a spread of activation in se- mantic networks. KDSA’s search control component is similar to the relatedness condition which controls the spread of markers in SCISOR and the path endorse- ments which direct spreading activation in GRANT. KDSA differs from these systems, however, in that it uses information from previous match evaluations to dynamically adjust the direction of the spread of ac- tivation. KDSA in effect runs a series of SCISOR- like or GRANT-like searches, starting each sub-search 60 The Arts zco’ ’ - * * ’ ’ ’ ’ B ’ 550 a0 650 700 m 800 850 900 950 mm 1050 #Node9 (4 04 Figure 3: Retrieval time for KDSA and standard SA as KB size grows, (a) as observed in the computer implemen- tation IDA in a small knowledge base, (b) as predicted by the theoretical model in a large knowledge base from the near-misses it has encountered in previous sub-searches, and using the evaluations of those near- misses to formulate its search control for the next sub- search. Other researchers have used spreading activation in semantic networks to retrieve analogues. Holland et. al.‘s PI (Holland et al. 1986), Anderson’s PUPS (Anderson & Thompson 1989), and Jones’s EUREKA (Jones 1989) are all general cognitive models which use spreading activation for analogue retrieval (as well as other knowledge retrieval). In all of these approaches, the architecture’s ability to control the spread of acti- vation is limited, so they will have difficulty retrieving semantically distant analogies without the help of ex- ternal cues. KDSA is able to use such cues when they are available, but also is able to retrieve semantically distant analogies spontaneously. Conclusion We have presented knowledge-directed spreading acti- vation, a task-independent method for retrieving ana- logues in a multi-domain knowledge base. KDSA over- comes the shortcomings that indexing methods may have in large knowledge bases by applying task-specific knowledge to a general semantic network search tech- nique. And it extends previous models of analogue re- trieval by using evaluations of failed analogies encoun- tered in the earlier stages of the search to influence the direction of the search in later stages. KDSA has been shown to be useful in retrieving analogues for a real task in the computer implementation IDA. And exper- imental and theoretical results provide evidence that KDSA will be tractable in a large knowledge base. References Anderson, J. R., and Thompson, R. 1989. Use of analogy in a production system architecture. In Vos- niadou, S., and Ortony, A., eds., Similarity and Ana- logical Reasoning. Cambridge: Cambridge University Press. 267-297. Anderson, J. R. 1983. The Architecture of Cognition. Harvard University Press. Cohen, P. R., and Kjeldsen, R. 1987. Information retrieval by constrained spreading activation in se- mantic networks. Information Processing and Man- agement 23(4):255-268. Hayes-Roth, B. 1990. Architectural foundations for real-time performance in intelligent agents. Journal of Real- Time Systems 2:99-125. Holland, J. H.; Holyoak, K. J.; Nisbett, R. E.; and Thagard, P. R. 1986. Induction: Processes of In- ference, learning, and Discovery. Cambridge, Mas- sachusetts: MIT Press. Hughes, T. P. 1971. How did the heroic inventors do it? American Heritage of Invention and Technology 1(2):22-23. Jones, R. 1989. Learning to retrieve useful informa- tion for problem solving. In Proceedings of the Sixth International Workshop on Machine Learning, 212- 214. Koestler, A. 1965. The Act of Creation.,Macmillan. Pearl, J., and Korf, R. E. 1987. Search techniques. Annual Review of Computer Science 2~451-467. Rau, L. F. 1987. Knowledge organization and ac- cess in a conceptual information system. Information Processing and Management 23(4):269-283. Simon, M. K.; Omura; Scholtz; and Levitt. 1985. Spread Spectrum Communications, Vol. 1. Computer Science Press. Sowa, J. F. 1984. Conceptual Structures: Information Processing in Mind and Machine. Addison-Wesley. Wolverton, M. 1994. Retrieving Semantically Distant Analogies. Ph.D. Dissertation, Computer Science De- partment, Stanford University. Case-Based Reasoning 61 | 1994 | 291 |
1,643 | The Capacity of Convergence-Zone Episodic Memory Mark Moll Risto Miikkulainen Department of Computer Science Jonathan Abbey Department of Computer Sciences Applied Research Laboratories University of Twent e The University of Texas at Austin P.O. Box 8029 P.O. Box 217, 7500 AE Enschede Austin, TX 78712 USA Austin, TX 78713 USA The Netherlands risto@cs.utexas.edu broccol@arlut.utexas.edu moll@cs.utwente.nl Abstract Human episodic memory provides a seemingly unlimited storage for everyday experiences, and a retrieval system that allows us to access the experiences with partial activation of their com- ponents. This paper presents a neural network model of episodic memory inspired by Dama- sio’s idea of Convergence Zones. The model con- sists of a layer of perceptual feature maps and a binding layer. A perceptual feature pattern is coarse coded in the binding layer, and stored on the weights between layers. A partial activation of the stored features activates the binding pat- tern which in turn reactivates the entire stored pattern. A worst-case analysis shows that with realistic-size layers, the memory capacity of the model is several times larger than the number of units in the model, and could account for the large capacity of human episodic memory. Introduction Human memory system can be divided into semantic memory of facts, rules, and general ,knowledge, and episodic memory that records the individual’s day-to- day experiences Tulving (1972, 1983). Episodic mem- ory is characterized by an extremely high capacity. New memories are formed every few seconds, and many of those persist in the memory for years, even decades (Squire 1987). Another significant characteristic of hu- man memory is content-addressability. Most of the memories can be retrieved simply by activating a par- tial representation of the experience, such as a sound, a smell, or a visual image. Although several artificial neural network models of episodic memory have been proposed (Hopfield 1982; Kanerva 1988; Kortge 1990; Miikkulainen 1992), they fall short of explaining the simultaneous huge capac- ity and content-addressability of human memory. For example in the Hopfield model of N units, N/4 log N patterns can be stored with a 99% probability of cor- rect retrieval when N is large (Hertz, Krogh, & Palmer 1991; Keeler 1988; McEliece et al. 1986). This means that storing and retrieving, for example, lo8 memo- ries would require in the order of lOlo nodes and 1020 68 The Arts connections. Given that the human brain is estimated to have about 1Ol1 neurons and 1015 synapses (Jesse11 1991), this is clearly unrealistic. Despite vast amount of research in human mem- ory, no clear understanding has yet emerged on ex- actly where and how the memory traces are repre- sented in the brain. There is evidence for both lo- calized encoding and for distributed encoding (Squire 1987). Damasio (198913, 1989a) proposed a general framework, based on observations of typical patterns of injury-related memory deficits, that can potentially account for much of the data. The main idea is that the memory system is organized in a hierarchy of as- sociational regions, or convergence zones, with each region serving as a basis for higher-level associations. The hierarchy is grounded in the sensory modality re- gions, and becomes more abstract and general as one moves from the sensory cortical regions to the fore- brain. The low-level and intermediate regions contain object representations, and the high-level regions con- tain representations for complete episodes, in terms of the lower-level entities. This paper presents a new episodic memory model loosely based on the convergence zone idea. The model consists of a number of perceptual maps and a bind- ing layer (a convergence zone). An episodic experi- ence appears as a pattern of local activations across the perceptual maps, and is encoded as a coarse-coded (Rosenfeld & Touretzky 1989; Touretzky & Hinton 1988) pattern in the binding layer. The connections be- tween the maps and the binding layer store the encod- ing so that the complete perceptual pattern can later be regenerated from partial activation. The details of the low-level neural implementation are left open in this paper. The goal is to analyze the behavior of the model at the functional level, and derive general results about its capacity and physical size. A worst-case analysis of the model shows that: (1) with realistic-size maps and binding layer, the capac- ity of the convergence-zone memory is extremely high, exceeding the number of units in the model by a fac- tor of 5; and (2) the majority of the neural hardware is required in the perceptual processing; the binding From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Feature Map 1 Feature Map 2 Feature Map 3 Feature Map 4 Binding Layer Figure 1: Storage. The weights on the connections be- tween the appropriate feature units and the binding repre- sentation of the pattern are set to 1. layer needs to be only a fraction of the size of the per- ceptual maps. Such results suggest how an extremely high capacity could be achieved in the human episodic memory with very little extra hardware beyond the perceptual maps. Storage and Retrieval The model consists of two layers of real-valued units (the feature map layer and the binding layer), and bidirectional binary connections between the layers (figure 1). Perceptual experiences are represented as vectors of feature values, such as color=red, shape=round, size- -small. The values are encoded as units on the feature maps. There is a separate map for each feature domain, and each unit on the map represents a particular value for that feature. For in- stance, on the map for the color feature, the value red could be specified by turning on the unit in the lower- right quarter (figure 1). The feature map units are connected to the binding layer with bidirectional bi- nary connections (i.e. the weight is either 0 or 1). An activation of units in the feature map layer causes a number of units to become active in the binding layer, and vice versa. In effect, the binding layer activation is a compressed, distributed encoding of the value-unit perceptual representation. Initially, all connections are inactive at 0. A percep- tual experience is stored in the memory through the feature map layer in three steps. First, those units that represent the appropriate feature values are activated at 1. Second, a subset of m binding units are ran- domly selected in the binding layer as the compressed encoding for the pattern, and activated at 1. Third, the weights of all the connections between the active units in the feature maps and the active units in the binding layer are set to 1 (figure 1). Note that only one presentation is necessary to store a pattern. To retrieve a pattern, first all binding units are set to 0. The pattern to be retrieved is partially specified in the feature maps by activating a subset of its feature units. For example, in figure 2a the memory is cued with the two leftmost features. The activation propa- gates to the binding layer through all connections that have been turned on so far. The set of binding units that a particular feature unit turns on is called the binding constellation of that unit. All binding units in the binding encoding of the pattern to be retrieved are active at 2 because they belong to the binding con- stellation of both retrieval cue units. A number of other units are also activated at 1, because each cue unit takes part in representing multiple patterns, and therefore has several other active connections as well. Only those units active at 2 are retained; units with less activation are turned off (figure 2b). The activation of the remaining binding units is then propagated back to the feature maps (figure 2~). A number of units are activated at various levels in each feature map, depending on how well their binding con- stellation matches the current pattern in the binding layer. Chances are that the unit that belongs to the same pattern than the cues has the largest overlap and becomes most highly activated. Only the most active unit in each feature map is retained, and as a result, a complete, unambiguous perceptual pattern is retrieved from the system (figure 2d). Retrieval Errors If there are n units in the binding layer and m units are chosen as a representation for a pattern, the number of possible different binding representations is equal to (z) . If n is sufficiently large and m is relatively small compared to n, this number is extremely large, sug- gesting that the convergence-zone memory could have a very large capacity. However, due to the probabilistic nature of the stor- age and retrieval processes, there is always a chance that the retrieval will fail. The binding constellations of the retrieval cue units may overlap significantly, and several spurious units may be turned on at the bind- ing layer. When the activation is propagated back to the feature maps, some random unit in a feature map may have a binding constellation that matches the spurious units very well. The “rogue” unit may receive more activation than the correct unit, and a wrong feature value may be retrieved. As more pat- terns are stored, the binding constellations of feature units become larger, and erroneous retrieval becomes more likely. To determine the capacity of the convergence-zone memory, the chance of retrieval error must be com- puted. Below, a probabilistic formulation of the model is first given, and bounds for retrieval error are then computed. Probabilistic Formulation Let Zi be the size of the binding constellation of a fea- ture unit after i patterns have been stored on it and Cognitive Modeling 69 Binding Layer Binding Layer Feature Map 1 Feature Map 2 Feature Map 3 Feature Map 4 (a) Retrieval cues activate a binding pattern. Binding Layer Feature Map 1 Feature Map 2 Feature Map 3 Feature Map 4 (c) Binding pattern activates feature units. Feature Map 1 Feature Map 2 Feature Map 3 Feature Map 4 (b) Less active binding units are turned off. Binding Layer Feature Map 1 Feature Map 2 Feature Map 3 Feature Map 4 (d) Less active feature units are turned off. Figure 2: Retrieval. A stored pattern is retrieved by presenting a partial representation as a cue. The size of the square indicates activation level of the unit. let Yi be its increase after storing the ith pattern on it. Obviously, Yr = m. To obtain the distribution of Yi when i > 1, note that the new active connections belong to the intersection of a randomly chosen subset of m connections among all n connections of the unit, and its all remaining inactive connections (a set with n - z elements, where t is the binding constellation at the previous step). Therefore, Yi, i > 1 is hypergeo- metrically distributed with parameters m,n - z, and n: P(K = ?JlZi-1 = z) = (“L”)(mry) / (ii)’ (‘) The constellation size Zi is then given by i Zi = >: Yk. (2) k=l Let I be the number of patterns stored on a par- ticular feature unit after p patterns have been stored in the entire memory. I is binomially distributed with parameters p and $, where f is the number of units in a feature map: I - B(P, f,. (3) Let 2 be the binding constellation of a particular feature unit after p patterns have been stored in the memory. It can be shown that E(Z) = n( 1- (1 -z)“). The binding constellation of a feature unit, given that at least one pattern has been stored on it, is denoted by 2’; obviously E(Z’) > E(Z). The variable 2’ can be used to denote the binding constellation of a retrieval cue, which necessarily must have been used once, as- suming that the retrieval cues are valid. Let 2; be the binding constellation of the jth retrieval cue and let Xj be the number of units in the intersection of the first j retrieval cues. Then X1 = 2;. To get Xj for j > 1, we remove from consideration the m units all re- trieval cues necessarily have in common (because they belong to the same stored pattern), and randomly se- lect z-m units from the total set of n-m units and see how many of them belong to the current intersection of LEj-1 - m units. This is a hypergeometric distribution 70 The Arts with parameters r - m, Xi-1 - m, and n - m: P(Xj = XjlZi = Z,Xj-1 = Xj-1) = (y--L:) (y::;) / (; I n”). (4) The intersection is taken over the binding constella- tions of all j retrieval cues. The number of units in common between a poten- tial rogue unit and the j retrieval cues is denoted by R j+r and is also hypergeometrically distributed, how- ever with parameters Z, x, and n because we cannot assume that the rogue unit has at least m units in common with the cues: P(Rj+l = TIZ = r,Xj = X) = (5) The correct unit in a feature map where a retrieval cue was not presented will receive an activation Xj+r . The correct unit will be retrieved if Xj+r > Rj+r, which is usually the case because E(Xj+r) > E(Rj+r). In each feature map there are (f - 1) potential rogue units, so the conditional probability of successful retrieval is (1 - P(Rj+l > Xj+r IXj+r, 2, Xj))(f-‘1, not address- ing tie-breaking. Unfortunately, it is very difficult to compute Psuccess, the unconditional probability of suc- cessful retrieval, because the distribution functions of 2, Xj, Xj+l and Rj+l are not known. But it is pos- sible to derive bounds for pSUCCeSS and show that with reasonable values for n, m, f, and p, the memory is re- liable. Lower bound for memory capacity Memory capacity can be defined as the maximum num- ber of patterns that can be stored in the memory so that the probability of correct retrieval with a given number of retrieval cues is greater than cy (a constant close to 1). In this section, worst-case bounds for the chance of successful retrieval will be derived. The anal- ysis consists of three steps: (1) bounds for the number of patterns stored on a feature unit; (2) bounds for the binding constellation size; and (3) bounds for the in- tersections of binding constellations. Given particular values for the system parameters, it is then possible to give a lower bound for the capacity of the model. 1. Number of patterns stored on a feature unit. Since I has a binomial distribution (with parameters p and $), Chernoff bounds can be applied: P(I 6 (1- 6);) < [(l:&y,oc~c 1, (6) P(I 2 (1+ 6):) 5 [(l+$)l+6]fY s’“* (7) The formal parameter 6 determines the tradeoff be- tween the tightness of the bounds and the probability of satisfying them. 2. Size of the binding constellation. Instead of choosing exactly m different units for the binding representation of each pattern, let us select k: not- necessarily-distinct units in such a way that the ex- pected number of different units is m. This will make the analysis easier at the cost of larger variance, so that the bounds derived will also be valid for the ac- tual process. Let us assume i patterns are stored on a unit, which is equivalent of selecting Ici units from the binding con- stellation at random. Let Z,, be the expected size of the binding constellation after v units have been selected. Then zv =2+(n - Z)(l- (1 - i!)ki-VI, (8) where ,% is the size of the binding constellation formed by the first v selected units. Now, E(Zv~Zv~r) = Zv-i, and the sequence of variables 20,. . . , zki is a martin- gale. Moreover, it can be shown that 12, - Z,-rl < 1, and bounds for 2 can be obtained from Azuma’s in- equality (see e.g. Alon & Spencer 1992): P(Z 2 n(1 - (l- L)k’,) - x&q < cA2, n (9) P(Z > n(l - (l- ;,kiu) + x&J 5 e-x2, (10) where il is the lower bound for I obtained from equa- tion 6, and i, the upper bound from equation 7. Sim- ilar bounds can be derived for 2’. 3. Intersection of binding constellations. The process of forming the intersection of j binding con- stellations incrementally one cue at a time can also be formulated as a martingale process. Let Xi denote the expected number of elements in the intersection of two sets, after the first j elements of the first set have been checked (the elements of the second set are assumed to be known at all times). Then xj =z+ (nl - j)(n2 - 2) n- j 7 (11) where X is the number of elements in the intersection of the second set and the set formed by the first j elements of the first set, and nl, 7x2 and n are the sizes of the first, second, and the superset. If nl and n2 are both smaller than in, Azuma’s inequality can be applied. Taking the intersection of the previous step as the first set, the binding constellation of the jth cue as the second set, and the binding layer as the common superset, this approach gives us the following upper bound for Xi: (x *- P(Xj 2 ’ lfu - m)cc - 4 (n-m) l km +XJXj-l,u - m) 5 eBx2i2, x > 0, (12) Cognitive Modeling 71 where Z: and Xj-r,u are upper bounds for 2’ and Xi-1 and are assumed to be less than in. When Xj is at its upper bound, a potential rogue unit has the largest chance of taking over. In this case, Rj+r has the upper bound PC-Q+1 2 Xj u&4 L + Am) 5 ewAai2, X > 0, (13) n where zu and xj,u are upper bounds for 2 and Xi. A lower bound for X j+r while using an upperbound for Xj is then given by P(Xj+l 5 Cxj,u - m>(s - m) + m (n-m> -Ad-) 5 eBA212, x > 0. 04 If the resulting lower bound is smaller than m, m can be used instead. The above analysis ignores correlations between binding constellations. The correlations originate from storing the same partial pattern multiple times and tend to increase the size of the intersections. The chance that two random patterns have more than one feature in common in j features is equal to (1 - (1 + &)(l - +>j>, which is negligible for sufficiently large values of f. We can now use equations 6-14 to derive a lower bound for the probability of successful retrieval with given system parameters n, m, F, j, f) and p. The re- trieval is successful if ~j+r,~, the upper bound for Rj+r , is lower than xj+r,u, the lower bound for Xj+r . Un- der this constraint, the probability that none of the variables in the analysis exceeds its bounds is a lower bound for successful retrieval. Obtaining the upper bound for Xj involves bounding 3 j - 1 variables: I and 2’ for the j cues and Xj for the j- 1 intersections. Computing xj+r,l and rj+r,u each involve bounding 3 variables (I, 2, and Xj+r; I, Z’, and Rj+l). Th ere are F - j maps, each with one xi+1 ,l bound and f - 1 different rj+r,u bounds (one for each rogue unit). The total number of bounds is therefore 3j - 1 + 3f(F - j). Setting the righthand sides of the inequalities 6-14 equal to a small constant ,0, a lower bound for successful retrieval is obtained: Psuccess > 1 - (3j - 1+ 3f(F - j))P. (15) For example, assuming each unit in the model corre- sponds to a vertical column in the cortex, it is reason- able to assume feature maps with lQs computational units (Sejnowski & Churchland 1989). We can further assume that the system has 15 feature maps, 10 of which is used to cue the memory, and the binding layer consists of lo5 units, with 150 used for each binding pattern. Assuming full connectivity between the fea- ,ture units and the binding units, there are 1.5 x 1012 connections in the system. If we store 0.85 x lo8 patterns in the memory, Z: and xj-r,u are less than in, the chance of partial overlap of more than 1 feature is less than 0.45 x 10-l’, and the analysis above is valid. Setting p = 0.5 x lo-’ yields bounds ~j+r,~ < Zj+r,l with psuccess > 99%. In other words, 0.85 x lo* memories can be stored in the mem- ory with 99% probability of successful retrieval. Such a capacity is approximately equivalent of storing one new memory every 17 seconds for 70 years, 16 hours a day. Conclusion Mathematical analysis shows that an extremely high number of episodes can be stored in the convergence- zone memory with reliable content-addressable re- trieval. Moreover, the convergence zone itself requires only a tiny fraction of the hardware required for per- ceptual representation. These results provide a pos- sible explanation for why human memory appears al- most unlimited, and why memory areas appear small compared to the areas devoted to low-level perceptual processing. The model makes use of the combinatorics and the clean-up properties of coarse coding in a neurally- inspired architecture. The storage capacity of the model appears to be at least two orders of magnitude higher than that of the Hopfield model with the same number of units, while using two orders of magnitude fewer connections. However, direct comparison is diffi- cult because the stored patterns in the Hopfield model are much larger (contain more information), and its N/4 log N capacity result only indicates how many pat- terns are stable instead of estimating the probability of correct retrieval with a partial pattern as a cue. The convergence-zone episodic memory model could be extended to make it more accurate as a model of ac- tual neural processes. For instance, lateral inhibitory connections between units within a feature map could be added to select the unit with the highest activity. A similar extension could be applied to the binding layer; instead of only one unit multiple units should stay active. A variation of the Hebbian learning mech- anism (Hebb 1949; Miller & MacKay 1992) could be used to implement the storage mechanism. Such re- search could lead to a practical implementation of the convergence zone memory, and perhaps even to a hard- ware implementation. Another important research di- rection is to analyze the behavior of the model as a psychological model, that is, to observe and character- ize its memory interference effects and compare them with experimental results on human episodic memory. Acknowledgements We would like to thank Greg Plaxton for pointing us to martingale analysis on this problem. This research was supported in part by NSF grant #IRI-9309273 to the second author. 72 The Arts References Alon, N., and Spencer, J. H. 1992. The Probabilistic Method. New York: Wiley. Damasio, A. R. 1989a. 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San Mateo, CA: Mor- gan Kaufmann. Sejnowski, T. J., and Churchland, P. S. 1989. Brain and cognition. In Posner, M. I., ed., Foundations of Cognitive Science. Cambridge, MA: MIT Press. chapter 8, 315-356. Squire, L. R. 1987. Memory and Brain. Oxford, UK; New York: Oxford University Press. Touretzky, D. S., and Hinton, G. E. 1988. A dis- tributed connectionist production system. Cogni- tive Science 12:423-466. Tulving, E. 1972. Episodic and semantic memory. In Tulving, E., and Donaldson, W., eds., Orga- nization of Memory. New York: Academic Press. 381-403. Tulving, E. 1983. Elements of Episodic Memory. Ox- ford, UK; New York: Oxford University Press. Cognitive Modeling 73 | 1994 | 292 |
1,644 | A Model of Creative Understanding* Kenneth Moorman and Ashwin Ram Georgia Institute of Technology College of Computing Atlanta, GA 30332-0280 {kennethm,ashwin}@cc.gatech.edu Abstract Although creativity has largely been studied in problem solving contexts, creativity consists of both a generative component and a comprehension component. In partic- ular, creativity is an essential part of reading and under- standing of natural language stories. We have formalized the understanding process and have developed an algo- rithm capable of producing creative understanding behav- ior. We have also created a novel knowledge organization scheme to assist the process. Our model of creativity is implemented as a portion of the ISAAC (Integrated Story Analysis And Creativity) reading system, a system which models the creative reading of science fiction stories. Introduction Creativity remains a largely unexplained facet of human intelligence; neither psychologists nor artificial intelli- gence researchers have produced complete theories of it. While most creativity researchers have investigated the behavior in a problem solving context, we are more interested in how creativity is manifested during com- prehension. We thus distinguish between two forms of creativity: a generative type, creative invention or cre- ativeproblem solving (e.g., Hofstadter & McGraw 1993; Kolodner & Wills 1993); and an explanatory type, cre- ative understanding (e.g., Kass, Leake, & Owens 1986; Ram 1993). Past research has shown the value of ex- ploiting the relationship between problem solving and understanding (e.g., Wilensky 1983; Birnbaum 1986); likewise, our study of creative understanding should aid general creativity research. Our model of creative understanding is functional in nature. A cognitiveprocess can be explained by describ- ing the function of each of its tasks, the relationships between them, the mechanisms which accomplish them, and the knowledge required. The resultingfunctional the- ory can then be used to guide implementation of a process model. We have identified four tasks which are sufficient for the modeling of creative understanding. For three of these, we extended well-known mechanisms from tradi- tional problem solving and comprehension domains. The *This work was supported by a Fannie and John Hertz Foun- dation fellowship and by the Georgia Institute of Technology. final one, problem reformulation, relies on a new mech- anism, function-driven morphological synthesis. While developed in a reading context, this is a general method which can apply to other creativity modeling. The cre- ative understanding processes, mechanisms, and a novel knowledge organization scheme which supports the pro- cesses are implemented in the ISAAC (Integrated Story Analysis And Creativity) system which creatively reads science fiction stories. Creative Understanding The reading of any story requires some level of creative understanding; it is when normal processing fails that creative understanding is most necessary. Consider the science fiction story, Men Are Diferent (Bloch 1963) seen in Figure 1. If a reader is unfamiliar with the concept of sentient robots, the story is impossible to appreciate. While the next section explains exactly what happens when such a need for creative understanding arises, the remainder of this section presents a discussion of creativ- ity in order to provide a common ground to an elusive and often controversial concept. Creativity Creativity is a directed, internal process of a cognitive agent which results in an artifact which is both novel and useful. This is intended as a working definition; the following elaborations should clarify our intended meaning. Process: For a process to be creative, it must be both internal and directed. The internal restriction ensures that the reasoner is not simply repeating a piece of knowl- edge just received from another source. The directedness restriction ensures that the reasoner is not simply a ran- dom generator of solutions, where one may eventually be “creative” through sheer chance. Artifact: An artifact results from a mental process by a reasoner and may be either physical or mental. Any ar- tifact can be described by a set of attributes which define its characteristics. One of these, function, represents the 74 The Arts From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. I’m an archaeologist, and Men are my business. Just the same, I wonder if we’ll ever find out about Men-I mean really find out what made Man dif- ferent from us Robots-by digging around on the dead planets. You see, I lived with a Man once, and I know it isn’t as simple as they told us back in school. We have a few records, of course, and Robots like me are filling in some of the gaps, but I think now that we aren’t really getting anywhere. We know, or at least the historians say we know, that Men came from a planet called Earth. We know, too, that they rode out bravely from star to star; and wherever they stopped, they left colonies-Men, Robots, and sometimes both-against their return. But they never came back. Those were the shining days of the world. But are we so old now? Men had a bright flame-the old word is “divine” I think-that flung them far across the night skies, and we have lost the strands of the web they wove. Our scientists tell us that Men were very much like us-and the skeleton of a Man is, to be sure, almost the same as the skeleton of a Robot, except that it’s made of some calcium compound instead of titanium. Just the same, there are other differences. It was on my last field trip, to one of the inner planets, that I met the Man. He must have been the last Man in this system, and he’d forgotten how to talk-he’d been alone so long. I planned to to bring him back with me. Something happened to him, though. One day, for no reason at all, he complained of the heat. I checked his temperature and decided that his thermostat circuits were shot. I had a kit of field spares with me, and he was obviously out of order, so I went to work. I pushed the needle into his neck to operate the cut-off switch, and he stopped moving, just like a Robot. But when I opened him up he wasn’t the same inside. And when I put him back together I couldn’t get him running again. Then he sort of weathered away-and by the time I was ready to come home, about a year later, there was nothing left of him but bones. Yes, Men are indeed different. Figure 1: Men Are DifSerent best-known uses of the artifact. The remaining attributes are divided into primary attributes, which contribute to an explanation for why the artifact can perform its func- tion; and secondary attributes, which are the rest. Novel: There are many arguments concerning whether a creative act must be novel and from whose perspective this novelty is judged (e.g., Boden 1991; Stewart 1950; Thurstone 1952). In reference to a given perspective, there are two important ways in which an artifact (M) may be novel with respect to a goal (6); to see these, consider a longsword used for combat. Evolutionary Novelty (E-Novel): M is defined to be E-Novel iff M is unknown and M accomplishes G in a better way than other examples of artifacts which accomplish G. This is generally the result of altering one of the primary attributes of M. A shortsword, a bastard sword, or a two-handed sword would all be E-Novel. Revolutionary Novelty (R-Novel): M is defined to be R-Novel iff M is unknown and M accomplishes G in a different way than other artifacts which accomplish G. For this, secondary attributes may need to be altered to cause them to participate in the function of M. The light saber from Star Wars is an R-Novel variation of the original longsword. Useful: UsejLZ is somewhat easier to define for an ar- tifact. A reasoner attempting to perform creatively will have a certain task to accomplish. In order for a cre- ative process to exist, it must produce an artifact which accomplishes this task in some manner. Creative understanding specification The presented definition of creativity is simply descrip- tive and is insufficient for implementing a model of cre- ative behavior. For this, we need to develop an algorith- mic view of creativity as it exists within creative under- standing. ormalization of problem solving Since understand- ing can be described as the complementary operation to problem solving, a formal view of problem solving can be helpful in developing an understanding formal- ization. Problem solving begins with the reasoner in an initial state. A reasoner knows of operations that it can perform which will move it through a search space. This stops when a goal state is achieved. The output from the process is a solution path which takes the reasoner from the initial state to the goal state (Newell & Simon 1972). The idea of con- straints on this process is also important (Sacerdoti 1974; Sussman 1973). These are conditions which cannot be violated in the final solution. Finally, there are times when the reasoner may already possess a solution. If so, problem solving can discover a better solution if the reasoner possesses a critique of why the current solu- tion is not a viable one (Hammond 1989). The complete formulation is shown in Figure 2. Formalization of understanding Based on Figure 2, a formal specification of understanding can be developed (Figure 3). Using the example of Men... : if a reader sees a robotic character “turn off” a man and then open him, they may understand the episode by reasoning that the robot had the goal of repairing the man (abduction): Cognitive Modeling 75 lNHJ.1’: Initial state (I) 1 Goal state desired (G) Set of constraints (C) (optional) Current solution (S) (optional) Critique why S is not good enough solution (K) (optional) OUTPUT: Solution path (S’) which achieves G given I and does not violate C Figure 2: FUNCTION Problem Solver a reader who learns that Mankind has become extinct and that the remaining robots are curious as to the fate of their creators may understand this by reasoning about upcoming story actions (prediction); finally, the reader may attempt to understand why the robot felt that field repairs was a good solution to the man’s discomfort (ex- planation). INPUT OUTPUT Behavior Solution (S) Goal (G) Abduction Goal (G) Solution (S) Prediction Solution (S) and Critique (K) of why Explanation Goal (G) S is a good solution Figure 3: FUNCTION Understander The creative understanding process If only known concepts are given to the understanding process, no creative behavior is necessary. If, however, a reasoner uses the understanding process to compre- hend novel artifacts in a way which is use&l, creative understanding occurs. Notice that the context of reading provides an exact meaning for the final part of this re- quirement, usefulness. Since the reasoner has the task of comprehending some piece of text, an understanding of an artifact from it is useful if this understanding allows comprehension to occur and reading to continue. This is in marked contrast with “traditional” approaches to cre- ativity which must make the context of usefulness more explicit. The tasks involved in creative understanding are car- ried out by a core set of cognitive mechanisms. This cycle of creative understanding (CUP) is shown in Fig- ure 4 (depicted for an abduction task, the same approach is used for explanation and prediction). Mundane under- standing exists if the reasoner only considers steps 1 and 2; that is, if the reasoner performs only memory retrieval and incorporation. Each cycle increases the potential for successful creative understanding. At some point the rea- soner will be so far removed from the original concept that further iterations will be useless; still, there is no theoretical limit to the “amount” of creativity generated Solution (S) OUTPUT: J 1 Goal state desired (G) Constraint set (K) PROCESS: REPEAT 1. Perform memory retrieval 2. If (1) fails * attempt incorporation 3. If (2) fails =+ attempt baseless analogy 4. If (3) fails j reformulate the problem UNTIL (successful OR concept is too bizarre) I -I Figure 4: FUNCTION Creative Understander The four steps of CUP The first step of the CUP algorithm involves a memory retrieval. If concepts are retrieved which cause under- standing of the novel concept, the cycle ends successfully. If nothing is returned which is immediately useful, pro- cessing continues. This may occur if nothing is available in memory or if the proper items are simply not returned (e.g., due to an indexing problem). In Men.. . , the reasoner will be confronted with the idea of a sentient robot. If only an industrial robot exists in memory, understanding will fail. The concept of industrial robot is insufficient to explain the robot’s actions. If normal memory retrieval fails to produce adequate understanding, the algorithm will attempt to perform in- corporation. Incorporation involves the discovery of relations between concepts which were retrieved from memory and the concept being explained. If a relation- ship can be discovered that explains the new concept, understanding is successful. This stage of the cycle may result in understanding which appears either mundane or creative, depending on exactly what was retrieved and what sorts of relations were discovered. In the example of Men..., incorporation fails because sentience is in con- flict between the concepts of industrial robot and story robot. If incorporation fails, the CUP algorithm attempts a technique known as baseless analogy. Analogy (e.g., Falkenhainer 1987; Gentner 1989) attempts to explain a concept (the target) by appealing to known informa- tion about an analogous concept (the base). However, if no existing base exists, it may be possible to dynami- cally build the base within a given domain if the reasoner possesses a great deal of information about the target’s domain and the intended base domain (e.g., Clement 1989). For example, atomic structure as in the Bohr model can be understood within the framework of gang warfare (WKRP Episode 60 1980). If the reasoner has a great deal of conceptual background knowledge con- cerning sentience and robots, it is possible that an under- standing of the story robot may result. Finally, if all of the above steps have failed to produce a satisfactory understanding, the reasoner must resort to 76 The Arts problem reformulation. There are some cases in which the initial statement of a problem is not the one which will lead to an optimal solution. By recasting the problem in a new way, a reasoner may gain insights into a possible solution. For Men..., the reader can attempt to take the retrieved concept of industrial robot and manipulate it with the goal of explaining the story robot. The method which accomplishes problem reformulations is function- driven morphological synthesis. 1. Consider an artifact in the world, designated as M. 2. Let f be defined as the function which returns the function of an artifact. 3. Let C be the class of functions which alter an object, either by changing some attribute of that object or by adding a new attribute to the object. 4. Cr through C, are a set of n such functions. 5. Thus, a set of objects S,ll can be created by U~=I...~ Ci. 6. Consider the subset, S’i defined as {+&I~ and f(s) = f(M)} 7. Finally, consider the subset S, defined as (sls&f where s is unknown } 8. The items in S, are useful (they fulfill the same role as the original object M) and they are novel to the reasoner. Therefore, they are creative. Figure 5: Function-driven Morphological Synthesis Function-driven morphological synthesis In order to model problem reformulation, we developed a new mechanism-function-directed morphological syn- thesis (FMS), depicted in Figure 5. It is assumed that the reasoner has an artifact that needs to be understood. The reasoner applies a set of manipulator functions to the artifact, altering its attributes and producing new ar- tifacts. The artifacts which possess the original func- tionality and are novel to the reasoner are considered to be creative ones. The FMS technique was inspired by Allen’s morphological synthesis (cited in Finke, Ward, & Smith 1992), in which a reasoner manipulates combina- tions of primary attributes to produce potentially creative results. Since only primary attributes were modified, Allen’s technique could not result in an R-Novel item. By removing this restriction, FMS is able to produce such novelty. Finally, FMS can exist in both a strong form and a weak form. Strong-FMS performs the manipulations by examining other objects with the same functionality to see how they accomplish their tasks. Weak-FMS does away with this constraint and guides the manipulation through the reasoner’s knowledge of given attributes and possible values. In Men..., FMS must attempt to understand the story robot. It knows that the robot is a willful agent, which violates the concept of industrial robot. Memory retrieval produces a concept which is a willful agent, but is not a robot-man. Thus, FMS begins with man as an input (whose “purpose” is willful agency). FMS is aided by the fact that it has the goal of understanding story robot. Thus, when it manipulates the attributes of man, it does so by examining the concepts of man and industrial robot (an example of strong-FMS). It adds attributes to man from industrial robot and deletes attributes which are no longer needed. The result is a man-like robot which can be used to explain the actions of the story robot. When to say when A central issue in concept manipulation systems is how does a reasoner know which manipulations are good ones and which ones are potentially dangerous. While a will- ing suspension of disbelief (Corrigan 1979) is required for creativity, too much suspension will lead to ridicu- lous outcomes. Various approaches have been taken to minimize this problem in other creativity models. One possibility is to have the system do little self-monitoring; this approach can be seen in Lenat’s AM system (1990). While AM did create a number of creative concepts, it also created a much larger number of worthless concepts which were filtered out by the human researcher. Alterna- tively, other systems exist which possess a large number of programmer-supplied heuristics for deciding what to manipulate and how far to carry the alterations; Turner’s MINSTREL system (1992) and SWALE (Kass, Leake, & Owens 1986) are examples. The problem with this ap- proach is that no techniques have been proposed which would allow the straightforward creation of these heuris- tics; instead, developing them is a “black-art.” Both approaches have been argued against from a theoreti- cal standpoint (Birnbaum 1986); we prefer a technique which would allow flexible modifications, decided by the system itself. As part of this, a new method of knowledge organization is needed. Our knowledge organization scheme resembles a stan- dard semantic network, but knowledge is tagged through the use of a multidimensional grid, as shown in Fig- ure 6. One axis of the grid represents a Schankian breakdown: action, agent, state, and object (Schank & Abelson 1977). The other dimension represents a natural breakdown: physical, mental, social, emotional, and temporal. For example, a TRANSfer is a generic action. In the physical column is PTRANS, the men- tal column contains MTRANS, and the social column contains ATRANS. Our extended representation also in- cludes emotional TRANSfers (the giving of one’s love); and temporal TRANSfers (March getting closer to us). Another difference between a standard semantic net- work and our organization scheme is the function tagging of each concept. Each concept within the knowledge sys- tem is tagged with a set of its common functions. If the reasoner is searching for similar concepts, possibly for use in an FMS attempt, this search can be aided by these tags. For example, in one memory retrieval, a car and a horse might be similar; with a different goal, a horse and a zebra would be a closer pair. This tagging allows a more flexible organization of knowledge than previ- ous methods which were forced to carefully place items into the network to ensure that proper similarities were Cognitive Modeling 77 Agents Actions Ph)&l person walking Mental ccnsciousness thinking Social boss selling Emotional Ares loving Temporal entropy getting closer to March objects rock idea teacher-student relationship hatred secmd States wng lackof knowledge public dishoner being angry early Figure 6: Knowledge representation grid I revealed wheh needed. The knowledge organization scheme allows concept manipulation which is bounded in a reasonable fashion. Each change may leave a concept in the same concep- tual grid cell (an intracellular shif) or it may cause the concept to cross a cell boundary (an extracellular shift. The system is biased against boundary crossings. As a result, conceptual movement within the same grid cell is the cheapest type to perform. Movement along either a row or a column is more difficult, and movement which must go along both is the most difficult. These costs act as a heuristic which guides a reasoner performing creative understanding-the greater the cost, the more conceptual movement has occurred. High amounts of conceptual movement indicates that it is likely that the result will be more bizarre than creative. This restricts how many iterations are permissible in the CUP algo- rithm. Each successive cycle creates concepts which are more and more distant from the original one. The first few iterations will result in concepts which fall within the same grid cell as the original concept. More cycles will create concepts which are shifted in the grid with respect to the beginning concept. By tracking this movement, the reasoner can decide when creative understanding has become too expensive to continue, based on the goals of the reasoner. Implementation The ideas discussed above are embodied in the ISAAC reading system, currently implemented at a level of func- tionality capable of reading the science fiction story Men Are DifSerent (Figure 1). It is built in Common Lisp and runs on RS/6000 machines. ISAAC uses the KR frame package (Giuse 1990) for knowledge representa- tion. More details of the ISAAC system, and its general reading capabilities can be found in (Moorman & Ram 1994). Upon beginning to read Men Are DiJferent, ISAAC realizes that the concept of robot it knows (an industrial tool) is insufficient to produce an understanding of the story robot. This realization arises when ISAAC is unable to reconcile its current definition of robot with the actions of the robot in the story, i.e., the predictions made by the existing conceptual definition are failing. Creative under- standing is given the task of explaining the novel robot, with the existing concept and the novel one passed to the routine. Incorporation fails to create an understanding since there is little similarity between the two concepts of robots. Next, baseless analogy is attempted. ISAAC attempts to transfer the concept of industrial robot to the domain of volitional agents (since this is how the story robot appears to be acting). Unfortunately, ISAAC does not have enough background knowledge to succeed in this case. ISAAC then attempts problem reformulation, using FMS to produce a merged concept containing ele- ments of the current robot concept and the best volitional agent it can retrieve from memory-a man. The result is a man-like, intelligent, volitional robot. The new con- cept maintains some characteristics of the original robot (it is made of metal, resistant to damage, uses sensors and feedback as a control mechanism, and so on.), but is sufficient to understand the robot in the story. ISAAC stores the new concept in memory as a story-robot. ISAAC needs to perform similar creative understand- ing on the man in the story. In this case, ISAAC is attempting to explain what goals the robot might have possessed to cause it to act in the fashion that it did. As a result of this understanding attempt, ISAAC understands that the robot is seeing the man as more similar to itself than is warranted. The irony in the story can be seen as a dual shift within our knowledge grid. First, ISAAC is presented with a robot character acting as an agent rather than as a physical object; the ending is ironic because the narrator then treats the Man, a physical agent, as a physical object and disassembles him, thereby killing him. Conclusions While the CUP algorithm has been successful in assist- ing ISAAC in the understanding of a single story, more work must be done. Additional stories need to be added to the system in order to evaluate the impact of possess- ing unneeded information during creative understand- ing. It is already decided that the next story will be Zoo (Hoch 1978), a story similar to Men... in several ways but different enough to test expansion possibilities. Objective evaluation of ISAAC’s creative performance is also needed. The best such test currently available, the Torrance Tests of Creative Thinking (Torrance 1988), is considered flawed in significant ways. While it is an objective test, opponents suggest that what it measures may be too abstract to apply to general creative behavior. We also intend to explore the relationship of concep- tual change to creative understanding (e.g., Ram 1993; Chi 1993). Finally, we plan to demonstrate our claim that creative understanding issues are important to cre- ative design by implementing a design algorithm based on the CUP and FMS algorithms. While many researchers have tried to “demystify” cre- 78 The Arts ativity, most models of the process which have been put forth have been too vague to allow implementation. See- ing creativity as having two aspects, a generative side and an understanding side, has permitted us to explore new issues in creativity and develop interesting results. The four steps of the CUP model are sufficient for producing behavior which is judged creative. Additionally, the de- scribed FMS algorithm is a mechanism which has proven capable of producing novel understanding of concepts. In addition, our reading area has forced us to confront real- world applications of creativity. Humans are certainly aided in reading comprehension by possessing creativity (Popov 1993); by incorporating creative understanding into artificial systems, they gain the ability to learn from experiences with novel concepts and thus grow in scope. References Birnbaum, L. 1986. Integrated Processing in Planning and Understanding. Ph.D. Dissertation, Yale Univer- sity. Research Report 489. Bloch, A. 1963. Men Are Different. In Asimov, I., and Conklin, G., eds., 50 Short Science Fiction Tales. 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1,645 | Orderi elations in Human and Machine Planning’ Lee Spector, Mary Jo Rattermann, and Kristen Prentice School of Communications and Cognitive Science Hampshire College, Amherst, MA 01002 { lspector, mrattermann, kprentice} @ hamp.hampshire.edu Abstract Analytical results from AI planning research provide the motivation for this experimental study of ordering relation- ships in human planning. We examine timings of humans performing specific tasks from the AI planning literature and present evidence that normal human planners, like “state of the art” AI planning systems, use partial-order plan representations. We also describe ongoing experiments that are designed to shed light on the plan representations used by children and by adults with planning deficits due to brain damage. Several points of interest for collaboration between AI scientists and neuropsychologists are noted, as are im- pacts that we feel this research may have on future work in AI planning. Introduction Recent analytical studies have mapped a rich territory of re- lations among AI planning algorithms, AI planning do- mains, and computational complexity classes (Chapman 1987, Bylander 1991, Chenoweth 1991, Gupta & Nau 1991, Erol et al. 1991, Minton et al. 1992, Barrett & Weld 1993). The work of Barrett and Weld, in particular, shows that planning algorithms based on partially-ordered plan repre- sentations have advantages over total-order planners when applied to problems of certain sorts. One of their results is that problems in the artificial domain called D’S’ are easy for partial-order planners but hard for total-order planners. Partial-order planners exhibit linear growth rates for plan- ning time as problem size increases in this domain, while to- tal-order planners exhibit exponential growth rates.2 This result motivates the present study of human plan- ning. We know that partial-order planners have specific ad- vantages over total-order planners in AI systems; by looking for signs of such advantages in human systems, we can draw tentative inferences about the representations and algorithms used in human planning. The lessons learned about human iThe first author acknowledges the support of the Dorothy and Jerome Lemelson National Program in Invention, Innovation, and Creativity. 2These results have only been proven for the particular plan- ning algorithms in the Barrett and Weld study, but we believe them to be indicative of the advantages of partial-order planning more generally. (Minton et al. 1992) provides some support for this belief. 80 The Arts planning can then be re-applied to AI systems, which still lag behind human competence in several areas. We presented human subjects with tasks from the D’S’ domain and noted the time spent planning, as well as the overall time needed to complete the task. As in AI planning systems, linear growth rates in human performance are sug- gestive of partial-order planning, while exponential growth rates are suggestive of total-order planning. An additional goal of this work is to shed light on the role of the frontal lobe of the brain in the ability of humans to perform com- plex planning tasks. To this end, we plan to compare the per- formance of normal adults, adults with frontal lobe lesions, and children at various stages of frontal lobe development. The remainder of the paper is organized as follows: after a brief refresher on partial-order planning we summarize the relevant complexity results of Barrett and Weld and discuss the neuropsychological background of our experi- ment. We then describe the Chores software with which the experiment was conducted, along with the details of the D’S’ task. This is followed by a summary of our results to date and a discussion of implications and directions for future work. Partial-order Planning Most AI planning systems since STRIPS (Fikes & Nilsson 1971) have represented actions as operator schemata. Op- erator schemata describe the conditions under which each action can be performed and the effects that the perfor- mance of each action will have on the world. STRIPS-style operator schemata are composed of precondition lists that represent the conditions under which the actions can be performed, and pairs of lists called add and delete lists that represent effects. A plan to achieve some given goal from some given initial state is a list of operator schemata, along with assignments for all variables in the schemata, such that the corresponding sequence of actions will appropri- ately transform the world. Early planners such as STRIPS worked by constructing sequential (linear, total-ordered) partial plans which achieved subsets of the goals, and which could be augment- ed, manipulated and combined to produce correct final plans. Given a list of goals to achieve, and a system that supports linear partial plans, the natural strategy is to pro- duce plans to achieve each of the goals and to concatenate the resulting partial plans. This strategy can be applied re- From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Initial Goal Figure 1. The Sussman Anomaly cursively to any subgoals introduced in trying to achieve any of the goals. But using linear partial plans in this way leads to a difficulty that can be illustrated with a blocks world problem known as the Sussman Anomaly: Given three blocks labeled A, B, and C, and an initial state in which C is on A, and in which A and B are both on the table, construct a plan for building a tower with A on B and with B on C (Figure 1). The difficulty is that no linear com- bination of the obvious partial plans for achieving On(A, B) and On(B, C) will yield a correct plan for achieving their conjunction. If On(A, B) is achieved first (by putting C on the table on then putting A on B) then the new {A, B} stack would have to be immediately dismantled in order to achieve On(B, C). (Only one block can be lifted at a time.) On the other hand, if On(B, C) is achieved first (by putting B on C) then once again the new stack would have to be dismantled in order to achieve the other conjunct. The literature contains several strategies for circumvent- ing this problem (e.g., (Sussman 1990, Sacerdoti 1975, Waldinger 1977)). One of the most popular strategies in- volves the representation of partial plans as partial-orders, rather than as total-orders. This allows for the representa- tion of partial plans in which some of the ordering deci- sions have been left temporarily unspecified. A partially ordered partial plan for the Sussman Anomaly might state that On(A, B) and On(B, C) are both to be achieved, but that the order in which their plans are to be executed has yet to be determined. Further computation may indicate that additional ordering constraints must be imposed; in the case of the Sussman Anomaly the actions into which the goals are decomposed will have to be interleaved. Fig- ure 2 illustrates a solution to the Sussman Anomaly using partially ordered action sequences.3 Most “state of the art” planning systems now use partially- ordered partial plans (e.g., (Chapman 1987, Currie & Tate 1991, McAllester & Rosenblitt 1991)). Several recent stud- ies have examined the trade-offs in total-order vs. partial- order planning; some of these studies quantify the differ- ences in performance profiles between total-order and 3See (Sacerdoti 1975, Tate 1977) for further detail. 4The third planner in the Barrett and Weld study (TOPI, for “Total-Order, Prior-Insertion”) differs from TOCL along a differ- ent dimension and hence is of no interest to the present study. Barrett and Weld mention that source code for all three planners is available-send mail to bug-snlp@cs.washington.edu. 5The full definition: “A set of n subgoals is laboriously serial- izable if there exists at least one serializable ordering yet at least l/n of the subgoal orders can not be solved sequentially without possibly violating a previously solved subgoal.” (p. 19) Figure 2. Solving the Sussman Anomaly with partially ordered partial plans. partial-order planners (Minton et al. 1992, Barrett & Weld 1993). With regard to human planning, we know of no pri- or literature on the ordering relations in partial plans. The results from AI planning systems can, however, be used to structure experiments that provide data on the ordering re- lations used by humans in constructing action plans. arrett & Weld’s Results and Domain Barrett and Weld examined the performance of three plan- ning algorithms on problems of several classes. Two of their planners are of interest here: POCK (for “Partial- Order, Causal-Links”) and TOCL (for “Total-Order, Causal-Links”). POCL and TOCL differ, to the extent that this is possible, only in the representation of ordering rela- tions within partial plans; POCL uses partial-order repre- sentations while TOCL uses total-order representations. Both POCL and TOCL use standard STRIPS-style operator schemata. POCL is a variant of the systematic nonlinear planning algorithm used in the SNLP planning system (McAllester & Rosenblitt 1991), and TOCL is a modi- fication of POCL in which an added “linearization” step forces all plans to be totally ordered.4 POCL and TOCL were run on large sets of problems from both “real” and artificial domains. The real domains includ- ed blocks world, transportation planning, and others, while the artificial domains were constructed to highlight the ef- fects of specific patterns of goal interactions. The runtimes for each planner on problems in each domain were ana- lyzed, and several interesting generalizations were noted. In accounting for the observed data, Barrett and Weld extended Korf’s taxonomy of subgoal collections (Korf 1987) to include two new classes: trivial serializability and laborious serializability. A set of subgoals is said to be trivially serializable “if each subgoal can be solved in any order without ever violating past progress,” while a set of subgoals is said to be laboriously serializable “if there exist an inadequate percentage of orders in which the subgoals may be solved without ever violating past progress”5 (pp. 3-4). Barrett and Weld also produced the following result: Proposition II Assuming that a problem’s subgoals can be achieved in constant time, the expected time to solve a problem rises linearly with the number of sub- Cognitive Modeling 81 goals if the problem is trivially serializable, but rises ning behavior, and specifically, to show that damage to the exponentially if the problem is laboriously serializ- frontal cortex will lead to deficits in the patient’s ability to able or nonserializable. (p. 36) form and carry out complex plans. It is important to note that the classification of a problem as trivially or laboriously serializable depends on the plan- ning algorithm that is being used; different planning algo- rithms induce different subgoal structures, and hence it is possible for a single problem to be trivially serializable in the search space of one planner and laboriously serializ- able in the search space of another. The artificial domain called D’S’ is the simplest of Barrett and Weld’s domains that is trivially serializable for POCL but laboriously seri- alizable for TOCL. In D’S each operator has exactly one precondition, one item on its add list, and one item on its delete list. The precondition lists and add lists are all mutu- ally disjoint, and each operator deletes the precondition of one of the other operators. The pattern for the construction of an n-operator D’S’ domain is: D’S’ in the Chores Experiment We are performing experiments built using the NINDV NIH Chores experiment software (Spector & Grafman 1994) to explore the ordering representations used in hu- man problem solving. The software was designed for hu- man planning experiments with normal subjects, with frontal lobe lesion patients, and with children at various stages of frontal lobe development.6 The subject interacts with a Macintosh computer that displays a map of a hypo- thetical city, with icons representing items that the subject is to acquire (the goal list), and icons representing items that the subject already possesses (the inventory). The sub- ject uses the mouse and/or arrow keys to navigate around the map and to perform chores. The subject can backtrack by clicking an “Undo Previous” button-this reverses the effects of the most recently performed chore and moves the subject to the location adjacent to that chore. A time- stamped protocol that lists all of the subject’s actions is produced; it can be analyzed to produce several data sets. Operator: Action: Ai, Preconditions: {Ii}, Add: (Gi}, Delete: {Zi-1) where i ranges from 1 to n and where the delete list for A 1 is empty. The maximal solvable problems in this domain have initial conditions consisting of all of the li and goal conditions consisting of all the Gi. Note that the pattern in- duces a linear order on the solution to each maximal prob- lem-each operator deletes the precondition to the opera- tor that must immediately precede it in the solution plan. The results of Barrett and Weld tell us that partial-order planners are capable of finding the correct order in linear time, while total-order planners will generally require ex- ponential time. Neuropsychology of Planning Neuropsychologists have long studied the role of the frontal cortex in human behavior, and in particular, the ef- fects of damage to this area of the brain. It has long been known that patients with frontal lobe lesions will often be- have inappropriately in social situations, experience radical mood swings, and display deficits in processing temporal relationships and order. These deficits appear despite seemingly normal abilities in language, perception, verbal expression, memory and attention (Grafman 1989, 1994; Robertson et al. 1991). In addition to the previously de- scribed deficits, it has also been proposed that these pa- tients experience deficits in planning and problem solving (Grafman 1989, Shallice 1988). Unfortunately, the majori- ty of neuropsychological models fail to explicate the pre- cise role of the frontal cortex in cognitive processes (Graf- man 1989), and also rely on evidence which is obtained from tasks not directly related to planning and problem solving. One of the goals of our experiment is to provide direct evidence for the role of the frontal cortex in plan- 6The general idea for the Chores software was derived from the chore planning experiments described in (Hayes-Roth & Hayes-Roth 1979). 82 The Arts The Chores software can be configured to require that constraints be obeyed on the ordering of the chore comple- tions. In our experiments we are using “resource” con- straints that are specified in a manner almost identical to STRIPS operator specifications. On a separate screen called “Item Info” each chore is listed along with its rela- tions to resources. The subject may switch between the map and Item Info screens at any time; the times of all such actions are recorded in the protocol. The Item Info screen may indicate that a particular chore “requires” one or more resources- this means that the chore cannot be completed if the resources are not currently in the invento- ry. The system produces a beep-sound and a time-stamped annotation in the protocol whenever a subject attempts to complete a chore without the necessary requirements. A chore may also “add” one or more resources-this means that successful completion of the chore will add the specified resources to the inventory. If the added item was a goal then it is also removed from the goal list. A chore may also “delete” one or more resources-this means that successful completion of the chore will delete the specified resources from the subject’s inventory. Note that the re- quire, add, and delete specifications for chores are strictly analogous to the precondition, add, and delete lists for STRIPS operators. This means that the human subjects will be performing tasks quite similar to those performed by AI planners that manipulate STRIPS operators. In the present experiment we are interested in the rela- tion between planing time and task size (number of goals). We are using the time spent viewing the Item Info screen as our principal indicator of planning time. The total time to trial completion is also of interest, but this will include time spent manipulating the user interface that may be un- related to planning time. The D’S’ Series is a set of trials built using the Chores ex- periment software. The entire task consists of two training trials, four test trials, and four foil trials, which are randomly presented to the subject. The first of the two training trials introduces the subject to the basic structure and rules of the task, including the “requires” and “adds” functions, while the second training trial introduces the “deletes” and “undo previous” functions. The four D’S’ trials are as follows: a 2- goal problem in a 2-operator D’S’ domain, a 3-goal problem in a 3-operator D’S’ domain, a 4-goal problem in a 4-opera- tor D’S’ domain, and a 5-goal problem in a 5- operator D’S’ domain. The foils are similar to the D’S’ trials, but they do not actually conform to the D’S’ pattern. To min- imize the effects of varying spatial reasoning abilities, all of the maps have the same simple linear layout. Subjects and Methods Seventeen normal adults and two frontal subjects were test- ed in this experiment. Normal subjects were screened for histories of motor and cognitive impairment, and any nec- essary corrective lenses were worn during testing. Frontal subjects were diagnosed to have cortical damage located in the frontal lobe. Testing took place in a testing room with only the sub- ject and experimenter present. The subject was seated in front of the computer monitor and was introduced to the experiment with the training trials. The following instruc- tions are a summary of those given to the subjects: The goal of this experiment is to obtain a set of items by going to the places on this map. Each time an item is ob- tained it is removed from the list of objects to get and added to the inventory. The places and items on the list are not thematically linked. Thus, going to the “library” will not result in a book being added to the inventory, rather, a triangle will be added. The small black square which designates position can move forward or backward one square at a time, and a particular place on the map is entered by moving the black square on top of it. [Subjects are shown how to ma- nipulate the square with the mouse and the arrow keys.] The “Item Info” screen displays the relationships be- tween the places on the map and the items. If a place “requires” an item, entry is prohibited unless that item is in the inventory. If a place “adds” an item, then that item will be added to the inventory when that place is en- tered. If a place “deletes” an item, then if that item is present in the inventory it will be deleted. If the item is not in the inventory then the deletion has no effect. The “undo previous” button can be used to undo a previ- ous move. This button may be pressed as many times as necessary to undo to the desired move. Subjects were encouraged to practice with the training trials and to ask questions until they were comfortable with the rules of the task. The subjects were informed that the trials would be timed and that they should move through them as quickly as possible, but that randomly guessing the order in which to complete the chores would not be beneficial. The four D’S trials and four foils were presented in a different random order to each subject. Upon the comple- tion of each trial the subject protocol was saved for later examination. esults We analyzed two aspects of the subjects’ performance in the Chores task: Total time to completion and time spent viewing the Item Info screen. The former is the amount of time spent both planning and executing the plan; the latter is a better measure of pure planning time, but it does not include time spent planning from memorized item infor- mation. We had predicted that both measures would reveal the hypothesized linear trend for the normal subjects, and as can be seen in Table 1 and in Figures 4 and 5, this pre- diction was confirmed by the normals’ performance on both measures. A linear trend analysis performed on the data from the normal subjects reveals a significant linear trend for total time to completion (F (1,48) = 31.14, pc.0001) and a significant linear trend for time spent view- ing the Item Information screen (F (1,48) = 48.88, g<.OOOl). Further support for our hypothesis is provided by analyses of variance performed on both sets of data which revealed a main effect of the number of Chores (F (3,48) = 10.48, g < .OOOl for time to completion, and F (3, 48) = 16.74, p < .OOOl, for time spent viewing the Item In- formation screen). Due to the small number of frontal subjects, statistical analyses were not possible; however, as can be seen in Fig- ures 4 and 5, their preliminary data is consistent with the predicted exponential function. iscussion Based on suggestions that planning algorithms using par- tially-ordered plan representations have clear advantages over total-order planners in particular AI planning do- mains, we set out to investigate the performance of human planning systems in the same domains. Our results suggest that our human subjects enjoy the same advantages. Using the Chores software to test subjects in D’S’ domains, we found that the subjects’ total time to completion and time spent viewing the Item Information screen exhibited linear growth rates as the problem size increased. The data suggests that human planners represent the or- Time to Viewing Item Number of Chores Completion Information Two Chores 54.9 1 12.35 Three Chores 131.76 48.71 Four Chores 225.12 93.12 Five Chores 343.53 159.76 Table 1. Mean total time and mean time spent viewing Item Info. Cognitive Modeling 83 g 1000 P # 800 u” 3 600 il ‘F 400 3 t2 200 0 - -D Normals - * Frontals I I I I I I I Two Three Four Number of Chores Five Figure 4. Mean Total Time to Completion, in seconds dering relations in partial plans using partial-orders. The data only shows that human planning time seems to in- crease linearly with increase in task size in the D’S’ do- main. The inference that this implies the use of partial-order representations relies on the assumption that the results of Barrett and Weld are generally indicative of the advantages of partial-order planning as opposed to total-order planning. Although we believe this to be the case, we note that the experiments provide data even if the results of Barrett and Weld fail to generalize. The human planners are managing to achieve linear performance somehow. They are either using partial-order representations or other algorithmic methods that achieve the same effect with respect to efficiency in this domain. One alternative is that the linear human performance owes to the brain’s use of parallel al- gorithms.7 While such alternatives deserve further study, we currently believe that partial-order representations pro- vide the best explanation for the data. An additional goal of this experiment was to examine the role of frontal cortex in planning by testing patients with frontal cortex lesions. Although preliminary, our re- sults suggest that the performance of frontal patients in this domain is more similar to that of total-order planners; specifically, their performance seemed to exhibit an expo- nential growth rate as problem size increased. More data from frontal patients is necessary to strengthen this claim. Our results have implications for both the psychology and the neuropsychology of planning, as well as for the AI community. First, we have provided evidence that in a do- main in which partial-order planning is advantageous, nor- mal adults perform in a way that suggests the representa- tion of partial-plan ordering relations as partial-orders. Second, we have preliminary evidence that suggests that the frontal cortex of the brain may play a role in this type of planning. While frontal lesion patients’ difficulty with social situations and with temporal ordering is well docu- 7We thank an anonymous reviewer for drawing our attention to this possibility. mented, the effect of this damage on planning is not as well studied. In our work, we have directly tested the abili- ty of these individuals to form and carry out plans, and we believe that their deficits lead to a specific pattern of per- formance with analogs in the computational literature. The utility of partial-order planning, discovered by AI planning researchers, receives further support from the evi- dence that normal humans appear to use partial-order plan representations. Further study may uncover additional fea- tures of the algorithmic basis of human planning, both in normal subjects and in subjects with planning deficits. These studies may provide further support for current AI techniques, but they may also provide alternative models. Given that human planners are proficient in ways that cur- rent AI models are not, the interplay between the human and machine studies should be of interest to those extend- ing the state of the art in AI planning. The fruitfulness of this interplay relies, however, on the coherence of the cross-disciplinary dialogue. We suggest that one way to maximize the impact of psychological experimentation on AI practice is to construct the experiments within the con- ceptual frameworks developed in AI research. Future Work In our ongoing studies we are continuing our examination of the role of frontal cortex in human planning. We are cur- rently testing more frontally lesioned patients, and we have adapted the procedure to make it appropriate for testing 7-ll-year-old children. Based on research suggesting that the frontal cortex does not fully develop until late in child- hood, we expect to find that the younger children display the same exponential performance that our frontal subjects exhibit. This work will provide further evidence for the role of the frontal cortex in human planning behavior. Although the present study focuses on the representation of ordering relations in partial plans, the same framework can be applied to study other aspects of planning, and other aspects of cognition more generally, across the human/ma- chine frontier. AI research often yields precise, quantitative 800 Two Three Four Number of Chores Five Figure 5. Mean Time Viewing Item Information, in seconds. 84 The Arts results that relate computational structures to aspects of performance. By using these results as guides, we can gather data on human cognition that will allow us to make inferences about human computational structures. And of course there is always the possibility that we will be sur- prised; that we will find that the human computational structures were other than we had expected. Since the con- cepts that underlie these investigations will be taken from the computational literature, there should be clear paths by which one could apply the lessons of the surprises in im- proving the state-of-the-art in AI. Conclusions In conclusion, we have found that the results of analytical work in AI planning can be used to investigate human planning. Specifically, we have evidence that suggests that normal human planners use partial-order representations for partial plans, as do most modern AI planning systems. We have further preliminary evidence that suggests that damaged human planning systems use methods akin to those used in less efficient AI systems; specifically, we be- lieve that adults with frontal lobe lesions will be shown to be using planning methods similar to those employed in to- tal-order planners. We believe that the parallels between the human and machine cases are instructive, and that they may lead to further developments in both human and ma- chine studies. Acknowledgments Jordan Grafman funded and guided the development of the Chores software, and, along with Jim Hendler, was instru- mental in launching the larger interdisciplinary effort of which this work is a part. Paula Koseff ran several trials of the experiment on subjects at NIH under Grafman’s super- vision. Chris Chase and Neil Stillings helped in analyzing the results. Jason Juneau worked on the software and is part of the ongoing’experimental team. References Barrett, A.; and Weld, D.S. 1993. 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1,646 | Experiment ally Evaluating Communicative St rat egies: The Effect of the Task Marilyn A. Walker Mitsubishi Electric Research Laboratories* 201 Broadway Cambridge, Ma. 02139, USA walker@merl.com Abstract Effective problem solving among multiple agents requires a better understanding of the role of communication in collaboration. In this paper we show that there are commu- nicative strategies that greatly improve the performance of resource-bounded agents, but that these strategies are highly sensitive to the task requirements, situation parameters and agents’ resource limitations. We base our ar- gument on two sources of evidence: (1) an analysis of a corpus of 55 problem solving dialogues, and (2) experimental simulations of collaborative problem solving dialogues in an experimental world, Design-World, where we parameterize task requirements, agents’ re- sources and communicative strategies. 1 Introduction A common assumption in work on collaborative prob- lem solving is that interaction should be efficient. When language is the mode of interaction, the measure of ef- ficiency has been, in the main, the number of utter- ances required to complete the dialogue [chapanis et al., 19721. One problem with this efficiency measure is that it ignores the cognitive effort required by re- source limited agents in collaborative problem solving. Another problem is that an utterance-based efficiency measure shows no sensitivity to the required quality and robustness of the problem solution. CJognitive effort is involved in processes such as mak- ing inferences and swapping items from long term mem- ory into working memory. When agents have limited working memory, then only a limited number of items can be SALIENT, i.e. accessible in working memory. Since other processes, e.g. inference, operate on salient items, an inference process may require the cognitive effort involved with retrieving items from long term *This research was partially funded by AR0 grant DAAL03-89-C:0031PRI and DARPA grant N00014-90-J- 1863 at the University of Pennsylvania and by Hewlett Packard, U.K. 86 The Arts memory, in addition to the effort involved with rea- soning itself. The required quality and robustness of the problem solution often determines exactly how much cognitive effort is required. This means that a resource-limited agent may do well on some tasks but not on others [Norman and Bobrow, 19751. For example, consider constraint-based tasks where it is difficult for an agent to simultaneously keep all the constraints in mind, or inference-based tasks that require a long deductive chain or the retrieval of multiple premises, where an agent may not be able to simultaneously access all of the required premises. Furthermore, contrary to the efficiency hypothesis, analyses of problem-solving dialogues shows that hu- man agents in dialogue engage in apparently ineffi- cient conversational behavior. For example, naturally- occurring dialogues often include utterances t,hat real- ize facts that are already mutually believed, or that would be mutually believed if agents were logically omniscient [Pollack et al., 1982; Finin et (I!., 1986; Walker, 19931. CJonsider l-26a, which repeats inforrna- tion given in l-20 . . . 1-23: (1) (20) H: Right. Th e maximum amount of credit that you will be able to get will be 400 that they will be able to get will be 400 dollars on their tax return (21) C: 400 dollars for the whole year? (22) H: Yeah it’ll be 20% (23) C: urn hnz (24) H: Now if indeed they pay the $2000 to your wife, that’s great. (25) C: urn hm (26a) H: SO WE HAVE 400 DOLLARS. (26b) Now as far as you are concerned, that could cost you more..... Utterances such as l-26a, that repeat, paraphrase or make inferences explicit, are collectively called INFOR- MATIONALLY REDUNDANT UTTERANCES, IRUs. In 1, the utterances that originally added the belief that they will gel 400 dollars to the context are in italics and the IRU is given in CJAPS. About 12% of the utterances in a corpus of 55 naturally-occurring problem-solving dialogues were IRUs [Walker, 19931, but the occurrence of IRlJs con- tradicts fundamental assumptions of many theories of From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. communication [Allen and Perrault, 19SO], inter dia. The hypothesis that is investigated in this paper is that IRUs such as 1-26a are related to agents’ limited atten- tional and inferential capacity and reflect the fact that beliefs must be salient to be used in deliberation and inference. r Hence apparently redundant information serves an important cognitive function. In order to test the hypothesized relationship of communicative strategies to agents’ resource limits we developed a test-bed environment, Design-World, in which we vary task requirements, agents’ resources and communicative strategies. Our artificial agents are based on a cognitive model of attention and mem- ory. Our experimental results show that communica- tive strategies that incorporate IRUs can help resource- limited cognitive agents coordinate, limit processing, and improve the quality and robustness of the prob- lem solution. We will show that the task determines whether a communicative strategy is beneficial, de- pending on how the task is defined in terms of fault intolerance and the level of belief coordination required. 2 Design-World Task and Agent Architecture KEY: F=FUCHSlA G=GREEN P= PURPLE 54 54 M G ~ n P 55 I G El G 53 1 I I ROOM#l ROOM#2 DESIGNWORLD COLL4BORATNEPIAN:434points Figure 1: Potential Final State for Design-World Task: A Collaborative Plan Achieved by the Dialogue The Design-World task consists of two agents who carry out a dialogue in order to come to an agreement on a furniture layout design for a two room house [Whit- taker et al., 19931. Figure 1 shows a potential final plan constructed as a result of a dialogue. The agents’ shared intention is to design the house, which requires two subparts of designing room-l (the study) and de- signing room-2 (the living room). A room design con- sists of four intentions to PUT a furniture item into the room. Each furniture item has a color and point value, which provides the basis for calculating the utility of ‘The type of IRU in l-26a represents the Attention class of IRUs; Attitude and Consequence IRUs are discussed else- where [Walker, 1992; Walker, 19931. a PUT-ACT involving that furniture item. Agents start with private beliefs about the furniture items they have and their colors. Beliefs about which furniture items exist and how many points they are worth are mutual. I ATl-ENllON/WORKING MEMORY (AW I I ’ Q options MEANS-ENDS REASONER DiTENllONS ri/ lI4TFMlON DELIBBRATION Figure 2: Design-World version of the IRMA Agent Ar- chitecture for Resource-Bounded Agents with Limited Attention (AWM) The agent architecture for deliberation and means- end reasoning is based on the IRMA architecture, also used in the TileWorld simulation environment [Brat- man et al., 1988; Pollack and Ringuette, 19901, with the addition of a model of limited Attention/Working memory, AWM. See figure 2. The Attention/Working Memory model, AWM, is adapted from [Landauer, 19751. While the AWM model is extremely simple, Landauer showed that it could be parameterized to fit many empirical results on human memory and learning [Baddeley, 19861. AWM consists of a three dimensional space in which propositions ac- quired from perceiving the world are stored in chrono- logical sequence according to the location of a moving memory pointer. The sequence of memory loci used for storage constitutes a random walk through memory with each loci a short distance from the previous one. If items are encountered multiple times, they are stored multiple times [Hintzmann and Block, 19711. When an agent retrieves items from memory, search starts from the current pointer location and spreads out in a spherical fashion. Search is restricted to a particular search radius: radius is defined in Hamming distance. For example if the current memory pointer loci is (0 0 0)) the loci distance 1 away would be (0 1 0) (0 -1 0) (0 0 1) (0 0 -1) (-1 0 0) (1 0 0). The actual locations are calculated modulo the memory size. The limit on the search radius defines the capacity of atten- tion/working memory and hence defines which stored Cognitive Modeling 87 beliefs and intentions are SALIENT. The radius of the search sphere in the AWM model is used as the parameter for Design-World agents’ resource-bound on attentional capacity. In the exper- iments below, memory is 16x16~16 and the radius pa- rameter varies between 1 and 16, where AWM of 1 gives severely attention limited agents and AWM of 16 means that everything an agent knows is salient. The advantages of the AWM model is that it was shown to reproduce, in simulation, many results on human memory and learning. Because search starts from the current pointer location, items that have been stored most recently are more likely to be retrieved, pre- dicting recency effects [Baddeley, 19861. Because items that are stored in multiple locations are more likely to be retrieved, the model predicts frequency effects [Lan- dauer, 19751. Because items are stored in chronological sequence, the model produces natural associativity ef- fects [Anderson and Bower, 19731. Because deliberation and means-end reasoning can only operate on salient beliefs, limited attention produces a concomitant infer- ential limitation, i.e. if a belief is not salient it cannot be used in deliberation or means-end-reasoning. This means that mistakes that agents make in their plan- ning process have a plausible cognitive basis. Agents can both fail to access a belief that would allow them to produce an optimal plan, as well as make a mistake in planning if a belief about how the world has changed as a result of planning is not salient. 3 Design-World Communicative Strategies KEY: I- I OPENING : ------T-----, - Speaker Change Possibly NO Speaker Change t PROPOSAL Maybe .---------- ! CLOSING : Figure 3: Discourse Actions for the Design-World Task A COMMUNICATIVE STRATEGY is a strategy for com- municating with another agent, which varies according to the agents’ initiative, amount of information about the task, degree of resource-bounds, and communica- tion style [Walker and Whittaker, 1990; Carletta, 1992; Cawsey ei al., 1992; Guinn, 19931. Design-World agents communicate with an artificial language whose primi- tive communicative a&S are PROPOSE, ACCEPT, RE- JECT, SAY. These primitive acts can be composed to produce higher level discourse acts such as PROPOSALS, ACCEPTANCES, REJECTIONS, OPENINGS and CLOSINGS [Walker, 19931. See figure 3. A discourse act may be left implicit, or may be var- ied to consist of one or more communicative acts. Dis- course acts are different from actions on the environ- ment because they are actions whose intended effect is a change in the other agent’s mental state. Because the other agent is an active intelligence, it is possible for it to supplement an underspecified discourse action with its own processing. The variation in the degree of explicitness of a discourse act is the basis of agents’ communicative strategies. Here we will compare three communicative strategies: (1) All-Implicit; (2) Close- Consequence; and (3) Explicit-Warrant. The All-Implicit strategy is a ‘bare bones’ strategy, exemplified by the partial dialogue in 2. In 2 each ut- terance is shown both as a gloss in italics, and in the artificial language that the agents communicate with. (2) 1: BILL: Th , en, let’s put the green rug in the study. (propose agent-bill agent-kim option-43: put-act (agent-bill green rug room-l)) 2: KIM: Then, let’s put the green lamp in the study. (propose agent-kim agent-bill option-61: put-act (agent-kim green lamp room-l)) 3: BILL: No, instead let’s put the green couch in the study. (reject agent-bill agent-kim option-75: put-act (agent-bill green couch room- 1)) . . . . . In Design-World, unlike TileWorld, an option that is generated via means-end reasoning or from proposals of other agents only becomes an intention if it is AC- CEPTED by both agents. See figure 3. In dialogue 2, Bill makes a proposal in 1, and then Kim implicitly ac- cepts this proposal with a new proposal in 2. In 2-3 Bill rejects Kim’s proposal and makes a counter-proposal. The content of communicative acts are beliefs and (potential) intentions. Dialogue 2 illustrates part of the cycle for achieving a DESIGN-HOUSE plan: (1) indi- vidual agents MEANS-END REASON about options in the domain; (2) individual agents DELIBERATE about which options are preferable; (3) then agents make PROPOS- ALS to other agents, based on the options identified in a reasoning cycle, about actions that CONTRIBUTE to the satisfaction of their intentions; (4) then these propos- als are ACCEPTED or REJECTED by the other agent, or acceptance/rejection is postponed by ASKING for more information. See figure 2. Deliberating whether to ac- cept or reject a proposal is based on beliefs about the proposed action’s utility [Doyle, 19921. Agents parameterized with the All-Implicit strategy do not include IRUs in any discourse ac.t or produce any discourse acts labelled as potentially implicit in figure 3. Agents parameterized with the Close-Consequence 88 The Arts and Explicit-Warrant strategies include IRUs at dia- logue segment closings and in proposals. In dialogue 3 agent CLC uses the Close-Consequence strategy. CLC makes explicit CLOSING statements, such as 3-2, on the completion of the intention associated with a discourse segment. CLC’s CLOSING discourse act also includes IRIJs as in 3-3; CLC makes the infer- ence explicit that since they have agreed on putting the green rug in the study, Bill no longer has the green rug (act-effect inference). (3) 1: BILL: Th en, let’s put the green rug in the study. (propose agent-bill agent-clc option-30: put-act (agent-bill green rug room-l)) 2: CLC: So, we’ve agreed to put the green rug in the study. (close agent-clc agent-bill intended-30: put-act (agent-bill green rug room-l)) 3: c:Lc:: AGENT-BILL DOESN'T HAVE GREEN RUG. (say agent-clc agent-bill bel-48: has n’t (agent-bill green rug)) The Close-Consequence strategy of making infer- ences explicit at the close of a segment is intended to parallel the naturally occurring example in 1. In both cases an inference is made explicit that follows from what has just been said, and the inference is sequen- tially located at the close of a discourse segment. The Explicit-Warrant strategy varies the proposal discourse act by including WARRANT IRUs in each pro- posal. In general a WARRANT for an intention iS a rea- son for adopting the intention, and here WARRANTS are the score propositions that give the utility of the pro- posal, which are mutually believed at the outset of the dialogues. In 4, the WARRANT IRU is in CAPS. (4) 1: IEI: PUTTING IN THE GREEN RUG IS WORTH 56 (say agent-iei agent-iei2 bel-265: score (option-202: put-act (agent-bill green rug room-l) 56)) 2: IEI: Then, let’s put the green rug in the study. (propose agent-iei agent-iei2 option-202: put-act (agent-bill green rug room-l)) Since warrants are used by the other agent in deliber- ation, the Explicit-Warrant strategy can save the other agent the processing involved with determining which facts are relevant for deliberation and retrieving them from memory. The Explicit-Warrant strategy also oc- curs in natural dialogues [Walker, 19931. 4 Design World Task Variations Design-World supports the parameterization of the task so that it can be made more difficult to perform by mak- ing greater processing demands on the agents. These task variations will be shown to interact with variations in communicative strategies and attentional capacity in section 5. Standard Task The Standard task is defined so that the RAW SCORE that agents achieve for a DESIGN-YOUSE plan, con- structed via the dialogue, is the sum of all the furniture DESIGN HOUSE LT..:. /\ /) DESIGN ROOM- 1 DESIGN ROOM-2 Figure 4: Evaluating Task Invalids: for some tasks in- valid steps invalidate the whole plan. DESIGN ROOM-2 2qT% .?f Pi Pi p <i r?, 4 ? ” ?” +.. w k. w ? . . ki Gi -- w. ‘5 1 Wi ,--------------------------------, I KEY : I I : P = Intention to PUT(A,F,R.T) : i W = belief that SCO~(F:NUM) ! c = contributes relation . w = warrants relation I L--------------------- ---------- Figure 5: Tasks can differ as to the level of mutual belief required. Some tasks require that the WARRANT W, a reason for doing P, is mutually believed and others don’t. items for each valid step in their plan. The point values for invalid steps in the plan are simply subtracted from the score so that agents are not heavily penalized for making mistakes. Zero Invalids Task The Zero-Invalids Task is a fault-intolerant version of the task in which any invalid intention invalidates the whole plan. In general, the effect of making a mistake in a plan depends on how interdependent different sub- parts of the problem solution are.2 Figure 4 shows the choices for the effect of invalid steps for the Design- World task. The score for invalid steps (mistakes) can just be subtracted out; this is how the Standard task is defined. Alternately, invalid steps can propagate up so that an invalid PUT-ACT means that the Design-Room plan is invalid. Finally, mistakes can completely propa- gate so that the Design-House plan is invalid if one step is invalid, as in the Zero-Invalids task. 2Contrast aircraft scheduling with furnishing a room. Cognitive Modeling 89 Zero NonMat thing Beliefs Task The Zero-Nonmatching-Beliefs task is designed to in- vestigate the effect of the level of agreement that agents must achieve. Figure 4 illustrates different degrees of agreeing in a collaborative task, e.g. agents may agree on the actions to be done, but not agree on the reasons for intending that action.3 The Zero-NonMatching- Beliefs task is defined so that a WARRANT W, a reason for doing P, must be mutually supposed. 5 Experimental Results cost - clc-kim bill-kim C= 1 , I = 1 , R = 0.01 Figure 6: Close-Consequence can be detrimental in the Standard Task. Strategy 1 is the combination of an All-Implicit agent with a Close-Consequence agent and Strategy 2 is two All-Implicit agents, Task = Standard, commcost = 1, infcost = 1, retcost = .Ol We wish to evaluate the relative benefits of the com- municati ve strategies in various tasks for a range of resource limits. In section 4 we defined an objecti ve performance measure for the DESIGN-HOUSE plan for each task variation. We must also take cognitive costs into account. Because cognitive effort can vary accord- ing to the communication situation and the agent ar- chitecture, performance evaluation introduces three ad- ditional parameters: (1) COMMCOST: cost of sending a message; (2) INFCOST: cost of inference; and (3) RET- COST: cost of retrieval from memory: PERFORMANCE= Task Defined RAW SCORE - (cOMMCOST x total messages) - (INFCOST x total inferences) - (RETCOST x total retrievals) 3CJonsider a union/ management negotiation party has different reasons for any agreement. where each We simulate 100 dialogues at each parameter setting and calculate the normalized performance distributions for each sample run. In the results to follow, COMM- COST, INFCOST and RETCOST are fixed at l,l, .Ol re- spectively, and the parameters that are varied are (1) communication strategy; (2) task definition; and (3) AWM settings. 4 Differences in the performance distri- butions for each set of parameters are evaluated for sig- nificance over the 100 dialogues using the Kolmogorov- Smirnov (KS) two sample test [Siegel, 19561. A strategy A is defined to be BENEFICIAL as com- pared to a strategy B, for a set of fixed parameter settings, if the difference in distributions using the Kolmogorov-Smirnov two sample test is significant at p < .05, in the positive direction, for two or more AWM settings. A strategy is DETRIMENTAL if the differences go in the negative direction. Strategies may be neither BENEFICIAL or DETRIMENTAL, since there may be no difference between two strategies. A DIFFERENCE PLOT such as that in figure 6 will be used to summarize a comparison of strategy 1 and strat- egy 2. In the comparisons below, strategy 1 is either Close-Consequence or Explicit-Warrant and strategy 2 is the All-Implicit strategy. Differences in perfor- mance between two strategies are plotted on the Y-axis against AWM parameter settings on the X-axis. Each point in the plot represents the difference in the means of 100 runs of each strategy at a particular AWM set- ting. These plots summarize the information from 18 performance distributions (1800 simulated dialogues). Every simulation run varies the AWM radius from 1 to 16 to test whether a strategy only has an effect at par- ticular AWM settings. If the plot is above the dotted line for 2 or more AWM settings, then strategy 1 may be BENEFICIAL, depending on whether the differences are significant .5 In the reminder of this section, we first compare within strategy, for each task definition and show that whether or not a strategy is beneficial depends on the task. Then we compare across strategies for a partic- ular task, showing that the interaction of the strategy and task varies according to the strategy. The compar- isons will show that what counts as a good collaborative strategy depends on cognitive limits on attention and the definition of success for the task. 5.1 Close Consequence The difference plot in figure 6 shows that Close- Consequence is DETRIMENTAL in the Standard task at AWM of 1 . . . 5 (KS > 0.19, p < .05). In contrast, if the task is the fault-intolerant Zero- Invalids task, then the Close-Consequence strategy is 4See [Walker, 1993; Walker, 19951 for results related to varying the relative cost of retrieval, inference and communication. 5Visual differ ence in means and distributional differences need not be correlated, however KS significance values will be given with each figure, and difference plots are much more concise than actual distributions. 90 The Arts inval - clc-kim bill-kim C- 1 , I = 1 , R = 0.01 match - clc-kim bill-kim CL 1 , I = 1 , R = 0.01 Figure 7: Close Consequence is beneficial for Zero- Invalids Task. Strategy 1 is the combination of an All-Implicit agent with a Close-Consequence agent and Strategy 2 is two All-Implicit agents, Task = Zero- Invalid, commcost = 1, infcost = 1, retcost = .O 1 BENEFICIAL. Figure 7 demonstrates that strategies which include Consequence IRIJs can increase the ro- bustness of the planning process by decreasing the fre- quency with which agents make mistakes (KS for AWM of 3 to 6 > .19, p < .05). This is a direct result of re- hearsing the act-effect inferences, making it unlikely that attention-limited agents will forget that they have already used a furniture item. Figure 8 shows that the Close-Consequence strategy is detrimental when the task requires agents to achieve matching beliefs on the WARRANTS for their intentions (KS 1,3) > 0.3, p < .Ol). This is because IRlJs dis- place other facts from AWM. In this case agents for- get the scores of furniture pieces under consideration, which are the warrants for their intentions. Thus here, as elsewhere, we see that IRUs can be detrimental by making agents forget critical information. 5.2 Explicit Warrant Figure 9 shows that Explicit-Warrant is beneficial in the Standard task at AWM values of 3 and above. Here, the scores improve because the beliefs necessary for de- liberating the proposal are made available in the cur- rent context with each proposal (KS for AWM of 3 and above > .23, p < .Ol), so that agents don’t have to search memory for them. At AWM parameter settings of 16, where agents can search a huge belief space for beliefs to be used as warrants, the saving in processing time is substantial. When the task is Zero-Invalid (no figure due to space), the benefits of the Explicit-Warrant strategy are Figure 8: Close-Consequence is detrimental for Zero- Nonmatching-Beliefs Task. Strategy 1 is the combina- tion of an All-Implicit agent with a Close-Consequence agent and Strategy 2 is two All-Implicit agents, Task = Zero-Nonmatching-Beliefs, commcost = 1, infcost = 1, retcost = .Ol cost - iei-iei2 bill-kim C= 1 , I = 1 , R = 0.01 A”e”b~“AVork”~ Memory Figure 9: Explicit-Warrant saves Retrieval costs: Strat- egy 1 is two Explicit-Warrant agents and strategy 2 is two All-Implicit agents: Task = Standard, commcost = 1, infcost = 1, retcost = .Ol dampened from the benefits of the Standard task, be- cause Explicit-Warrant does nothing to address the rea- sons for agents making mistakes. In comparison with the All-Implicit strategy, it is detrimental at AWM of Cognitivr: Modeling 91 1 and 2, but is still beneficial at AWM of 5,6,7, and 11. match - iei-iei2 bill-kim C- 1 , I = 1 , R = 0.01 Figure 10: Explicit-Warrant is beneficial for Zero- NonMatching-Beliefs Task: Strategy 1 is two Explicit- Warrant agents and strategy 2 is two All-Implicit agents: Task = Zero-Nonmatching-Beliefs, commcost = 1, infcost = 1, retcost = .Ol In contrast to Close-Consequence, the Explicit- Warrant strategy is highly beneficial when the task is Zero-NonMatching-Beliefs, see figure 10 (KS > .23 for AWM from 2 to 11, p < .Ol). When agents must agree on the warrants underlying their intentions, including these warrants with proposals is a good strategy even if the agent already knows the warrants. This is due to agents’ resource limits, which means that retrieval is indeterminate and that there are costs associated with retrieving warrants from memory. At high AWM the differences between the two strategies are small. 6 Related Work Design-World was inspired by the TileWorld simula- tion environment: a rapidly changing robot world in which an artificial agent attempts to optimize rea- soning and planning [Pollack and Ringuette, 1990; Hanks e1 al., 19931. TileWorld is a single agent world in which the agent interacts with its environment, rather than with another agent. Design-World uses similar methods to test a theory of the effect of resource limits on communicative behavior between two agents. The belief reasoning mechanism of Design-World agents was informed by the theory of belief revision and the multi-agent simulation environment developed in the Automated Librarian project [Galliers, 1991; Cawsey et al., 19921. Th e communicative acts and dis- course acts used by Design-World agents are similar to those used in [Carletta, 1992; Cawsey et al., 1992; Sidner, 1992; Stein and Thiel, 19931. Design-World is also based on the method used in Carletta’s JAM simulation for the Edinburgh Map- Task [Carletta, 19921. JAM is based on the Map-Task Dialogue corpus, where the goal of the task is for the planning agent, the instructor, to instruct the reactive agent, the instructee, how to get from one place to an- other on the map. JAM focuses on efficient strategies for recovery from error and parametrizes agents accord- ing to their communicative and error recovery strate- gies. Given good error recovery strategies, Carletta ar- gues that ‘high risk’ strategies are more efficient, where efficiency is a measure of the number of utterances in the dialogue. While the focus here is different, we have shown that that the number of utterances is just one pa- rameter for evaluating performance, and that the task definition determines when strategies are effective. 7 Conclusion In this paper we showed that collaborative communica- tive behavior cannot be defined in the abstract: what counts as collaborative depends on the task, and the definition of success in the task. We used two empirical methods to support our argument: corpus based anal- ysis and experimentation in Design-World. The meth- ods and the focus of this work are novel; previous work on resource limited agents has not examined the role of communicative strategies in multi-agent interaction whereas work on communication has not considered the effects of resource limits. We showed that strategies that are inefficient un- der assumptions of perfect reasoners with unlimited attention and retrieval are effective with resource lim- ited agents. Furthermore, different tasks make different cognitive demands, and place different requirements on agents’ collaborative behavior. Tasks which require a high level of belief coordination can benefit from com- municative strategies that include redundancy. Fault intolerant tasks benefit from redundancy for rehearsing the effects of actions. Because the communicative strategies that we tested were based on a corpus analysis of human human fi- nancial advice dialogues and because variations in the Design-World task were parametrized, we believe the results presented here may be domain independent, though clearly more research is needed. Here we fixed the parameters for the cost of commu- nication, inference and retrieval, only discussed a few of the implemented discourse strategies, and didn’t dis- cuss Design-World parameters that increase the infer- ential complexity of the task and that limit inferential processing. Elsewhere we show that: (1) when retrieval is free or when communication cost is high, that the Explicit-Warrant strategy is detrimental at low AWM [Walker, 19931; (2) some IRU strategies are only bene- ficial when inferential complexity is higher than in the Standard Task [Walker, 19931; (3) IRUs that make in- ferences explicit can help inference limited agents per- form as well as logically omniscient ones [Walker, 19951. 92 The Arts One ramification of the results presented here is that experimental environments for testing agent ar- chitectures should support task variation [Pollack and Ringuette, 1990; Hanks e2 al., 19931. Furthermore the task variation should test aspects of the interaction of the agents involved. These results also inform the de- sign of multi-agent problem solving systems and for sys- tems for teaching, advice and explanation. References [Allen and Perrault, 19SO] James F. Allen and C. Ray- mond Perrault. Ahalyzing intention in utterances. 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1,647 | A Reading Agent Tam&ha Carpenter Richard Alterman* tamitha@cs.brandeis.edu alterman@cs.brandeis.edu (617) 7362718 (617) 736-2703 Department of Computer Science and Center for Complex Systems Brandeis University Waltham, MA 02254 Abstract * Improving the reading skill. Recent work in agency has explored the interactive nature of goal-driven behavior (“activity”). An interactive agent is responsive to events and is affected by and effects the context in which it exists. Our contention is that interaction is also an important characteristic of a reader. By treating reading as an activity, the reading agent can interact with the text, achieving goals and planning what to read, when to read, and how to read. This paper will discuss how reading within a context of activity provides goals and enables planning, thus creating the reading agent. The system described, SPRITe, reads natural language, primarily instructions, in order to facilitate other activities. e Responding to changes in the environment (interactivity). Other systems have explored some of these properties. Maybury (1991) shows a planning system that creates instructions (as well as other types of text). In Ram (199 1 ), knowledge goals were used to take advantage of information as it was read; however, the reading was not a planned activity, and so text was read sequentially from beginning to end. Several other systems have developed models of instruction usage (e.g., Chapman, 1990; Badler et al., 1990; Vere and Bickmore, 1990). However, these models have not taken the step towards building a reading agent that interacts with the instructions, using goals and planning strategies. Introduction Recent work in agency (e.g., Suchman, 1987; Agre, 1988; Chapman, 1990) has explored the interactive nature of goal-driven behavior (“activity”). When reading is viewed as an activity, the same issues come into play. In order to define a “reading agent”, it is important to establish how an agent interacts with text, how reading interacts with action, and how activity changes the reading process. For example, consider trying to read the instructions for assembling a lawnmower. If reading occurs in isolation from the assembling activity, the instructions must be read from beginning to end, they can only be understood in general terms (e.g., the reference to a “bolt” can only be concrete once the reader has experienced the bolt used in the lawnmower), and the understanding that results may or may not be adequate for the agent to successfully assemble the lawnmower without referring back to the instructions. A reading agent has several properties that make the reading process active. These include: 0 Using goals. * Planning the reading activity. 0 Reading in the context of a larger activity. The properties of a reading agent have been implemented in a model called SPRITe (using Structure to Plan the Reading of Instructional TExt). Instead of reading sequentially, SPRITe uses reading goals and planning techniques to guide how it reads instructions. In addition, SPRITe is integrated in a model of agent intelligence known as FLOABN (Alterman et al., 1991). FLOABN works with and learns about mechanical and electronic devices and their instructions. SPRITe primarily interacts with FLOABN’s activity planner, an adaptive planning system for engaging in activity (see Z&o-Wolf, 1993, for details). A Cognitive eading Model In Carpenter (1993), a protocol study was presented which studied 12 people using instructions. The subjects, students and faculty who had never before used a fax machine, were given the machine’s instructions and asked to send a fax. The instructions were presented on a computer monitor one line at a time and the instruction usage was recorded. Subjects were also asked to talk aloud while sending the fax. Their comments were recorded and matched to the instructions showing on the monitor at the time each comment was made. * This author is supported in part by a grant from Digital Equipment Corporation. In spite of the length (approx. 70 pages) and difficulty of the instructions, every subject was able to use the instructions well enough to complete the requested task. 62 The Arts From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. No one actually read the entire set of instructions. With one exception (a subject who read none of the instructions), the subjects all used the instructions periodically during the interaction until they found text that clarified whatever part of the task was at hand. This text was then read to whatever depth was necessary to extract enough content to continue with the activity. The subjects used structural and contextual clues in their navigation of the text. The ability to use the structural properties of the instructions is due to their predictable nature. Van Dijk and Kintsch (1983) call the nature of a type of text (e.g., instructions, short stories, et cetera) its superstructure. That is, certain structural features (e.g., numbered lists) are used by instructions for specific purposes (e.g., listing a set of steps). The better a reader’s knowledge of structure usage, the better he is able to predict the organization of a text. We have endeavored to create a model of reading that has abilities similar to those portrayed by the subjects of the protocol study. Three primary conclusions from the protocol study reflect the design principles of SPlUTe: 1. The subjects interleaved reading with action (e.g., see figure 1). 2. The subjects generally seemed to have some goal in mind, which caused them to skip or reread certain portions of text. 3. The subjects became increasingly confident and skilled in their usage of the instructions. For example, the subjects would often remember where a certain piece of text was located. By following these behaviors, SPRITe is able to choose when to read, what to read, and how to read. 1 TEXT Uee the keypad to enter the telephone number, then prees the Start key. : 2 SARA "Use the keypad to enter the telephone number. And then press the..." : 3 FAX <dial beeps> : 4 SARA Then press the &art key. She looks for the start key, This... 5 FAX <beep> 6 TEXT Lift the telephone handset, Using the telephone, press the Start key When the remote ready tones are heard, then replace the handset. Figure 1: An excerpt fiom the protocol study illustrating the interleaving of reading and action. ‘TEXT refers to the line of text showing on the monitor during the current point of interaction and ‘FAX’ showsthe sounds made by the device in response to the user’s actions. FLOABN’s primary method of activity is based on adaptive planning (Alterman, 1988). The main components of FLQABN (see figure 2) are independent agents (cf. “Society of Mind”: Minsky, 1986). Each is capable of rmming without the other, but in combination, they can accomplish more. This is because the action planner provides the reader with goals and activity against which a concrete understanding of text is made, and the reader provides access to new sources of knowledge that aid the activity’s interaction. In order for the exchange of information to be made successfully, the communication process between SPlUTe and the action planner must be defined. For FLOABN’s communication, we have defined a set of request and response frames -- a set of templates that, when filed out, provide a predictable structure for information. When the action planner requests information from SPRITe, it chooses one of about 10 request frames to ftll out. A request frame suggests a reading goal and provides information such as which plan is in use, a trace of the activity, and the how the plan failed. Each request frame corresponds to a type of breakdown the action planner is likely to encounter, and is designed to provide information about the agent’s activity that the reader is likely to need in order to read the instructions and help the action planner recover. Consider the following “Find-part-r&” request: (request :name find-part-ref :device fax-machine-001 :plan photocopier :part BDF) When this request was made, the action planner was attempting to use a fax machine by adapting its plan for using a photocopier. When the planner encountered the unfamiliar term “ADF” (produced by an earlier access to the instructions), it asked the reader for a deftition. ABN Figure 2: Communication between reading and action agents. Cognitive Modeling 63 The reader has a list of about 20 response frames. Each request frame has a subset of associated response frames from which the reader must choose. For example, if the planner had made a “Find Object” request, the reader would choose one of the following: * Object location- gives the location of object. l Alternative ‘object- indicates a different object can be used for the same task. * Missing objed- indicates the object does not exist and suggests plan modifications. The “find-part-r&’ request frame has only one associated response frame: term-defmition. In order to fill out the term-definition response frame, SPRITe first reads the instructions and determines that the definition of ADF is “automatic document feeder”. SPRITe then fills out the response frame as follows: (response:name term-definition :devicefax-machine-001 :plan photocopier :term ADF :def automatic- document-feeder) With this new knowledge, the action planner can use the ADF as part of its interaction with the fax machine. How to Read SPRITe (see figure 3) reads instructions using several methods. The overall control of SPRITe is based on the same adaptive planning model as FLOABN’s main system. When SPRITe first starts reading, it selects one of about 25 reading plans (e.g., see figure 5) based on the information provided by the request frame and the observable characteristics (i.e., top-level structure) of the text. As reading takes place, the selected plan is adapted to better suit the instructions and/or reading goal of the current situation. This allows SPRITe to react to differences in organization and style between various pieces of text. This also allows the same request frame to cause different reading behavior depending on the instructions and the context. When SPRITe has successfully read the instructions, it stores three types of information: 1. SPRITe remembers the successful reading steps that were performed as a new plan. This plan is indexed and stored in plan memory. 2. SPRITe remembers the characteristics of the instructions that corresponded to the successful reading steps, thus building a representation of the instructions that will facilitate future usage. 3. SPRJTe augments semantic memory with the knowledge it gained through reading. SPRITe’s ability to learn in these ways increases its ability to read effectively and efficiently in the future. 64 The Arts 1%: The Reading Agent Plan Seiection: I -b FlowofControl e FbwofKnowledge Figure 3: SPRITe -- Inside the Reading Agent During the execution of reading plans, SPRITe must *understand’ the text it is reading. Understanding is accomplished, at least in part, by establishing coherence. SPRITe establishes two types of coherence: l Wfzzal coherence: The coMection of the meaning of text to other text being read. * coherence with actitity The connection of the meaning of the text to the activity of the agent. Even if the text is coherent with itself, if the connection of the text with the device and its activity cannot be established, the instructions are useless because they cannot be applied. Coherence of text with activity is not only the association of terms in the text with objects in the world (external rekkence), but also the association of the text with the agent’s current interaction (i.e., results of plan steps taken), knowledge of how devices work, and possibilities for future action. Currently, coherence is established using a modification of the marker passing techniques described in Norvig (1989). SPBITe’s knowledge source is a semantic network in which basic concepts (e.g., hierarchy for types of money) are combined with detailed representations of approximately 50 devices. Top Level Control This section will describe in detail the process SPBITe uses to read instructions in the context of FLOABN using a simulated1 Airfone for the first time. To begin, FLOABN approaches the device, and has the expectation that it will work like a pay telephone. lSimulations are based on actual usage of the device. However, when FLOABN tries to execute its plan for using a pay phone by lifting the receiver, it doesn’t work. FLOABN tries adapting its plan, but none of the steps in the pay phone plan is executable. So, FLOABN calls SPRITe with the following request: (request :name next-step :deviceAirfone-001 :plan pay-phone :failed-steps (lift-receiver listen-for- dial-tone insert-coin)) This request frame has four required entries: a the name of the request (which generally is the reading goal) * what device FLOABN is trying to use * which action plan FLOABN is using * what plan steps have failed so far A fifth optional entry, what plan steps have succeeded, is not present in this instance of the request frame. SPRITe’s algorithm is shown in figure 4. In step 1, SPRITe notes that the request type is “next-step”. In step 2, SPRITe locates the Airfone instructions and builds a representation of them, which initially contains a list of the instructions’ top-level text structures: ‘title’, ‘italic-text’, plain-text', ‘enumerated-list’, and ‘big-text’ . In step 3, SPRITe chooses a reading plan based on the reading goal and indices. The reading goal is matched against the name of the request frame, and the indices are function calls which probe the current situation (i.e., characteristics of the instructions and details from the request frame). For the current example, the plan in figure 5 was chosen because the goal, “next-step”, matches the current request frame and because the index evaluates to true (the Airfone instructions are shorter than 2 pages). Since all the indices match, no future change is anticipated. Step 4 executes the plan. Each plan has three tasks: 1. locate a likely location for relevant text 2. verify that the content of the selected location is going to help (optional) 3. extract the content of the text The verify and extract steps require the coherence mechanism to build representations of the text at varying levels of detail, while the locate step uses SPRITe’ s knowledge of instructional text structure and usage to choose the most likely candidate for reading. The locate step is responsible for finding a starting point in the instructions from which the rest of the plan can work and storing that location in the variable location. The locate step can occur in two ways: using the method in the :locate portion of the plan or using the representation that SPRITe has built of the instructions. In the current example, SPRITe has not developed its representation of the instructions yet, so the :locate method of the “find-steps-short-text” plan is used, which locates the enumerated list in the Airfone instructions. If no enumerated list had been found, the plan would fail, and SPRITe would either attempt adapting the plan or choosing another plan. The vetifi step uses the coherence mechanism to determine whether the “dumb” search done by the locate step actually found an appropriate piece of text. The verify portion of the “find-steps-short-text” plan looks for a description component - a piece of text that describes the purpose or content of the list. According to SPRITe’s knowledge of instruction superstructures, the description component is an optional first line of text in the list that is not preceded by the “\item” formatting command. In the Airfone example, the enumerated list does not have a description component. This is not a failing condition for this plan. Only if a description does exist but is not coherent with the reading goal would the verify step fail. If this were the case, SPRITe would go back to the locate step and find another location. Finally, SPRITe performs the extract step. The call to “read-enum-list” is actually a call to a sub-plan that uses marker passing to establish coherence between the content of the enumerated list and the plan steps provided 1. Identify request type. 2. If instructions for current reading task have been used before: then locate previously constructed representation else build an initial representation for the instructions 3. Select reading plan based on request iFame and characteristics of the instructions. a. If any unmatched indices occur, anticipate future change. 4. Execute readingplan and adapt. a. Sequence through steps to locate text, verify position, and extract content. b. If failure occurs, adapt and either restart step 4 or continue. c. If adaptation is unsuccessful restart step 3. 5. Remember successful plan steps and store in plan memory. 6. Prepare and send response ii-am. 7. Return control to ACTION AGENT (or to READING AGENT during a recursive call). Figure 4: SPRITe's top-level control. Cognitive Modeling 65 (plan -name * find-steps-short-text :goal next-step :indices (short-text) :plan (:locate (assoc f\begin(enumerate) text) :verify (if (not (next-type location '\item)) (skim (first location) 'find-steps)) :extract (read-enum-list location (getf :failed-steps request) (getf : successful-steps request) 1) 1 Figure 5: The reading plan chosen in the Airfone example. by the request frame. This instance of “read-enum-list” skims the first item (line 5) of the enumerated list and discovers the coherence between the instruction “insert credit card” and the failed-step “insert-coin”. Step 4 also includes the provision for adaptation. In the Airfone example, the plan was successfully executed without the need to adapt. If adaptation had been necessary, SPRITe would have first examined any unmatched indices, as well as features of the text and the request frame that were not utihzed by the indices. Using this information, SPRITe would have selected either a new locate step (possibly with a related verify step) or a new extract step from a library of location and extraction techniques. The new step would be inserted into the plan and execution would proceed. Adding to Plan Memory SPRITe performs step 5 of its procedure and creates a new plan. The new plan, shown in figure 6, is a copy of the original plan with a few changes. First, the text that was used to develop this plan is remembered (line 2). Although this plan could be used with any text, it will receive preferential treatment when the Airfone instructions are used again. Second, the plan has been modified to specifically find the iirst step of an action plan. This is reflected in the creation of a new index (line 5) which remembers that no successfil-steps were provided in the request frame. Also, the extract step (line 7) has been shortened to skim only the hrsf item in the enumerated list. In addition, the verify step was dropped, since it was not successfully executed. SPRITe then prepares the folIowing response frame: (response :name replace-step :deviceAirfone-001 :plan pay-phone :old-step (insert-coin) *new-step . (insert credit-card)) Control is then returned to the action planner, which proceduralizes the “insert credit-card” step into its own plan and continues interaction with the Airfone. (For discussion of the procedurahzation of instructions, see Alterman et al., 1991.) The Airfone procedure continues to deviate from the expectations provided by the pay telephone action plan. After inserting the credit card, the action planner is still unable to lift the receiver. Control is given to SPRITe with the following request frame: (request:name next-step :deviceAirfone-001 :plan pay-phone :successful-steps (insert-credit-card) :failed-steps (lift-receiver listen-for-dial-tone)) SPRITe selects the plan shown in figure 5 again, because both its goal and its index match. The plan created by the previous episode (figure 6) is not selected, even though the :text field matches the current text, because the new index (no :successful-steps field in the request frame) is not matched. Unlike the previous episode, SPRITe does not use the :locate step provided by the plan, since SPRITe’s current representation of the Airfone instructions contains the enumerated list. The :verify step is tried again, with the same results as before. Finally, the :extract step skims the list items, recognizing that the “insert credit card” (plan 1 :name find-steps-short-text-001 2 :text Airfone-instructions 3 :goal next-step 4 :indices ((short-text text) 5 (null (getf :successful- steps request))) 6 :plan (:locate (assoc '\begin(enumerate) text) 7 :extract (skim-item (assoc '\item location) (getf :failed-steps request) 1) 1 Figure 6: A new reading plan created during interaction with the Airfone. 66 The Arts item matches the successful step “insert-credit-card“. SPRITe then looks at the next item in the list: “lower door handle over card”. This is interpreted as a “close” step, similar to the close step required to play a cassette in a tape deck. A new plan is created in the same way as the plan in figure 6. However, the :locate step is changed to reflect the usage of SPRITe’ s representation of the instructions. Control is then returned to the action planner with the new information. With this information, the action planner is finally able to lift the receiver, but is immediately thwarted once again when the “listen for dial tone” step fails. This time, when SPRITe receives control, it selects the new plan (shown in figure 7). The new plan is selected over the original plan because the :text field matches. The enumerated list is selected from SPRITe’s representation of the instructions, and the list is perused. SPRITe matches the first two items in the enumerated list with the successful steps given in the request frame. The third item in the instructions says to “observe lighted display”. SPRITe interprets this as a reading instruction. However, the display is blank since the action planner has already lifted the receiver. So, SPRJTe reads the entire instruction, which indicates that the display would have said when to lift the receiver. Since the action planner already successfully lifted the receiver, SPRITe interprets this instruction as being equivalent to the step of “lift-receiver”. The next item in the list, “press green DIAL TONE button”, is then interpreted as an activation step. FLOABN is now able to complete interaction with the Airfone without further help from the instructions. Conchsion This paper has described an intelligent reading agent, (plan :name find-steps-short-text-002 :text Airfone-instructions :goal next-step :indices((short-text text)) :plan ( : locate (or (getf : enum- list in&-rep) (assoc '\begin(enumerate) text)) : extract (read-enum-list location (getf : failed- steps request) tgetf :successful-steps request)))) Figure 7: Another reading plan created during interaction with the Airfone. SPRITe. SPRITe uses planning techniques to perform efficient, goal-driven reading. It develops plans to read a given set of instructions in the context of engagement with a particular device. By planning, adapting, and storing new reading plans, SPRITe builds a library of concrete methods for reading which over time improves SPlUTe’s ability to read both the texts from which the methods were created, and with instructions in general. SPRITe is embedded in a larger agent, FLOABN. Combining the activities of reading and action produces an agent more capable than the separate activities could be. The action provides context and goals for reading, which allow reading to be selective and produce concrete representations of the text. In return, reading provides a detailed knowledge source to the activity planner. eferences Agre, P.E. (1988). The dynamic structure of everyday life. Technical Report AI-TR 1085, MIT Artificial Intelligence Laboratory. Alterman, R., Zito-Wolf, R., & Carpenter, T. (1991). Interaction, Comprehension, and Instruction Usage. Yi%e Journal oflearning Sciences, 1(3&4):361-398. Alterman, R. (1988). Adaptive Planning. Cognitive Science, 12:393-421. Badler, N., Webber, B., Kalita, J., & Esakov, J. (1990). Animation from instructions. In Badler, N., Barsky, B., & Zeltzer, D. (Eds.), Making Them Move: Mechanics, Control and Animation of Articula ted Figures, pp. 5 l- 93. Morgan Kaufmann, Los Altos, CA. Carpenter, T. (1993). Using Instructions -- A Protocol Study. Presented at the Third Annual Meeting of the Society for Text and Discourse. Chapman, D. (1990). Vision, instructions, and action. Technical Report AI-TR 1024, MIT Artificial Intelligence Laboratory. Maybury, M.T. (1991). Planning Multisentential English Text Using Communicative Acts. PhD thesis, University of Cambridge, pp. 178-192. Norvig, P. (1989). Marker passing as a weak method for text inferencing. Cognitive Science, 13 (4) : 569620. Ram, A. (1991). A Theory of Questions and Question Asking. T&e Journal of Learning Sciences, 1(3&4). Suchman, L. A. (1987). Plans and Situated Actions. Cambridge University Press. van Dijk, T. & Kintsch, W. (1983). Strategies of discourse comprehension. Academic Press. Vere, S. & Bickmore, T. (1990). A basic agent. Computational Intelligence, 6:41-60. Zito-Wolf, R. (1993). Case-Based Representations for Procedural Knou3edge. PhD thesis, Brandeis University. Cognitive Modeling 67 | 1994 | 296 |
1,648 | Automated Accompaniment of Musical Ensembles Lorin Grubb and Roger B. Dannenberg School of Computer Science, Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213 lgrubb@cs.cmu.edu and rbd@cs.cmu.edu Abstract’ This paper describes a computer accompaniment sys- tem capable of providing musical accompaniment for an ensemble of performers. The system tracks the per- formance of each musician in the ensemble to determine current score location and tempo of the ensemble. “Missing parts” in the composition (i.e., the accompaniment) are synthesized and synchronized to the ensemble. The paper presents an overview of the component problems of automated musical accompani- ment and discusses solutions and their implementation. The system has been tested with solo performers as well as ensembles having as many as three performers. ducing an accompaniment in synchrony with the detected performance. A solution for each subproblem and a method for its implementation is also provided. Introduction Musical performance in ensembles requires more than just mastery of an instrument. Ensemble performers must be able to listen to one another and react to changes in the per- formance. These include changes in tempo and loudness, for example. Even following the flow of performance can be difficult as instruments drop out and re-enter. Each per- former must synchronize with the ensemble, that is, play at the appropriate time and with the appropriate tempo. The computer accompaniment problem is to track, in real-time, a performance by a solo musician or a group of musicians and to produce the “missing” voices of the composition in synchrony with the other performers. It is assumed that all performers, including the computer, play from a score that specifies the pitches and their musical timing. An ensemble accompaniment system is a flexible alternative to playing along with a recording when a full ensemble is not avail- able. It also enables new compositions combining human and machine performers. The system presented here extends the capabilities of previous accompaniment systems by performing with mul- tiple musicians. To follow an ensemble, the solutions to the first and second subproblems in the solo accompaniment system must be simultaneously applied to multiple per- formers. Before taking actions to control an accompaniment (the solution to the third subproblem), the ensemble system must examine and combine the score position and tempo suggestions produced through tracking multiple performers. Note that this may require resolution of conflicting information. This paper details specifics of the problem of tracking multiple performers and combin- ing the results in order to produce an accompaniment. A solution to the problem and a brief description of its imple- mentation are provided. We conclude with a discussion of some qualitative results of actually using the system to accompany multiple performers. Problem Description We describe a system developed to provide accompani- ment for an ensemble. Several computer accompaniment systems for following solo performers have been described (Dannenberg 1984, Vercoe 1984, Baird et. al. 1993). In (Dannenberg 1984) the accompaniment problem is parti- tioned into three distinct subproblems: 1) detecting what the soloist has performed, 2) determining the score position of the soloist from the detected performance, and 3) pro- The performance-monitoring component of a computer accompaniment system must process a digital representa- tion of the performance in order to extract required parameters. These parameters might include fundamental pitch, note duration, dynamic (relative loudness), and artic- ulation. The representation of the performance, in the simplest case, might be MIDI (Musical Instrument Digital Interface) messages (Rothstein 1992) sent from an elec- tronic keyboard. Since most of the required parameters are explicitly represented in MIDI messages, extracting the needed information is simple. In a more difficult case, the representation is an audio signal from a microphone. This is often the representation obtained from wind instruments, for example. Extracting musical parameters from this type of input requires more analysis than does processing MIDI messages. Fortunately, there exist commercially available devices for converting analog input into MIDI-encoded pitch and amplitude information. The most difficult case is multiple instruments recorded with a single microphone. We do not address this case. 1. This material is based upon work supported under a Once basic parameters (like pitch) have been extracted National Science Foundation Graduate Research Fellow- from the performance, the next task for accompaniment ship systems is to estimate the performer’s location in the score. 94 The Arts From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. This involves comparing the sequence of extracted perfor- mance parameters to the expected sequence of parameters (the given score), attempting to find the best match. A robust pattern matcher is required because a perfect perfor- mance cannot guaranteed. As successive score locations are identified and time stamped, tempo is estimated by comparing the actual time difference between performed events and the expected time difference between the corresponding score events. Since it is well-known that performers alter durations of particular beats within a measure for expressive purposes (Desain & Honing 1992), the accompaniment system must average successive time difference comparisons to avoid sudden drastic tempo changes. Accompaniment systems also produce the actual accom- paniment. Generally, an accompaniment must be continuous and aesthetically acceptable, yet reactive to the performer’s omissions, errors, and tempo changes. If the performer increases or decreases the tempo slightly for interpretive reasons, the accompaniment should do like- wise. If the performer pauses or jumps ahead in the score, the accompaniment should follow as much as possible, but the accompaniment should always sound “musical” rather than “mechanical”. Thus, a considerable number of deci- sions must be made by the accompaniment generation component in response to tempo and location information. The task of estimating score location and tempo in an ensemble accompaniment system is complicated by the fact that multiple performers must be tracked and their indi- vidual score locations and tempi combined and resolved. Several considerations affect this resolution process. For instance, if one performer’s tracking system is having dif- ficulty tracking the performance, possibly because of signal processing difficulties or because the performer is making mistakes, then the estimates from that tracking sys- tem should not strongly affect the final estimation. Also, performers who become inactive for a relatively long dura- tion (i.e., have a rest or a sustained pitch) should affect the final estimations less than recently active voices, which are more likely to indicate the current tempo and score posi- tion. Additionally, a performer whose score position is relatively distant from the majority of the ensemble, pre- sumably indicating that this performer is lost or has fallen behind, should be ignored. A combination of the tracking systems’ estimates must satisfy these considerations as much as possible in order to produce an accurate, unified ensemble score location and tempo. Approach To identify the score location of a single performer, we use a modified version of the dynamic programming algorithm for identifying the longest common subsequence of two strings (Cormen et. al. 1990). Regarding the performance as a sequence of pitches, the objective is to delete a minimal number of notes from performance and score sequences to obtain an exact match. In practice, a prefix (the performance) is matched against a complete string (the score), and only a portion of the score is examined in order to save time. The matching algorithm is applied on every recognized note in the performance. The objective is to find the “best” match between performance and score according to the evaluation function: evaluation =a X matched notes - c x extra notes b x omissions - Although the number of ways the performed pitches can be matched against the score is exponential in the number of performed notes, dynamic programming allows us to com- pute the best match in time that is linear in the length of the score, and which gives a result after each performed note. By using a “window” centered around the expected score location, the work per performed note is further reduced to a constant. A more detailed presentation of this algorithm can be found in (Bloch & Dannenberg 1985), which also shows how to modify this algorithm to handle polyphonic performance input (e.g., chords played on a keyboard). If a new score location has been posited, it is placed in a buffer along with a timestamp indicating the “real time” when that location was reached by the performer. If one views these buffer entries as points in a graph mapping real time of the performance on the abscissa to “score time” (the position in the score) on the ordinate, the tempo of the per- formance at any instant is given by the slope of the graph (since tempo is the amount of score traversed in a unit of real time). Figure 1 graphs a tracked performance. Since performers are noticeably inconsistent within a tempo, it is necessary to apply some form of averaging in order to avoid occasional drastic tempo change estimates. Although many averaging techniques are available, we have elected to simply take the slope of the line between the first and last points in the location buffer. Since the buffer size is limited and relatively small, with older entries discarded one at a time once the buffer’s capacity is exceeded, this tempo esti- mation is still responsive to actual changes in tempo but less “jerky” than estimates based solely on the two most recent entries in the buffer. If the matching algorithm detects a performance error, the buffer is emptied and no tempo or score position estimates are possible until several correct notes are played. For an ensemble accompaniment system which must track multiple performers simultaneously, separate instances of the match state and the score location buffer must be maintained. Notes from different performers are identified by different MIDI channels, and the appropriate state is updated. Since score location information for each performer is available, it is possible to estimate each per- former’s current score location at any time. For example, consider Figure 2. If at time tl, the performer is at score location sl and maintaining an estimated tempo of 0.5; then at time t1+2, the performer’s expected score location would be st+l (if no intervening input is received tiom the per- former). The various estimates must eventually be consolidated into a single ensemble score position and tempo. The accompaniment system estimates an ensemble score posi- tion and tempo on every input from every performer. To accomplish this in accordance with the criteria presented in Music / Audition 95 Time (msecs) t1 t1+2 Time Figure 1, Figure 2, Example performance graph. Estimated score position. section two, each pair of estimations from each tracking system is rated, and a weighted average is computed from both score location and tempo estimates. The ratings are constructed so that an estimate is given more weight when it is more recent, and less weight when it does not cluster with other estimates. Figure 3 presents the rating function. The final rating (FIX) used for the weighted average is the product of the squares of two independent ratings-a recency rating (RR) and a clustering rating (CR). The recency rating for each tracking system (as given in Figure 3) decays from a value of one to zero during a three- second interval. If the score-position buffer of the tracking system is empty, then the recency rating is zero. This value is squared in the final rating product, causing the final rat- ing to decay more rapidly (in a quasi-exponential fashion) over the three-second interval. The rating is designed to give preference to the most recently active performers, thereby making the accompaniment performance more reactive. The clustering rating (also given in Figure 3) char- acterizes the relative separation of voices. It is the ratio of the summed distance of the i’th voice from all other voices, divided by the maximum possible summed distance at the time of rating. The rating decays from a value of one for the best case (i.e., all voices and the accompaniment are at identical score positions) to a value of zero in the worst case (i.e., all voices except the i’th voice are at the same position). This rating, like the recency rating, is squared in the final rating so as to give an even stronger preference to voices which are “relatively” tightly clustered. The final rating is a product of the squares of the other ratings so that it is guaranteed to be less than or equal to the minimum of the individual squares (since each square ranges from zero to one). Thus, as the criteria characterized by the compo- nent ratings fail to be satisfied, the final rating decreases. The ensemble sco e position and tempo are calculated as a weighted average f f the tracking system estimates. Each estimate is weighted by its final rating, and thus affects the overall estimate according to its “relative” satisfaction of the specified criteria compared to the estimates of the other tracking systems. For example, consider a performance of the section of score presented in Figure 4. As the first per- former proceeds, the recency rating of the other voices will decay. The tempo and score position estimated by the first performer’s tracking system will quickly dominate the ensemble average, causing the accompaniment to more closely follow that performer. Once the ensemble score position and tempo estimates have been calculated, they are used to make adjustments to the accompaniment performance according to a set of accompaniment rules. These rules are based upon studies of how real accompanists react to similar situations encountered during a performance (Mecca 1993). First, the time difference between the ensemble score position and the accompaniment score position is calculated. If the time difference is less than a pre-determined “noise” threshold, then the accompaniment tempo is simply set to the ensem- ble tempo. The noise threshold is used to prevent excessive jumping and tempo alterations, since performers do make subtle alterations in note placement (Bilmes 1992). This threshold is adjustable but is generally set to around 100 msecs. If the performer is ahead of the accompaniment by a difference at least as great as the noise threshold, but less than the “jump” threshold, then the accompaniment tempo is increased to an abnormally fast tempo (even faster than the actual ensemble performance) so that the accompani- ment will catch-up to the ensemble. If the accompaniment catches the ensemble prior to calculating another estimate, the tempo is reset to the previous tempo estimate. The jump threshold indicates how large a score position difference is too large to bother trying to perform in order to catch the ensemble. If the time difference is at least as great as this threshold, then the accompaniment system will skip to the estimated ensemble score position and start using the esti- mated ensemble tempo. Finally, if the performer is behind the accompaniment by a time difference at least as great as the noise threshold, then the accompaniment will pause until the performer reaches the accompaniment’s current position. To prevent the accompaniment from continuing too far ahead of the performers, it is necessary to maintain an input expectation point. If this point is passed without additional input from any performer, then the accompani- ment system pauses until additional input is received. Once input is received, the score position and tempo are esti- mated, necessary alterations to the performance parameters 96 The Arts are implemented as just described, and the accompaniment is restarted. iFR(i) xpos(i) Ensemble Score Position = ’ = ’ iFR(i) i=l FR (i) = (RR(i))2x (CR(i))2+c FR(i) = Final rating for estimate from tracking system i RR(i) = Recency rating for estimate from tracking system i CR(i) = Clustering rating for estimate from tracking system i c = Very small constant to prevent FR from reaching zero 1 (rtime - ltime (i) ) RR(i) = - 3 (rtime - ltime (i) ) I 3 0 if (rtime - ltime (i) ) > 3 r-time = Current time for which estimates are made ltime(i) = Time of last match made by tracking system i CR(i) = l- Ipos(i) -pas(j) I)-Jacc-pos(i)J n x (pos (max ) - pos (min ) ) n = Number of active tracking systems pas(i) = Score position for tracking system i pas(j) = Score position for tracking system j act = Score position for accompaniment pos(max) = Maximum of all pas(i), pas(i), and act pos(min) = Minimum of all pas(i), pas(j), and act but NOT pos(m=) Figure 3, Function to calculate ensemble score position. Implementation The ensemble accompaniment system is constructed using the CMU MIDI Toolkit (Dannenberg 1993) which pro- vides MIDI message handling, real-time scheduling, and performance of MIDI sequences. It is possible to adjust the position and tempo of a sequence (score) performance on- the-fly as part of processing input or generating output. The system is written in C and runs on DOS-based PCs, Macin- toshes, Amigas, and Unix workstations. The ensemble accompaniment system has been tested on both a DOS- based system and an Amiga. Figure 4, Score excerpt. To obtain performance input, both MIDI keyboards and pitch-to-MIDI converters have been used. The keyboards themselves generate MIDI messages which can be directly sent to the ensemble accompaniment system. The pitch-to- MIDI converter is an IVL Pitchrider, designed for use pri- marily with wind instruments. It takes input directly from a microphone, analyzes the input to identify fundamental pitch and attack, and generates MIDI messages that can be sent to the ensemble accompaniment system. For wind instruments, the data from this device can be used by the accompaniment system without modification. A software preprocessor has been developed to further analyze the data sent from this device when receiving vocal input (singing). The ensemble system consists of four software compo- nents: a matcher, which receives input from a performance and uses dynamic programming to determine score loca- tion; an estimator, which maintains the score location buffer, calculates tempi, and generates estimates on request; a voter, which rates and combines multiple score location and tempo estimates into an ensemble location and tempo; and a scheduler, which uses the ensemble estimates to change the accompaniment performance according to the rules described in section three. A matcher-estimator combination forms a single performance tracking system. The accompaniment system may instantiate multiple track- ing systems at initialization depending on user-supplied specifications. Only one voter and one scheduler are ever present. Figure 5 diagrams the interaction between these components for the case when the system is to accompany an ensemble of two performers. When MIDI messages are received as input, the appro- priate matcher is invoked according to the channel number of the message. (Each performer’s input must be sent on a separate MIDI channel.) The matcher applies the dynamic programming algorithm to determine the score location of the performer. The success or failure of this process is passed along to the estimator. If the match was successful then the estimator will pass its score position and tempo estimates to the voter. The voter will then request similar estimates from each of the other active tracking systems. The ratings are then generated for each set of estimates, as previously described. When an ensemble score position Music / Audition !I7 Tracking System I Figure 5, Components of the accompaniment system. and tempo have been generated, they are passed to the scheduler which determines any necessary and appropriate modifications to the accompaniment performance, accord- ing to the rules presented in the previous section. Our toolkit automatically manages the activation of input han- dling routines and MIDI message generation for performance of the accompaniment. The MIDI output can then be sent to a synthesizer for sound production. Results The ensemble accompaniment system has performed with ensembles of one, two, and three players consisting of both MIDI keyboards and acoustic wind instruments. The pieces used for testing range in difficulty from a simple canon on “Row, row, row your boat” to excerpts from Handel’s Water Music. In the case of a single performer, the system functions exactly the same as the solo accompaniment sys- tem previously constructed. It is highly reactive to tempo changes of the soloist and tolerant of omitted notes, wrong notes, and extra notes. If too many wrong notes or extra notes appear in the performance (as in a heavily embel- lished rendition), the matcher becomes unable to recognize the part, but the accompaniment will continue according to the last tempo estimate. The occasional mistake from a competent performer does not present a problem. In the case of omitted notes (such as when the performer jumps ahead), the system will ignore the performer until enough notes are correctly matched so that the matcher’s score overcomes the penalty imposed by the skipped notes. The farther the performer jumps, the larger is the penalty and the corresponding delay. Note that this penalty increases only for notes skipped by the performer-if the soloist omits a rest during which time the accompaniment plays, no penalty is generated and the accompaniment almost immediately re-synchronizes with the performer. In the case of an ensemble of two performers, the system is able to simultaneously track both performers. If either performer drops out, the system continues to accompany the other. Tempo changes of the latter performer are recog- nized by the system-readily so, once the silent performer’s recency rating has decayed. Also, since the score position of the accompaniment affects the clustering rating for each performer, if one performer should skip ahead or fall behind, the system will continue to synchro- nize with the other performer-ignoring the “lost” performer until he or she rejoins the ensemble or until the 98 The Arts first performer stops or becomes lost. If both performers skip ahead or change tempo in synchrony, then the accom- paniment does likewise according to the accompaniment rules described in section three. The system acts similarly in the case of three performers. In addition, should two of the three performers jump ahead or fall behind to the same position in the score, leaving only one performer in syn- chrony with the accompaniment, the system will quickly re-synchronize with the two performers since they repre- sent the majority of the ensemble. Note also that when tracking multiple performers, the accompaniment is less affected by a single performer playing wrong notes or omit- ting notes, providing the other performers are accurate and in synchrony. While the system works well with small ensembles, sev- eral problems must be addressed in order for the system to perform with larger ensembles. Two problems at the input level are that MIDI only permits sixteen logical channels and that individual microphones in large ensembles will experience cross-talk, making pitch estimation more diffi- cult. There is no reason to believe that either of these problems is insurmountable. Compute time is another consideration. Processing an input requires time linear in the ensemble size (since esti- mates from all tracking systems must be re-rated). In the worst case, if all parts simultaneously play a note, the amount of work to be completed before the next note in the score is performed is quadratic in the ensemble size. On the slowest PC used, handling a single input requires 1.4 msec. for an ensemble of one. The expense of recomputing one rating (for larger ensembles) is 0.3 msec. Based on these numbers, a conservative estimate indicates that we can pro- cess 16 inputs in 100 msec. A sixteenth note of 100 msec. duration implies a tempo of 150 quarter notes per minute. This is a fast tempo. If we were to update the voter once every 1OOms instead of on each input, we could handle hundreds of instruments in real time with current processor technology. For large acoustic ensembles, the computation will be dominated by signal processing of acoustic input. Conclusions Developing this accompaniment system has helped to define important criteria and considerations relevant to ensemble accompaniment. When generating score location and tempo estimates for an ensemble, it is useful to con- sider both the recency of the input from individual performers and the clustering, or relative proximity, among the performer’s score positions. This information assists in distinguishing recent and reliable performer input from that which has come from a lost or resting performer, or one who is not following the score. Construction and testing of this system has demonstrated there exists a trade-off between reactivity and stability of an accompaniment. As previously indicated, the ensemble accompaniment system currently attempts to be reactive to the performers. For example, in the case of three perform- ers where two performers have jumped ahead in the score but one has remained with the accompaniment, the system will quickly jump to the score location of the ensemble majority. This reactivity could be questioned, since in some cases maintaining a stable accompaniment that does not skip ahead with the majority might be preferred. A more stable accompaniment might also be desired if the majority of the ensemble is consistently dragging the tempo, as opposed to changing tempo for expressive purposes. This trade-off must be considered during construction of both the rating functions used to calculate the ensemble position and tempo, and the rules used to determine when to change tempo and score position of the accompaniment. Although the ensemble accompaniment system gener- ally reacts to performance situations in a reasonable manner, there remain some questionable actions which might be improved. Some of these are related to the reac- tivity-stability trade-off just mentioned. One example is the placement of expectation points used to pause the accom- paniment if no performer input is received. The more frequently these points are placed, the more reactive to tempo reductions and missed entrances the system becomes. The more sparse their placement, the more stable the accompaniment and the more performers are forced to compensate for their own mistakes. The use of knowledge- based rules to better define the relative rating of each per- former’s score location and tempo is also a consideration. If it is clear from the score that a particular performer should be inactive at present, then perhaps that performer’s estimates should be ignored. This might make the system more immediately reactive to the contrapuntally active per- formers, as opposed to waiting for the inactive performer’s recency rating to decay. It is hoped that further experimen- tation with the present system will help to define a more comprehensive understanding of these trade-offs and alter- natives, leading to a more versatile accompaniment system. Additionally, pre-performance analysis of the score might help develop useful performance expectations. Annotations in scores can provide useful performance hints to the scheduler (Dannenberg & Bookstein 1991). Auto- mating this annotation process would, however, require significant musical knowledge pertinent to interpreting scores. Alternatively, we are also interested in experiment- ing with learning through rehearsal, possibly by using techniques similar to those presented in (Vercoe & Puck- ette 1985). Ideally, an accompaniment system should be able to improve by practicing a piece with an ensemble and noting where to expect consistent tempo changes, embel- lishment, or performer error. This could be done with a single ensemble and single score, as well as with a single score performed by multiple ensembles. Since even two expressive performances by the same ensemble may vary greatly, the challenge will be to extract reliable character- izations of multiple ensemble performances and use them to enhance the accompaniment in successive perfor- mances, beyond what the naive and score-independent expectations allow. Using our current system as a starting point, techniques for effectively learning performance nuances can now be explored. eferences Baird, B., Blevins, D., and Zahler, N. 1993. Artificial intelligence and music: implementing an interactive computer performer. Computer Music Journal 17(2): 73-9. Bilmes, J. 1992. A model for musical rhythm. In Proceedings of the 1992 International Computer Music Conference, 207- 10. Bloch, J. and Dannenberg, R. 1985. Real-time computer accompaniment of keyboard performances. In Proceedings of the 1985 International Computer Music Conference, 279-90. Cormen, T., Leiserson, C., and Rivest, R. 1990. Introduction to Algorithms, 314-19. New York: McGraw- Hill Book Co. Dannenberg, R. 1984. An on-line algorithm for real-time accompaniment. In Proceedings of the 1984 International Computer Music Conference, 193-8. Dannenberg, R., and Bookstein, K. 1991. Conducting. In Proceedings of the 1991 International Computer Music Conference, 537-40. Dannenberg, R. 1993. The CA4U MIDI Toolkit. Pittsburgh: Carnegie Mellon University. Desain, P., and Honing, H. 1992. Tempo curves considered harmful. In Music, Mind, and A4achine: Studies in Computer Music, Music Cognition, and Artificial Intelligence, 25-40. Amsterdam, Thesis Publishers. Mecca, M. 1993. Tempo following behavior in musical accompaniment. Master’s thesis, Carnegie Mellon University. Rothstein, J. 1992. MIDI: A Comprehensive Introduction. Madison: A-R Editions. Vercoe, B. 1984. The synthetic performer in the context of live performance. In Proceedings of the 1984 International Computer Music Conference, 199-200. Vercoe, B and Puckette, M. 1985. Synthetic rehearsal: training the synthetic performer. In Proceedings of the 1985 International Computer Music Conference, 275-78. Music / Audition 99 | 1994 | 297 |
1,649 | Auditory Stream Segregation in Auditory Scene Analysis with a Multi-Agent System Tomohiro Nakatani, Hiroshi G. Qkuno, and Takeshi Kawabata NTT Basic Research Laboratories 3-l Morinosato-Wakamiya, Atsugi, Kanagawa 243-01 Japan { nakatani, okuno, kawabata}@nuesun.ntt .jp Abstract We propose a novel approach to auditory stream segregation which extracts individual sounds (au- ditory stream) from a mixture of sounds in audi- tory scene analysis. The HBSS (Harmonic-Based Stream Segregation) system is designed and devel- oped by employing a multi-agent system. HBSS uses only harmonics as a clue to segregation and extracts auditory streams incrementally. When the tracer-generator agent detects a new sound, it spawns a tracer agent, which extracts an au- ditory stream by tracing its harmonic structure. The tracer sends a feedforward signal so that the generator and other tracers should not work on the same stream that is being traced. The qual- ity of segregation may be poor due to redun- dant and ghost tracers. HBSS copes with this problem by introducing monitor agents, which detect and eliminate redundant and ghost trac- ers. HBSS can segregate two streams from a mix- ture of man’s and woman’s speech. It is easy to resynthesize speech or sounds from the cor- responding streams. Additionally, HBSS can be easily extended by adding agents of a new capa- bility. HBSS can be considered as the first step to computational auditory scene analysis. Introduction Over the past years a considerable number of stud- ies have been made on human auditory mechanisms. Although we have many techniques for processing par- ticular sounds such as speech, music, instruments, and the sounds made by specific devices, we don’t have enough mechanisms for processing and understanding sounds in real acoustic environments. Research into the latter is being made in the field of Auditory Scene Analysis (Bregman 1990)) which is to speech recogni- tion is what scene analysis is to character recognition. Auditory scene analysis is a difficult challenging area, partly because acoustic theory is not still rather inad- equate (e.g., there is no good acoustic design method- ology for concert halls), and partly because most re- search in acoustics has been focused exclusively on speech and music, ignoring many other sounds. Ad- ditionally, the reductionist approach to auditory scene 100 The Arts analysis, which tries to sum up various techniques for handling individual sounds, is not promising. Looking and listening are more active than seeing and hearing (Handel 1989). The essentials of our ap- proach to auditory scene analysis are twofold: e Active perception of observer - looking and listen- ing rather than seeing and hearing, and e Multi-sensor perception - may use multi-modal in- formation perceived by means of sensor organs The multi-agent system was recently proposed as a new modeling technology in artificial intelligence (Brooks 1986) (M aes 1991) (Minsky 1986) (Okuno 1993). We assume like Minsky that an agent has a limited capability, although in Distributed Artificial Intelligence, an agent is supposed to be much more powerful like a human being than ours. Each agent has its own goal and competes and/or cooperates with other agents. Through interactions among agents, in- telligent behavior emerges (Okuno & Okada 1992). Consider the approach that the multi-agent paradigm is applied to model auditory scene analysis. We expect that it will enhance the following functional- ities: (1) Goal-Orientation - Each agent may have its own goal. (2) Adaptability - According to the current situation, the behavior of the system varies between reactive and deliberate. (3) Robustness - The system should respond sensibly even if the input contains er- rors, or is ambiguous and incomplete. (4) Openness - The system can be extended by adding agents of new capabilities. It can also be integrated into other systems as a building block. In this paper, auditory stream segregation, the first stage of auditory scene analysis, is modeled and imple- mented by a multi-agent system. The rest of this paper is organized as follows: Section 2 investigates issues in auditory stream segregation. In Section 3, the basic system of auditory stream segregation with a multi- agent system is explained and evaluated to identify its problems. Section 4 presents and evaluates the HBSS (Harmonic-Based Stream Segregation) that copes with the problems. Related work and the conclusions are given in Section 5 and 6, respectively. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Auditory stream fop auditory scene analysis Auditory stream Auditory scene analysis understands acoustic events or sources that produce sounds (Bregman 1990). An acoustic event consists of auditory streams (or simply stream, hereafter), each of which is a group of acoustic components that have consistent characteristics. The process that segregates auditory streams from a mix- ture of sounds is called auditory stream segregation. Many techniques have been proposed so far. For ex- ample, Brown uses auditory maps in auditory stream segregation (Brown 1992) (Brown & Cooke 1992). These are off-line algorithms in the sense that any part of the input is available to the algorithm at any time. However, off-line algorithms are not well suited for many applications. Additionally, it is not easy to incorporate schema-based segregation and grouping of streams into such a system, since it does not support a mechanism of extending capabilities. To design a more flexible and expandable system, we adopted a multi-agent system to model auditory stream segregation, and used a simple characteristic of the sounds, that is, the harmonic structure. Definitions - Harmonic representation We use only the harmonic structure or hurmonicity of sounds as a clue to segregation. Other characteris- tics, including periodicity, onset, offset, intensity, fre- quency transition, spectral shape, interaural time dif- ference and interaural intensity difference, may be used for further processing. A harmonic sound is characterized by a fundamen- tal frequency and its overtones. The frequency of an overtone is equal to an integer multiple of the fun- damental frequency. In this paper, harmonic stream refers to an auditory stream corresponding to a har- monic sound, harmonic component refers to a single overtone in the harmonic stream, and agent’s stream refers to the stream an agent traces. We also define the harmonic intensity E(w) of the sound wave z(t) as (1) where (2) t is time, k is the index of the harmonic components, and w is the fundamental frequency. We call the ab- solute value of Hk the intensity of the harmonic com- ponent, and call the phase of Hk the phase of the har- monic component. In this paper, the term common fundamental frequency is extended to include the case where the fundamental frequency of one sound coin- cides with overtone of another sound. Input -jr’ Genarator 1 \ feedforwad signal Figure 1: Structure of basic system Issues in segregation To extract an auditory stream from a mixture of sounds, it is necessary to find out the harmonic struc- ture, its fundamental frequency and the power of each overtone. The system should segregate auditory streams incrementally, since it will be used as a build- ing block for real-time applications. The important is- sues to cope with these requirements are summarized below: How to find the beginning of a new harmonic struc- ture, How to trace a harmonic structure, How to reduce the interference between different t ratings, and How to find the end of a harmonic structure, Basic stream segregation Agents for Basic system The basic system (Nakatani et al. 1993) consists of two types of agents, the stream-tracer generator (hereafter, the generator) and stream tracers (hereafter, tracers). The generator detects a new stream and generates a tracer. The tracers trace the input sound to extract auditory streams. Figure 1 shows the structure of these agents. The input signal consists of the mixed audio waveform. System parameters The basic system uses three parameters to control the sensitivity of segregation: 1. Power threshold array 191 to check for overtones, 2. Power threshold 02 to check for fundamental fre- quencies, 3. Duration Ti to check for the continuity of sounds. These three parameters are global and shared among all the agents. The parameter 81 is a array of thresh- olds for frequency regions and plays the most impor- tant role in controlling the sensitivity. Music / Audition 101 Input L Pitch Watcher (active) Pitch Watcher Pitch Watcher(active) - Pitch Watcher Generator - Figure 2: Structure of Generator Adive pitch watch detects a sound. Generator The generator detects the beginning of harmonic struc- tures included in the input sounds and generates a new tracer agent. It consists of agents called pitch watchers (Figure 2), which monitors the harmonic structure at each frequency w by evaluating the harmonic intensity defined by Equation 1. Each pitch watcher treats w as a candidate fundamental frequency, and is activated if the following conditions are satisfied: 1. There is at least one overtone of w whose power is larger than 81, 2. the power of the fundamental frequency, w, is larger than 82, and 3. there is a peak near w in the acoustic spectrum. The active pitch watcher with the largest harmonic in- tensity generates a new tracer, which traces the new stream whose fundamental frequency is w in Equa- tion 2. Tracer Each tracer searches for the fundamental frequency w, within the neighborhood of the frequency w,-~ of the previous input frame by maximizing the harmonic in- tensity (Equation 1). In evaluating Equation 1, over- tones whose power is less than 81 are discarded. Then, the tracer calculates the intensity and the phase of each harmonic component by using Equation 2. The tracer terminates automatically if one of the following conditions is satisfied for a period of Ti: e there is no overtone whose power is larger than 81, or e the power of w is less than 81. Reducing interference between tracers A stream should be extracted exclusively by one tracer. For this purpose, two tasks are performed by each agent. Table 1: Benchmark mixtures of two sounds No soundi sound2 1 man’s speech synthesized sound (Fundamental Fre- quency is 200 Hz) 2 man’s speech synthesized sound (F.F. is 150 Hz) 3 man’s speech woman’s speech Male and female speech utter “aiueo” independently. Subtract signal As shown in Figure 1, a tracer guesses the input of the next frame and makes a feed- forward signal (called a subtract signal), which is sub- tracted from the input mixture of sounds. The wave- form to be subtracted is synthesized by adjusting the phase of its harmonic components to the phase of the next input frame. The remaining input (called the residual input) goes to all the tracers and to the gen- erator. Each tracer restores the sound data, x(t), by adding the residual signal to its own subtract signal. By this mechanism, the generator does not generate a new tracer for existing streams and one tracer cannot trace another tracer’s stream. Updating the global parameters 191 and 62 Each tracer increases the array elements of 81 for the regions in the vicinity of the frequency it is tracing. The in- crease is in proportion to the estimated trace error of each harmonic component, and results in lower sensi- tivity around the neighboring frequency regions. When terminating, each tracer decreases the array elements of 191 in its frequency regions, thereby raising the sen- sitivity. Let A be the intensity of a traced harmonic compo- nent, w be the frequency of the harmonic component, and w’ be the representative frequency for each fre- quency region. We estimate the trace error for the harmonic component at frequency w’ as T(w’) = c. 11 x A sin(&) exp(-jm’t) 11, t where c is a constant. Since the frequency of higher- order harmonic components is more sensitive to the fundamental frequency than that of lower-order com- ponents, the threshold for a higher-order component should be increased over a wider region. Consequently, we use T(w + (we/w) . ( w’ - w)) to increase the local threshold for the harmonic component at frequency w’. Each tracer also updates the global parameter 02 for every input frame. This is increased by the amount in proportion to the square root of the harmonic intensity. In most regions in vicinity of harmonic components, this value is set much lower than 02. 102 The Arts Input Generator [ _ Input AflFh _ :put At e Generator ] - Tracer - - Tracer -----o + (a) no streams are detected. (b) one stream is being traced. (c) two streams are being traced. Figure 3: Dynamic generation and termination of Tracer agents 0 0 50 100 150 200 250 (7.5-ms time units) Figure 4: Dynamics of tracer agents (Exp. 1) (Total number of generated agents = 5) System Behavior Figure 3(a) shows the initial state of the system. No sound is input to the generator and no tracer is gener- ated. When a new sound enters the system, the gen- erator is activated and a new tracer is generated (Fig- ure 3(b)). S ince a tracer is not complete, some errors may be fed into the generator. However, the tracer increases the threshold values adaptively according to the harmonic components, so this mechanism inhibits the generation of inappropriate tracers due to trace er- rors. The next stream is detected in almost the same way as the first stream (Figure 3(c)). When two or more tracers are generated, each tracer ignores com- peting components that are excessively influenced by the other streams. As a result, each stream is expected to be well segregated. Evaluation We evaluate this system by using three sets of sound ,nixtures as shown in Table 1. The input signals con- sisted of combinations of a male speaker and a female speaker uttering Japanese vowels “aiueo”, and a sta- tionary synthesized sound with an exponentially atten- uating sequence of harmonic components up to 6 kHz. The input sounds were sampled at 12 kHz, 16-bit quantized, and analyzed with a 30-ms Hamming win- dow. The frame period was 7.5 ms. Fundamental frequency in Hz 250 I 200 I-- -----_-----_-__c__-~ 1 150 - 1-----"~ 100 - 50 - 01 I 0 50 100 150 200 250 300 (7.5ms unit time) Figure 5: Segregated streams (Exp. 1) Experiment 1 Figure 4 depicts the dynamic gen- eration and termination of tracers in response to the first set of input sounds (Table 1). It shows that three inappropriate tracers (called redundant tracers) follow a stream assigned to another tracer, but terminate im- mediately. The segregated streams are depicted in Fig- ure 5. Both of the sounds resynthesized’ from the seg- regated streams are very similar to the original sounds. Additionally, the formants of the original voice are pre- served in the resynthesized voice. Experiment 2 Figure 6 depicts the dynamic gener- ation and termination of tracers in response to the sec- ond set of input sounds. The first redundant tracer ter- minates immediately, while three inappropriate tracers continue to operate for as long as the second sound lasts. One of the three tracers is a redundant tracer. The rest are two ghost tracers that traces non-existing streams. The segregated streams are depicted in Fig- ure 7. The sound resynthesized from the segregated stream corresponding to the 150-Hz synthesized sound was very similar to the original sound, but the man’s speech was not so good, sounding more like “aiueo-h”. Most formants of the original voice are preserved in the resynthesized voice. ‘At the presentation, the original and resynthesized sounds will be demonstrated. Music / Audition 103 # of agents # of agents 8 , I 5 0 4 - 3 - 2 - I I 0 0 50 100 150 *;.5 *=O 300 - ms unit time) Figure 6: Dynamics of Tracer agents (Exp. 2) Figure 8: Dynamics of tracer agents (Exp. 3) (Total number of generated agents = 5) (Total number of generated agents = 70) Fundamental frequency in Hz 2so 1 150 200 250 300 (7.5-ms time units) Figure 7: Segregated streams (Exp. 2) Experiment 3 The third input signal results in the generation of 70 tracer agents, many of which were short-lived as shown in Figure 8. There are many re- dundant and ghost tracers. However, none of these agents traced both the man’s and woman’s speech at the same time, as shown in Figure 9. Each of the sounds resynthesized from the corresponding segre- gated stream was quite poor compared with the origi- nal. Additionally, it is not easy to resynthesize a sound by grouping segregated streams. Some formants of man’s and woman’s original voice are destroyed in each resynthesized voice, respectively. Summary The basic system occasionally generates redundant and ghost tracers. A redundant tracer is caused by imperfect subtract signals and poor termi- nation detection. A ghost tracer, on the other hand, is caused by self-oscillation, because the phase of the sub- tract signals is not considered. A pair of ghost tracers usually trace two streams with opposite phases. Since each tracer extracts a stream according to the current internal status of the tracer and the current residual signal, it is difficult to determine which tracer is inappropriate. In the next section, we extend the basic system to cope with this problem. (7.5-ms time units) Fundamental frequency in Hz 300 , I Figure 9: Segregated streams (Exp. 3) Advanced stream segregation An advanced stream segregation is proposed to cope with the problems encountered by the basic system (Nakatani et al. 1993). The advanced system is also called the HBSS (Harmonic-Based Stream Segregation) system. Monitors We introduce agents called monitors to detect and kill redundant and ghost tracers. A monitor is generated simultaneously with a tracer, which it supervises (Fig- ure 10). The monitor starts a log for its tracer, and uses it to do the following. 1. Eliminate a redundant tracer, and 2. Adjust the intensity of harmonic components ac- cording to the input sound. Eliminating redundant tracers Redundant trac- ers should be killed for stable segregation. When the following conditions are met, the monitor judges that its tracer is tracing the same stream as some other tracer. 1. The tracer shares a common fundamental frequency with others for a constant period of time, and 104 The Arts feedforward signal Figure 10: Structure of advanced system (HBSS) 2. The tracers have a common harmonic balance. The harmonic balance is defined as the vector B, where (hl , . . ., h,) is a sequence of components each of which is nearly equal to some overtone of the other stream. Two streams have a common harmonic bul- unce if the following condition is met: m x Qi < 1.0 + E, m (4) i=l { Qi = ri,i/ra,i if r 1,i > r2,i, Qi = ra,i/ri,i otherwise. Here (rl,l. . -rl,m) and (n,l . . .r2,m) are the harmonic balances of two streams and E is a constant. The first condition is easily detected by comparing the trace logs. When a number of monitors detect that their tracers are monitoring the same stream, they all kill each other, along with their tracers, except for the monitor that was generated earliest to trace their common fundamental frequency. Adjusting the stream Since the feedforward sig- nals of the tracers are subtracted from the waveform, sound components not included in the original sound may be created through tracer interactions. The moni- tors continuously reduce such sound components in the following way. Let Ecomp be the intensity of a harmonic component whose frequency is w, Ei, be the intensity of the ac- tual input sound at the corresponding frequency w in the acoustical spectrum, and r be Ecomp/Eins If r is greater than the constant c for the past r frames, the monitor substitutes the value of Ecomp with the value given by E camp = a(log(r/c)/~ + 1.0) * En, where (u is a constant. If r = 1, the change in Ecomp is small. As r becomes larger, Ecomp approaches aEi,. # of agents 5 4- 3 - 2 - l- I (I: 0 0 50 loo 150 200 250 300 (7.5-ms time units) Figure 11: Dynamics of tracer agents (Exp. 4) (Total number of generated agents = 7) Fundamental frequency in Hz 250 200 - 150 - -..-- -1_;-'.-cy-z7 ~~ -- _ 100 - 50 - 0 0 50 100 150 200 250 300 (7.5-ms time units) Figure 12: Segregated streams (Exp. 4) System Behavior We will briefly explain why inappropriate tracers can- not survive for long. A ghost tracer will be killed as follows: e A tracer which does not trace an existing stream will be attenuated by the adjustment of its monitor. o A tracer which traces an existing stream of another tracer will be terminated. On the other hand, a tracer that is tracing an actual stream is influenced little by the adjustment of its mon- itor. A redundant tracers will be killed, leaving the oldest tracer to trace the stream stably. Evaluation The performance of the advanced system (HBSS) was evaluated using the same set of benchmark signals. Since the first mixture was well segregated even by the basic system, we skipped the result of this experiment with the advanced system. Experiment 4 Figure 11 shows the dynamic gen- eration and the termination of tracers in response to the second set of input sounds, and segregated streams are depicted in Figure 12. These figures show that Music / Audition 105 # of agents 8 6 5 4 I A 11 vi IA I : loo 150 200 250 300 350 (7.5-ms time units) Figure 13: Dynamics of tracer agents (Exp. 5) (Total number of generated agents = 37) Fundamental frequency in Hz 300 , 250 0 50 100 150 200 250 300 350 (7.5-ms time units) Figure 14: Segregated streams (Exp. 5) redundant and ghost tracers are killed well. Both sounds resynthesized from the corresponding segre- gated streams are very similar to the original. Ad- ditionally, the formants of the original voice are well preserved in the resynthesized voice. Experiment 5 The third input signal results in to- tal of 37 generated agents, and Figure 13 shows that redundant and ghost tracers are killed soon. The segre- gated streams are depicted in Figure 14. Both sounds resynthesized from the segregated streams are not too bad. Additionally, it is easy to resynthesize sounds, be- cause the women’s speech was resynthesized from only one stream and the man’s speech from two streams. The formants of the man’s and woman’s original voice are preserved in each resynthesized voice, respectively. Related Work Auditory Scene Analysis Bregman classifies the mechanisms of auditory scene analysis into two cate- gories: simultaneous (spectrum) and sequential group- ing (Bregman 1990). The former extracts auditory streams from a mixture of sounds, while the latter groups together auditory streams that belong to the same acoustic source. The Experiment 3 with the third mixture of two sounds in Table 1 shows that it is very difficult to segregate man’s and woman’s speech by simultaneous grouping followed by sequential group- ing. The proposed system integrates both grouping processes and proves to be effective. Brown and Cooke proposed computational auditory scene analysis (Brown 1992) (Brown & Cooke 1992), which builds auditory map to segregate speech from the other sound such as siren and telephone rings. This system extracts various acoustic characteristics on batch basis, but the extension or interface to other systems is not considered. Integrated Architecture IPUS (Integrated Pro- cessing and Understanding Signals) (Lesser & Nawab 1993) integrates signal processing and signal interpre- tation into blackboard system. IPUS has a small set of front-end signal processing algorithms (SPAS) and choose correct parameters setting for SPA and correct interpretations by dynamic SPA reconfiguration. In other words, IPUS views the reconfiguration as a diag- nosis for discrepancy between top-down search for SPA and bottom-up search for interpretation. IPUS has various interpretation knowledge sources which under- stand actual sounds such as hair driers, footsteps, tele- phone rings, fire alarms, and waterfalls (Nawab 1992). Since IPUS is a generic architecture, it is possible to implement any capability, but IPUS is fully-fledged. The initial perception can be much simplified. Addi- tionally, a primitive SPA (or agent, in our terminology) that segregates a stream incrementally is not consid- ered so far. Okuno (Okuno 1993) proposed to use subsumption architecture (Brooks 1986) to integrate bottom-up and top-down processing to realize cognition capabilities. The term “subsumption architecture” is often confused with “behavior-based control” (Brooks 1986), but they are different. The former indicates that interaction be- tween agents is specified by inhibitors and suppressors, or activation propagation (Maes 1991), while the latter indicates that it is behavior that is subsumed. We will use subsumption architecture rather than blackboard architecture, because the former allows agents to in- teract directly with the environment and can make it easier to extend the capabilities of system. Wada (Wada & Matsuyama 1993) employed a multi- agent system in deciding regions of image. An agent is placed to a candidate region and then communicates with adjacent agent to determine the boundary of two regions. The interaction of agents is similar to that of HBSS. This and our result proves that a multi-agent system is promising in pattern recognition. Conclusions We have presented basic and advanced methods for auditory steam segregation with a multi-agent system, which use only the harmonic structure of input sounds. The advanced system, HBSS, is able to segregate man’s 106 The Arts and woman’s speech. This result suggests a clue to un- derstanding the cocktail party prob2em. We are about to investigate this problem by designing a new agent that extracts only human voice including consonants by using the information HBSS extracted. This new agent will be added to HBSS with subsumption archi- tecture so that its output subsumes (overwrites) hu- man voice stream segregated by HBSS. HBSS is currently being evaluated with a wide range of sound mixtures such as a mixture of speech and, white noise of a sound of breaking glass. The perfor- mance of segregating human voice from white noise is shown to become worse as the power of white noise increases. However, it is known that constant white noise can be reduced by the spectral subtraction (Boll 1979). We will develop a new agent that reduces white noise by employing the spectral subtraction and use it as a front-end of HBSS. One might argue that HBSS would not treat tran- sient or bell sounds. This is somewhat true, but is not fatal, because the current HBSS holds and uses just a previous state to segregate auditory streams. We are working to design a new agent that holds longer previ- ous states to restore missing phonemes caused by loud noise. This process is similar to phonemic restoration in auditory perception. In case a mixture of sounds comprises only harmonic sounds and any pair of sounds have not any common fundamental frequency, HBSS would be able to seg- regate all sounds. This situation is an extension of the first benchmark mixture. Of course, as the num- ber of pairs of sounds that have common fundamental frequency increases, it becomes more difficult to seg- regate such sounds. This is also the case for human perception. Therefore, we think that, active hearing, or listening, is essential. The typical example of listen- ing is a cocktail party problem. HBSS uses only harmonics in segregation. This is because we don’t either have enough acoustic charac- teristics to represent a sound or know their hierarchy. In vision, there are a set of visual characteristics and Marr (Marr 1982) proposed their hierarchy, that is, primary and 2; sketch. It is urgent and important in the research of auditory scene analysis to develop a methodology to represent general acoustics, not re- stricted to speech or music. Acknowledgments. We would like to thank M. Kashino of NTT, H. Kawa- hara and M. Tsuzaki of ATR for discussions on audi- tory perception. We would like to thank S.H. Nawab of Boston University and other participants of Abstract Perception Workshop held at Japanese Advanced In- stitute of Science and Technology for comments on an earlier draft. We would also like to thank I. Takeuchi and R. Nakatsu of NTT for their continuous encour- agement of our inter-group research. References Boll, S.F. 1979 A Spectral Subtraction Algorithm for Suppression of Acoustic Noise in Speech, In Pro- ceedings of International Conference on Acoustics, Speech, and Signal Processing, IEEE, 200-203. Bregman, A.S. 1990. Auditory Scene Analysis - the perceptual organization of sound, The MIT Press. Brooks, R.A. 1986. A Robust Layered Control System for a Mobile Robot, IEEE Journal of Robotics and Automation RA-2( 1): 14-23. Brown, 6. 1992. Computational auditory scene anal- ysis: A representational approach, PhD thesis, Dept. of Computer Science, University of Sheffield. Brown, G.J.; and Cooke, M.P. 1992. A computational model of auditory scene analysis, In Proceedings of International Conference on Spoken Language Pro- cessing, 523-526, IEEE. Handel, S. 1989. Listening. The MIT Press. Lesser, V.; Nawab, S.H.; Gallastegi, I.; and Klassner, F. 1993. IPUS: An Architecture for Integrated Signal Processing and Signal Interpretation in Complex En- vironments. In Proceedings of the Eleventh National Conference on Artificial Intelligence, 249-255. Maes, P. ed. 1991. Designing Autonomous Agents: Theory and Practice from Biology to Engineering and Buck, special issue of Robot and Autonomous Systems, The MIT Press/Elsevier. Marr, D. 1982. Vision. Freeman. Minsky, M. 1986. Society of Minds. Simon & Schus- ter, Inc. Nakatani, T.; Kawabata, T.; and Okuno, H.G. 1993. Speech Stream Segregation by Multi-Agent System. In Proceedings of International Workshop on Speech Processing (IWSP-93), 131-136, The Institute of Electronics, Information and Communication Engi- neers. Also numbered Technical Report, SP93-97. Nawab, S.H.; and Lesser, V. 1992. Integrated Process- ing and Understanding of Signals, 251-285. in Oppen- heim, A.V.; and Nawab, S.H. eds. 1992. Symbolic and Knowledge-Bused Signal Processing, Prentice-Hall. Okuno, H.G.; and Okada, M. 1992. Emergent Com- putation Model for Spoken Language Understanding (in Japanese). Technical Report SIG-AI 82-3, 21-30, Information Processing Society of Japan. Okuno, H.G. 1993. Cognition Model with Multi- Agent System (in Japanese), 213-225. In Ishida, T. ed. 1993. Multi-Agent and Cooperative Computation II (Selected Papers from MACC ‘92), Tokyo, Japan: Kindai-Kagaku-sha. Wada, T.; and Matsuyama, T. 1993. Region- Decomposition of Images by Distributed and Coop- erative Processing. Proceedings of the Workshop on Multi-Agent and Cooperative Computation (MACC ‘93). Japanese Society for Software Science and Tech- nology. Music / Audition 107 | 1994 | 298 |
1,650 | ulating Creativity in Jazz Performance Geber Ramalho Jean-Gabriel Ganascia LAFORIA-IBP-CNRS Universite Paris VI - 4, Place Jussieu 75252 Paris Cedex 05 - FRANCE Tel. (33-l) 44.27.37.27 - Fax. (33-l) 44.27.70.00 e-mails: { ramalho, ganascia} @laforia.ibp.fr Abstract This paper considers the problem of simulating creativity in the domain of Jazz improvisation and accompaniment. Unlike most current approaches, we try to model the musicians’ behavior by taking into account their experience and how they use it with respect to the evo)ving contexts of live performance. To represent this experience we introduce the notion of Musical Memory, which explores the principles of Case-Based Reasoning (Slade 1991). To produce live music using this Musical Memory we propose a problem solving method based on the notion of PACTS (Potential ACTions) that are activated according to the context and then combined in order to produce notes. We show that our model supports two of the main features of creativity: non-determinism and absence of well-defined goals (Johnson-Laird 1992). 1 - Introduction Our research is concerned with the study of the strengths and limitations of AI techniques to simulate creative behavior on a computer. Although creativity has always been present on the AI research agenda there is no accurate understanding of human creativity; its simulation on a computer still remains an open problem (AAAI 1993). In fact, there is an apparent paradox in the formalization of creativity due to the common sense opinion that, by definition, creativity embodies what cannot be formalized. To avoid both real and imaginary difficulties of simulating creative behavior on a computer, we have decided to concentrate on modeling particular kinds of creative activities such as musical ones. We do not intend to model creativity from a psychological point of view but rather to investigate it by seeking the simple computational mechanisms that may underlie it. In other words, we attempt to model creativity in terms of problem solving (Newell & Simon 1972; Nilsson 1971, Laird, Newell & Rosembloom, 1987). We have chosen to work on Jazz improvisation and accompaniment because of their spontaneity, in contrast to the formal aesthetic of contemporary classical music composition. From an AI point of view, modeling Jazz performance raises interesting problems since performance requires both theoretical knowledge and great 10s The Arts skill. In addition, Jazz musicians are encouraged to develop their musical abilities by listening and practicing rather than studying in conservutoires (Baker 1980). In Section 2 we present briefly the problems of modeling musical creativity in Jazz performance. We show the relevance of taking into account the fact that musicians integrate rules and memories dynamically according to the context. In Section 3 we introduce two basic notions of our model: PACTS and Musical Memory. A general description of our model is given in Section 4. In Section 5 we give further details about the modules of our model, showing particularly how the composition module integrates the two above-mentioned notions to create music. In the last section we discuss our current work and directions for further developments. 2 - Modeling Musical Creativity 2.1- The Problem and the Current Approaches Let us begin by defining some simple musical concepts. A note is a triplet (pitch, duration, amplitude) and can be considered as the basic tonal music element. Putting notes together one obtains other musical elements such as a melody (temporal sequence of notes) or a chord (set of simultaneous notes). Scales and rhythm concern respectively the pitches and durations of a set of notes. The tasks of improvisation and accompaniment consist in playing notes (melodies and/or chords) according to the guidelines laid down in a given chord grid (sequence of chords underlying the song). But, it is in the strikingly large gap between the actually played music and the chord grid instructions that the richness of live Jazz performance lies (Ramalho & Pachet 1994). Musicians cannot justify all the local choices they make (typically at note-level) even if they have consciously applied some strategies in the performance. This is the greatest problem of modeling the knowledge used to fill the gap referred to above. To face this problem, the first approach is to make random-oriented choices from a library of musical patterns weighted according to their frequency of use (Ames & Domino 1992). The second approach focuses on very detailed descriptions so as to obtain a complete explanation of musical choices in terms of rules or grammars (Steedman From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. 1984). In the first case, since there is no explicit semantics associated to random-oriented choices, it is difficult to control changes at more abstract levels than the note level. In the second, the determinism of rule- based framework lacks flexibility because of the introduction of “artificial” or over-specialized rules that do not correspond to the actual knowledge used by musicians. This crucial trade-off between “flexibility and randomness” and “control and semantics” affects the modeling of other creative activities too (Rowe & Partridge 1993). 2.2 - Claims on Knowledge and Reasoning in Jazz Performance If musical creativity is neither a random activity nor a fully explainable one, then creativity modeling requires a deeper understanding of the nature and use of musical knowledge. This section presents two general results of our early work where we interviewed Jazz musicians and recorded live performances in order to elicit this knowledge. Our first claim is that Jazz musicians’ activities are supported by two main knowledge structures: memories and rules. More specifically, we claim that these memories are the main source of knowledge in intuitive composition tasks and that most Jazz rules are either abstract or incomplete with respect to their possibility of directly determining the notes to be played. Jazz musicians use rules they have learned in schools and through Jazz methods (Baudoin 1990). However, these rules do not embody all knowledge. For example, there is no logical rule chaining that can directly instantiate important concepts such as tension, style, swing and contrast, in terms of notes. This phenomenon is a consequence of the Jazz learning process which involves listening to and imitating performances of great Jazz stars (Baker 1980). The experience thus acquired seems to be stored in a long term musical memory. To put it in a nutshell, musicians integrate rules and memories into their actions dynamically. Sometimes, note-level rules (that determine the notes directly) are applied but, very often, these rules are not available. In these cases a fast search for appropriate musical fragments in the musician’s auditory memory is carried out using the available general rules. This memory search is both flexible and controlled because of the mechanism of partial matching between the memory contents and requirements stated by the general rules. In terms of modeling, this is an alternative approach that avoids the need for “artificial” rules or randomness. Our second claim is that musical actions depend strongly on contexts that evolve over time. The great interaction between either musicians themselves or musicians and the public/environment may lead them to reinforce or discard their initial strategies while performing. The constraints imposed by real-time performance force musicians to express their knowledge as a fast response to on-going events rather than as an accurate search for “the best musical response”. Jazz creativity occurs within the continuous confrontation between the musician’s background knowledge and the context of live performance. asic Notions of our ode 3.1 - Potential ACTions (PACTS) Pachet (Pachet 1990) has proposed the notion of PACTS (at this time called “strategies”) as a generic framework for representing the potential actions (or intentions) that musicians may take within the context of performance. Focusing the modeling on musical actions rather than on the syntactic dimension of notes, additional knowledge can be expressed. In fact, PACTS can represent not only notes but also incomplete and abstract actions, as well as action chaining. PACTS are frame-like structures whose main attributes are: start-beat, end-beat, dimensions, abstract-level, type and instrument-dependency. Let us now see how PACTS are described, through a couple of examples. PACTS are activated at a precise moment in time and are of limited duration which can correspond to a group of notes, a chord, a bar, the entire song, etc. PACTS may rely on different dimensions of notes: rhythm (r); amplitude (a); pitch (p) and their arrangements (r-a, r-p, p- a, r-p-a). When its dimensions are instantiated, the abstract level of a PACT is low , otherwise it is high. For instance, “play loud”, “play this rhythm” and “play an ascending arpeggio” are low-level PACTS on amplitudes, rhythm and pitches respectively. “Play this lick transposed one step higher” is a low-level PACT on all three dimensions. “Play syncopated” and “use major scale” are high-level on respectively rhythm and pitches. PACTS can be of two types: procedural (e.g. “play this lick transposed one step higher”) or property-setting (e.g. “play bluesy”). PACTS may also depend on the instrument. For example, “play five-note chord” is a piano PACT whereas “play stepwise” is a bass PACT. For the sake of simplicity we have not presented many other descriptors that are needed according to the nature and abstract level of the PACTS. For instance, pitch PACTS have descriptors such as pitch-contour (ascending, descending, etc.), pitch-tessitura (high, low, middle, etc.), pitch-set (triad, major scale, dorian mode, etc.) and pitch- style (dissonant, chord-based, etc.). From the above description two important properties of PACTS appear. The first one is the playability of a PACT. The less abstract a PACT is and the more dimensions it relies on, the more it is “playable” (e.g. “play ascending notes” is less playable than “play C E G”, “play bluesy” is less playable than “play a diminished fifth on the second beat”, etc.). A fully playable (or just playable) PACT is defined as a low-level PACT on all three dimensions. The second property is the combinability of PACTS, i.e. they can be combined Music / Audition 109 to generate more playable PACTS. For instance, the PACT “play ascending notes” may combine with “play triad notes” in a given context (e.g. C major) to yield “play C E G”. In this sense, PACTS may or may not be compatible. “Play loudly” and “play quietly” cannot be combined whereas “swing”, “play major scale” and “play loudly” can. These properties constitute the basis of our problem solving method. As discussed in Section 4, solving a musical problem consists in assembling (combining) a set of PACTS that have been activated by the performance context. 3.2 - Musical Memory There is no guarantee that a given set of PACTS contains the necessary information so as to produce a playable PACT. As discussed in Section 2.2, this lack of information is related to the fact that musical choices cannot be fully expressed in terms of logical rule chaining, i.e. Jazz rules are often either abstract or incomplete to determine directly the notes to be played. To solve this problem we have introduced the notion of Musical Memory which explores the principles of case- based reasoning [Slade 911. This Musical Memory is a long term memory that accumulates the musical material (cases) the musicians have listened to. These cases can be retrieved and modified to provide missing information. The contents and representation of the Musical Memory can be determined: the cases must correspond to low-level PACTS that can be retrieved during the problem solving according to the information contained in the activated PACTS. These cases are obtained by applying transformations (e.g. time segmentation, projection on one or two dimensions, etc.) to transcriptions of actual Jazz recordings. This process (so far, guided by a human expert) yields cases such as melody fragments, rhythm patterns, amplitude contours, chords, etc. The cases are indexed from various points of view that can have different levels of abstraction such as underlying chords, position within the song, amplitude, rhythmic and melodic features (Ramalho & Ganascia 94). These features are in fact the same ones used to describe high- level PACTS. For instance, pitches are described in terms of contour, tessitura, set and style as discussed in last section. It is important to stress that high-level PACTS have also been determined from transcriptions of Jazz recordings but not automatically, since this would require much more complex transformations on the transcriptions. These PACTS were in fact acquired during an earlier knowledge acquisition phase working with experts. 4 - General Description of our Model 4.1 - What is a Musical Problem? Johnson-Laird (Johnson-Laird 1992) among other researchers has identified three features of creative tasks that show the difficulties of formalizing creativity as classical problem solving (Newell & Simon 1972; Nilsson 1971): non-determinism (for the same given composition problem it is possible to obtain different musical solutions which are all acceptable); absence of well-defined goals (there is only a vague impression of what is to be accomplished, i.e. goals are refined or changed in the on-going process); no clear point of termination (because of both the absence of a clear goal and the absence of aesthetic consensus for evaluating results). Taking an initial state of a problem space as a time segment (e.g. bars) with no notes, a musical problem consists in filling this time segment with notes which satisfy some criteria. This intuitive formulation of what a musical problem is underlies the above criticism of formalizing musical creativity. Some AI researchers have encountered many difficulties in exploring this point of view (see for instance Vicinanza’s work (Vincinanza & Prietula 1989) on generating tonal melodies). However, we present here a different point of view that allows us to formalize and deal with musical creativity as problem solving. We claim that the musical problem is in fact to know how to start from a “vague impression” and go towards a precise specification of these criteria. In other words, the initial state of the music problem space could be any set of PACTS within a time interval and the goal could be a unique playable PACT. The goal is fixed and clearly defined (i.e. the goal is to play!) and solving the problem is equivalent to assembling or combining PACTS. An associated musical problem would be to determine the time interval continuously so as to reach the end of the song. 4.2 - The Reasoner What we do is model a musician as a reasoner whose behavior is simulated by three modules which work coordinately in parallel (see Figure 1). The modules of our model resemble the Monitoring, Planning and Executing ones of some robotics applications (Ambros- Ingerson & Steel 1988). The context is composed of a chord grid which is given at the outset and events that occur as the performance goes on, i.e. the notes played by the orchestra and reasoner and also the public reactions. The perception module “listens to” the context events and puts them in the Short-Term Memory. The composing module computes the notes (a playable PACT) which will be executed in the future time segment of the chord grid. This is done using three elements: the Short-Term Memory contents, the reasoner’s mood and the chords of the future chord grid segment. The reasoner’s Mood changes according to the context events. The execution module works on the current chord grid segment by executing the playable PACT previously provided by the composing module. This execution corresponds to the sending of note 110 The Arts Short Term Memory . IEm7(b5) IA7(b9) I Cm7 I F7 IFm7 I . . External Events (public & environ.) l 0 - Orchestra (Soloist) * * IEm Reasoner (Bass Player) . . / Figure 1 - Overall Description of the Model information at their start time to the perception module and to a MIDI synthesizer, which generates the corresponding sound. 5 - Components of our Model 5.1 - The Perception Module Modeling the dialog between musicians and their interaction with the external environment is a complex problem since the context events are unpredictable and understanding them depends on cultural and perceptual considerations. To achieve an initial validation of our model, our current work focuses on the implementation of the composing module, since it is at the heart of the improvisation tasks. And instead of implementing the perception module, we have proposed a structure called a Performance Scenario which is a simpler yet still powerful representation of the evolving context. The idea is to control the context events by asking for the user’s aid. Before the performance starts, the user imagines a virtual external environment and characterizes it by choosing some features and events from a limited repertoire and assigning an occurrence time to the events. As for the dialog between the musicians, the user listens to a previous orchestra recording and gives a first level interpretation by leaving some marks such as “soloist using dorian mode in a cool atmosphere” or “soloist is playing this riff”. In short, the Performance Scenario is composed of marks that are obtained from the interpretation of the orchestra part and the setting of external environment events. These marks are only available to the system at their specified start time. Unfortunately, the user cannot interpret the notes the reasoner himself has just played. However, the reasoner can take into account some simple features of these notes (e.g. last note, pitch and amplitude direction, etc.) when activating and assembling PACTS. 5.2 - The Composition module The problem of playing along a given chord grid can be viewed as a continuous succession of three sub-problems: establishing the duration of the new chord grid segment; determining the PACTS associated to this segment; and assembling this group of PACTS in order to generate a unique playable PACT. The first two are more questions of problem setting, the third is a matter of problem solving and planning. The composition model is supported by a Musical Memory and Knowledge Base. The former contains low- level PACTS that can be retrieved during the PACT assembly. The latter contains production rules and heuristics concerned with the segmentation of the chord grid, changes in the Mood and the selection/activation of PACTS. These rules are also used to detect and solve incompatibilities between PACTS, to combine PACTS and to modify low-level PACTS retrieved from the Musical Memory. 52.1 - Segmenting the Chord Grid and Selecting PACTS The chord grid is segmented in non regular time intervals corresponding to typical chord sequences (II-V cadences, modulations, turnarounds, etc.) abundantly catalogued in Jazz literature (Baudoin 1990). In fact, the reasoning of musicians does not progress note by note but by “chunks” of notes (Sloboda 1985). The criteria for segmenting the chord grid are simple and are the same as those used for segmenting the transcription of Jazz recordings in order to build the Musical Memory. Given the chord grid segment, the group of associated PACTS derives from three sources. Firstly, PACTS are activated according to the chords of the grid segment (e.g. “if two chords have a long duration and a small interval distance between them then play an ascending arpeggio”). Other PACTS are activated from the last context events (e.g. “if soloist goes in descending direction then follow him”). The activation of a PACT corresponds to the assignment of values to its attributes, i.e. the generation of an instance of the class PACT in an Object-Oriented Music / Audition 111 Language. Finally, the previously activated PACTS whose life time intersects the time interval defined by the segmentation (e.g. “during the improvisation play louder”) are added to the group of PACTS obtained from the first two steps. The reasoner can be seen as an automaton whose state (Mood) changes according to the context events (e.g. “if no applause after solo then Mood is bluesy” or “if planning is late with respect to the execution then Mood is in a hurry”). So far, the reasoner’s Mood is characterized by a simple set of “emotions”. In spite of its simplicity, the Mood plays a very important role in the activation and assembling of PACTS. It appears in the left-hand side of some rules for activating PACTS and also has an influence on the heuristics that establish the choice preferences for the PACT assembly operators. For instance, when the reasoner is “in a hurry” some incoming context events may not be considered and the planning phase can be bypassed by the activation of playable PACTS (such as “play this lick”) which correspond to the various “default solutions” musicians Play- 5.2.2 - Assembling PACTS The initial state of the assembly problem space is a group of selected PACTS corresponding to the future chord grid segment. The goal is a playable PACT. A new state can be reached by the application of three operators or operator schemata (since they must previously have been instantiated to be applied): delete, combine and add. The choice of operator follows an opportunistic problem solving strategy which seeks the shortest way to reach the goal. Assembling PACTS is a kind of planning whose space state is composed of potential actions that are combined both in parallel and sequentially since sometimes they may be seen as constraints and other times as procedures. Furthermore, the actions are not restricted to primary ones since potential actions have different abstract levels. Finally, there is no backtracking in the operator applications. The delete operator is used to solve conflicts between PACTS by eliminating some of them from the group of PACTS that constitute the next state of the space problem. For instance, the first two of the PACTS “play ascending arpeggio”, “play in descending direction”, “play louder” and “play syncopated” are incompatible. As proposed in SOAR (Laird, Newell & Rosembloom, 1987), heuristics state the preferences for choosing a production rule from a set of fireable rules. In our example, we eliminate the second one because the first one is more playable. The combine operator transforms compatible PACTS into a new one. Sometimes the information contained in the PACTS can be merged immediately to yield a low- level PACT on one or more dimensions (e.g. “play ascending notes” with “play triad notes” yields “play C E G” in a C major context). Other times, the information is only placed side by side in the new PACT waiting for future merger (e.g. “play louder” and “play syncopated” yields, say, “play louder and syncopated”). Combining this with “play ascending arpeggio” generates a playable PACT. The add operator supplies the missing information that is necessary to assemble a playable PACT by retrieving and adapting adequate cases (low-level PACTS on one or more dimensions) from the Musical Memory. The retrieval is done by a partial pattern matching between case indexes, the chords of the chord grid segment and the current activated PACTS. Since the concepts used in the indexation of cases correspond to the descriptors of high- level PACTS, it is possible to retrieve low-level PACTS when only high-level PACTS are activated. For instance, if the PACTS “play bluesy” and “play a lot of notes” are activated in the context of “Bb7-F7” chords, we search for a case that has been indexed as having a bluesy style, a lot of notes and IV7-I7 as underlying chords. When there is no PACT on a particular dimension, we search for a case that has “default” as a descriptor of this dimension. For instance, it is possible to retrieve a melody even when the activated PACTS concern amplitudes only. The cases may correspond to some “chunks” of the note dimensions that may not fit in the “gaps” that exist in the current activated PACTS. Thus, retrieved cases may carry additional information which can be partially incompatible with the activated PACTS. Here either the conflicting information is ignored or it can “short-circuit” the current PACT assembly and lead to a different playable PACT. Let us suppose that the activated PACTS concern pitches and amplitudes and the retrieved case concerns pitches and rhythm. Only the activated PACTS on amplitude can be considered to be combined with the retrieved case generating a playable PACT. But, if the retrieved case concerns rhythm and amplitudes, perhaps the latter information could be ignored. Choosing the add operator balances the cost in terms of memory search time with the possibility of short- circuiting the assembly process. Short-circuiting is an important feature of music creativity. For instance, in melody composition there is no chronological ordering between rhythm and pitches (Sloboda 1985). Sometimes, both occur together! This feature is often neglected by computational formalisms (Vincinaza & Prietula 1989). 5.3 - The Execution Module The problem of planning in a dynamic world is that when the plan is being generated new events may occur and invalidate it. In music performance, it suffices that the musician plays to provoke changes in the context. Thus, monitoring context changes at the same time as replanning what is being executed is very difficult in real- time conditions. In our model we consider that the reasoning mechanisms that underlie planning and replanning in music performance are not the same. The replanning that can be done while playing is related more to simple and 112 The Arts fast anatomic reactions than to complicated and refined reasoning. Consequently, beyond the role of controlling a MIDI synthesizer, the execution module has also to perform the changes in already generated plans. The idea is that particular context events trigger simple replanning such as “modify overall amplitude”, “don’t play these notes”, “replace this note by another”, etc. In short, since the composition module has finished its task, it is no longer concerned by changes to the plan it has generated. The context events occurring during a given plan generation will only be taken into account in the following plan generation. At the current stage, the execution module has no replanning facilities. Notes are executed by a MIDI scheduler developed by Bill Walker (CERL Group - University of Illinois). 6 - Discussion We have shown how an extension to classical problem solving could simulate some features of musical creativity. This extension attempts to incorporate both the experience musicians accumulate by practicing and the interference of the context in the musicians’ ongoing reasoning. Although we do not use randomness in our model, there is no predetermined path to generate music. The musical result is constructed gradually by the interaction between the PACTS activated by the context and the Musical Memory’s resources. The notion of PACTS was first implemented (Pachet 1990) for the problem of generating live bass line and piano voicing. At this time, results were encouraging but, exploring exclusively a rule-based approach, various configurations of PACTS were hardly treated, if at all. This was due to the difficulty of expressing all musical choices in terms of rules. Our work has concentrated on improving the formalization of PACTS within a problem solving perspective. We have also introduced the notion of Musical Memory and seen how it can be coupled with PACTS. Today, Pachet’s system is being reconsidered and r-e-implemented to take into account both the Musical Memory and a wider repertoire of PACTS. In our model we have bypassed perceptual modeling. This is a tactical decision with respect to the complexity of modeling creativity in music. However, this modeling is essential for two reasons: to provide a machine with full creative behavior in music and, if coupled with machine learning and knowledge acquisition techniques, to help us in acquiring PACTS. Acknowledgments We would like to thank Francois Pachet, Jean-Daniel Zucker and Vincent Corruble who, as both musicians and computer scientists, have given us continuous encouragement and technical support. This work has been partly supported by a grant from the Brazilian Education Ministry - CAPESMEC. References AAAI ‘93 Workshop on Artificial Intelligence & Creativity 1993. Melon Park, AAAI Press. Ambros-Ingerson, J. & Steel, S. 1988. Integrating Planning, Execution and Monitoring, In Proceedings of the Sixth National Conference on Artificial Intelligence, 83-88, AAAI Press. Ames, C. & Domino, M. 1992. Cybernetic Composer: an overview, In M. Balaban, Ebicioglu K. & Laske, 0. eds., Understanding Music with AI: Perspectives on Music Cognition, The AAAI Press, California. Baker, M. 1980. Miles Davis Trumpet, Giants of Jazz Series, Studio 224 Ed., Lebanon. Baudoin, P. 1990 Jazz: mode d’emploi, Vol. I and II. Editions Outre Mesure, Paris. Johnson-Laird, P. 1992. The Computer and the Mind, Fontana, London. Laird, J., Newell, A. & Rosembloom, P. 1987. SOAR: An Architecture of General Intelligence, Artificial Intelligence 33, 1-64. Newell, A. & Simon, H. 1972. Human Problem- Solving, Englewood Cliffs. Prentice Hall, NJ. Nilsson, N. 1971. Problem-Solving Methods in Artificial Intelligence, McGraw-Hill Book Co., New York. Pachet, F. 1990. Representing Knowledge Used by Jazz Musicians, In the Proceedings of the International Computer Music Conference, 285-288, Montreal. Ramalho, G & Ganascia, J.-G. 1994. The Role of Musical Memory in Creativity and Learning: a Study of Jazz Performance, In M. Smith, Smaill A. & Wiggins G. eds., Music Education: an Artificial Intelligence Perspective, Springer-Verlag, London. Ramalho, 6. & Pachet, F. 1994. What is Needed to Bridge the Gap Between Real Book and Real Jazz Performance?, in the Proceedings of the Fourth International Conference on Music Perception and Cognition, Liege. Rowe, J. & Partridge, D. 1993. Creativity: a survey of AI approaches, Artificial Intelligence Review 7, 43-70, Kluwer Academic Pub. Slade, S. 1991. Case-Based Reasoning: a Research Paradigm, AZ Magazine, Spring, 42-55. Sloboda, J., 1985. The Musical Mind: The Cognitive Psychology of Music, Oxford University Press, New York. Steedman, M. 1984. A Generative Grammar for Jazz Chord Sequences, Music Perception, Vol. 1, No. 2, University of California Press. Vincinanza, S. & Prietula, M. 1989. A Computational Model of Musical Creativity, In Proceedings of the Second Workshop on Artificial Intelligence and Music, 21-25, IJCAI, Detroit. Music / Audition 113 | 1994 | 299 |
1,651 | Can we enforce full compositionality in uncertainty cak Didier Dubois and Henri Prade Institut de Recherche en Informatique de Toulouse (I.R.I.T.) - C.N.R.S. Universite Paul Sabatier, 118 route de Narbonne 3 1062 Toulouse Cedex, France (dubois, prade)@irit.irit.fr Abstract compositionality. At AAAI’93, Elkan has claimed to have a result trivializing fuzzy logic. This trivialization is based on too strong a view of equivalence in fuzzy logic and relates to a fully compositional treatment of uncertainty. Such a treatment is shown to be impo- ssible in this paper. We emphasize the distinction between i) degrees of partial truth which are allowed to be truth functional and which pertain to gradual (or fuzzy) propositions, and ii) degrees of uncertainty which cannot be compositional with respect to all the connectives when attached to classical proposi- tions. This distinction is exemplified by the differen- ce between fuzzy logic and possibilistic logic. We also investigate an almost compositional uncertain- ty calculus, but it is shown to lack expressiveness. I. Introduction There is a very active research trend in Artificial Intelligence concerning the management of uncertainty in knowledge-based systems. This trend is still influenced by the MYCIN experiments (Buchanan & Shortliffe, 1984), where a basic idea was to attach weights expressing uncertainty to facts and rules in a knowledge base. Then we are faced with the problem of how to propagate these weights in reasoning procedures. This problem has usually been dealt with on a rule-by-rule basis, by splitting it into three subproblems: i) computing the weight bearing on a compo-site fact from the weights bearing on the elementary parts of this fact; ii) propagating the weight bearing on the conditions of the rule to the conclusion, by integrating the weight bearing on the rule; iii) combining the weights bearing on partial conclusions pertaining to the same matter. However, investigating the validity of such a method requires a proper interpretation of the weights. Reading the literature in this area, it appears that these weights may have two interpretations: degrees of uncertainty and degrees of partial truth and that people tend to make a confusion between these two notions. One of the reasons why this confusion was made is the need for a compositionality law for computing the resulting weights in the style of many-valued logics where all the connectives are usually truth-functional. Even degrees of probability are sometimes called degrees of truth (e.g., Nilsson, 1986) although probabilistic logic excludes The emergence of fuzzy rule-based systems in process control problems has led AI researchers, that criticized MYCIN-like systems, to reject fuzzy logic on the same grounds of dubious compositionality assumptions. For instance, in a recent paper, Elkan (1993) has questioned its well-foundedness and cast serious doubts on the reasons of its success, arguing that “fuzzy logic collapses mathema- tically to two-valued logic”. This claim is in fact due to the use of too strong a notion of logical equivalence which is valid in two-valued logic, but which has nothing to do with fuzzy logic. Furthermore, Elkan (1993) does not mention the important distinction between two totally different problems to which fuzzy set-based methods apply, namely the handling of gradual (thus non-Boolean) properties whose satisfaction by a completely known state of facts is a matter of degree on the one hand, and the handling of uncertainty pervading Boolean propositions and induced by incomplete states of knowledge (which can be represented by means of fuzzy sets) on the other hand. The first problem can be addressed by means of a truth functional fuzzy (multiple-valued) logic, while the second one is the realm of possibility theory (Zadeh, 1978; Dubois & Prade, 1988a) which is a non-fully compositio- nal uncertainty calculus (i.e., the degree of uncertainty of a compound proposition cannot systematically be computed from the degrees of uncertainty of its components only). Elkan (1993)‘s paper is thus pervaded by the wrong but alas rather common idea that truth functional fuzzy logic has something to do with uncertainty handling. Assuming a fully compositional many-valued calculus on a Boolean algebra of propositions (a structure enforced by his equivalence requirement), the logical system collapses to two-valued logic. This paper is a presentation of the authors’ view on the problem of handling uncertainty and partial truth in the framework of information systems. In Section 2 we argue in favor of a clear distinction between (un)certainty and truth and propose a practical definition of truth based on approximate matching between a proposition and the description of a state of facts. Section 3 recalls the impo- ssibility of a fully compositional calculus for dealing with uncertainty about Boolean propositions, and illustrates this impossibility result by comparing fuzzy logic and possi- bilistic logic. In Section 4 we investigate the possibility Automated Reasoning 149 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. of an aEmost fully compositional uncertainty calculus, but its expressiveness turns to be very limited. 2. Partial Truth vs. Uncertainty The distinction between degrees of truth and degrees of uncertainty goes back to De Finetti (1936), and seems to have been almost completely forgotten by Artificial Intelligence people. The confusion pervading the relation- ship between truth and uncertainty in the expert systems literature is apparently due to the lack of a dedicated paradigm for interpreting partial truth, and grades of uncertainty in a single framework. Such a paradigm can derive from a commonsense view of truth, as the compatibility between a statement and reality. This ndive definition of truth has been criticized by philosophers (see, e.g., Gochet in his discussion of Dubois & Prade (1988b)) but can be suitably modified by changing the debatable word “reality” into “what is known about reality” and interpreting the latter as “the description of some actual state of facts as stored in a data base”. Hence computing the degree of truth of a statement S comes down to estimating its conformity with the description of what is known of the actual state of facts. As a consequence, truth evaluation comes down to a semantic matching procedure. This point of view is in accordance with Zadeh (1982) test- score semantics for natural languages. Four interesting situations can be encountered. a) Classical two-valued logic. In order to compute truth- values, we need a precise definition of what “proposition” means. This is a matter of convention. The usual convention is that a proposition is identified with a set of “possible worlds” or “states of fact”. Moreover a proposition is said to be true if and only if the actual state of facts is one of those which the proposition encompasses. By convention a proposition is true or false. If the actual state of facts is known and encoded as an item d in a database, the truth-value xd(S) (=l (true) or 0 (false)) of a proposition S in a state of facts d can be computed. b) Partial truth. This convention can be changed. Instead of defining a proposition as a binary entity that fits the actual state of fact or not, we can decide to use a more refined scale to evaluate the compatibility between a proposition S and a precisely known state of facts d. This is usual in natural language. For instance, the compatibility of “a tall man”, with some individual of a given size is often graded: the man can be judged not quite tall, somewhat tall, rather tall, very tall, etc. Changing the usual true/false convention leads to a new concept of pro- position whose compatibility with a given state of facts is a matter of degree, and can be measured on a scale L that is no longer { 0,l > , but the unit interval for instance. It reflects linguistic levels such as “somewhat”, “rather”, “very”, etc. This kind of convention leads to identifying a “fuzzy proposition” S with a fuzzy set of possible words; the degree of membership of a possible world to this fuzzy set evaluates the degree of fit between the proposition and the state of facts it qualifies. This degree of fit r&S) E L is called degree of truth of proposition S in the possible world d. Many-valued logics, especially truth-functional ones, provide a calculus of degrees of truth, including degrees between “true” and “false”. c) Uncertainty. On the other hand, even if we keep the convention that a proposition is either true or false, it is not always possible to determine whether it is actually true or false in given circums+cances, because the actual state of facts is not known. In such a situation, we face uncertainty. Clearly uncertainty is a meta-level concept with respect to truth, since the uncertainty bears on whether a proposition is true or false (and nothing else). Moreover uncertainty is knowledge-dependent, i.e., refers to an agent. If uncertainty is encoded in a binary way, there can be only 3 situations: the agent is sure that S is true, he is sure that S is false, or he does not know. This last situation does not correspond to a third truth-value but to a suspended choice. More refined models of uncertainty will use an ordered scale U (again, the unit interval [O,l] usually) then g(S) E U will express to what extent one is sure that S is true, and g(4) to what extent one is sure that S is false. A typical example of degree of uncertainty is a degree of probability. Then our imperfect knowledge of the actual state of facts is modelled via a probability distribution over possible worlds, g(S) being the probability of the set of possible worlds identified with S. In other situations our knowledge of the actual state of facts is described by a set K of propositions that are believed as being true by some agent (what Gardenfors (1988) calls a belief set). The available knowledge is then described by the set D of possible worlds where all propositions in K are true; a proposition S is surely true if D c S, surely false if D z 4 (the complement of S) and S is uncertain if D n S f 0, D n -S# 0. This is again the crude trichotomy mentioned above in the presence of incomplete knowledge. Between this crude model, and the sophisticated, additive probabilistic approach to uncertainty lies a third more qualitative approach. Suppose that the set D of possible states of fact is ordered in terms of plausibility, normality and the like. Then D can be viewed as a fuzzy set of possible states of facts. The overlapping between D and the ordinary set of possible worlds identified with a proposition S will be a matter of degree. This is possibility theory that handles two degrees n(S) and N(S) attached to S, respectively the possibility and the necessity that S is true. n(S) = 1 means that S is true in one of the most plausible worlds in D. N(S) = 1 means that S is true in all possible worlds in D. Total ignorance on the truth value of S is expressed by n(S) = 1, N(S) = 0. Moreover N(S) = 1 - n(--S) while P(--S) = 1 - P(S) in the probabilistic approach. Note that the presence of uncertainty does not affect the truth-value scale which is always {O,l }: degrees of uncertainty are not truth-values. @ Uncertain martial truth. In that case truth may altogether be a matter of degree and may be ill-known. Then, all values a = xd(S) such that d is compatible with the available information D, is a candidate truthvalue for S. When both S and D can be expressed as fuzzy sets, we 150 Automated Reasoning can consider for each truth-value a E L, such that a = xd(S) a degree of possibility pD(d) that a is the truth-value of S. This fuzzy set of more or less possible truth-values forms a so-called fuzzy truth-value (Zadeh, 1979) denoted zD(S). A fuzzy truth-value combines the ideas of partial truth and of uncertainty about truth. It is thus a more complex construct than degrees of truth and degrees of uncertainty. Changing the fuzzy set D into a probability distribution on possible worlds, Z,(S) becomes a random truth-value over a non-binary truth set L. A standard analogical example that points out the difference between degrees of truth and degrees of uncertainty is that of a bottle. In terms of binary truth- values, a bottle is viewed as full or empty. If one accounts for the quantity of liquid in the bottle, one may say the bottle is “half full” for instance; under this way of speaking “full” becomes a fuzzy predicate and the degrees of truth of “The bottle is full” reflects the amount of liquid in the bottle. The situation is quite different when expressing our ignorance about whether the bottle is either full or empty (given that we know only one of the two situations is the true one). To say that the probability that the bottle is full is l/2 does not mean that the bottle is half full. Degrees of uncertainty are clearly a higher level notion than degrees of truth. 3. Fuzzy Logic vs. Possibilistic 3.1. The Compositionality Problem An important consequence of the above distinction between degrees of truth and degrees of uncertainty is that degrees of uncertainty bearing on classical propositions cannot be compositional for all connectives. Namely there cannot exist operations 0 and * on [O,l], nor negation functions f such that g(S) f 0,l for some S, g(T) = 1, g(l) = 0 and the following identities simultaneously hold for all classical propositions S 1, S2, S g(not s> = fWN (1) ; g(S1 A 53 = gel) * gc$ (2) 0 1 ” S2) = gcq @ g(S2) (3) This result is proved independently in (Dubois & Prade, 1988b) and (Weston, 1987). A family of propositions represented by a classical language form a Boolean algebra. The lack of compositionality is then a direct consequence of the well-known fact in mathematics that a non-trivial Boolean algebra that is linearly ordered has only two elements. However weak forms of compositionality make sense; for instance n(S, v S2) = max(17(S1), n(Q) in possibility theory, but generally, n(S, A S2) c min(n(S I), n&N; l-KS1 A s,> = min(IT(S $n(S2)) holds only for logically independent propositions; see Sec. 3.3. Similarly with grades of probability where P(S) = 1 - P(not S) but P(S 1 A S2) = P(S 1) . P(S2) only in situations of stochastic independence. The above impossibility result is a new way of stating a well known fact, i.e., that the unit-interval is not a Boolean algebra. It rejects many usual uncertainty handling compositional techniques currently used in expert systems into ad-hocery. This result is based on the assumption that the propositions to evaluate are not fuzzy ones. By contrast, truth values of fuzzy propositions can be compositional when they can be precisely evaluated (i.e., under complete information). This is because closed sets of fuzzy propositions are no longer Boolean algebras but form weaker structures compatible with the unit interval. For instance, using max, min, 1 - (a) for expressing disjunction, conjunction and negation of fuzzy propositions equips sets of such propositions with a distributive lattice structure that is compatible with the unit interval; this structure is the only one where all laws of Boolean algebra hold except the laws of non- contradiction and of excluded middle (Bellman & Giertz, 1973). Sometimes, arguments against fuzzy set theory rely on the impossibility of compositionality (e.g., Weston, 1987; Elkan, 1993). Usually these arguments are based on the wrong assumption that the algebra of propositions to be evaluated is Boolean. Note that fuzzy truth values (case d above) are not truth- functional, generally. 3.2. Fuzzy Logic Equivalence is not Classical Elkan (1993) claims that in fuzzy logic the four following requirements hold for any propositions S1 and S2,2 being a truth assignment function such that VS, z(S) E [O,l] W1 A S2> = minWlMS2)) (4) QS1 v S2> = max(QS1),@2)) (3 T(4) = 1 - z(S) (@ 7(S1) = @2) if S1 and S2 are logically equivalent. (7) While (4)-(5)-(6) are indeed the basic relations governing degrees of truth in fuzzy logic (as well as fuzzy set membership degrees) as proposed by Zadeh (1965), requirement (7) where “logically equivalent” is understood in a stronger sense than the equivalences induced by (4)- (5)-(6) has never been seriously considered by any author in the fuzzy set literature (up to a few erroneous papers which may always exist in a large corpus of publications). Indeed assuming that degrees of truth can be intermediary between 0 and 1, the propositions under consideration are no longer classical ones. Hence logical equivalence must be redefined from scratch. (7) should be understood the other way around: “S1 is equivalent to S2” means z(S ]) = z(S2) in all possible worlds. Obviously some classical logic equivalences still hold with fuzzy propositions obeying (4)-(5)-(6), namely the ones allowed by the De Morgan’s structure induced by (4)-(5)-(6), as for instance sAs=s; SVS=S (idempotency) s~A(s~Vs3)“(s~As~)“(s~As3); S~V(S~ASS~)~(S~ v S2) A (Sl v S3) (distributivity). But other Boolean equivalences do not hold, for instance S A -S Z I since (4) and (6) only entail z(S A 7s) = min(z(S), 1 - z(S)) I l/2 Autbmated Reasoning 151 S v 43 # T since (5) and (6) only entail z(S v 4) = max(z(S), 1 -z(S)) 2 l/2 where z(l) = 0 and z(T) = 1. Indeed the failme of contradic- tion and excluded-middle laws is typical of fuzzy logic as emphasized by many authors. This is natural with gradual properties like ‘tall’. For instance, in a given context, somebody who is 1.75 meter tall, may be considered neither as completely tall (i.e., tall with degree 1) nor as completely not tall (i.e., tall with degree 0); in this case we may have, for example, j.tt& 1.75) = 0.5 = btdl( 1.75). Idempotency is thus preserved by using min and max for intersection and union respectively but not the excluded middle and contradiction laws. If we change the truth- functions in (4,5,6), we change the structure of the set of propositions (hence the underlying conventions). For instance using max(O, a + b - 1) in (4) and min(a + b, 1) we recover the laws of excluded middle and of non- contradiction but we lose idempotency of conjunction and disjunction. Indeed, the laws of excluded middle and non- contradiction are not consistent with idempotency of conjunction and disjunction, when truth is no longer a binary notion (Dubois & Prade, 1980). Note that Elkan (1993) finds it natural to require that propositions -(A A TB) and B v (TA A -B) be equivalent, and shows that this requirement is incompatible with the convention of propositions having more than 2 truth-levels in the presence of (4,5,6). Many-valued logics are trivialized by this result only insofar as the proposed equivalence is so intuitively compelling that any fuzzy logic system should adopt it. The intuitive appeal of this equivalence is far from striking since in the presence of (4,5,6), -,(A A-B) = TA v B and B v (lA A -B) = (-A v B) A (B v TB). Elkan’s suggested equivalence is clearly related to the acceptance of the excluded middle law (for B), a unusual requirement in fuzzy logic. 3.3. Possibility and Qualitative Uncertainty The presence or absence of compositional rules is thus a criterion to distinguish between logics of graded truth (that handle vague propositions under complete information) and logics of uncertainty (that handle usual propositions under incomplete information). This is well exemplified by the distinction between fuzzy logic and possibilistic logic. Fuzzy sets can be used not only for modelling the gradual nature of properties but can also be used for representing incomplete states of knowledge. In this second use, the fuzzy set plays the role of a possibility distribution which provides a complete ordering of mutually exclusive states of the world according to their respective levels of possibility or plausibility. For instance, if we on2y know that “John is tall” (but not his precise height), where the meaning of ‘tall’ is described in the context by the mem-bership function of a fuzzy set, i.e., ~~~11, then the greater ptall(x) is, the greater the possibility that height(John) = x and the smaller l.~dl(x), the smaller this possibility. Given a [O,l]-valued possibility distribution n; describing an incomplete state of knowledge, Zadeh (1978) defines a so-called possibility measure II such that II(S) = sup(~(x), x makes S true} (8) where S is a Boolean proposition, i.e., a proposition which can be true or false only. It can be easily checked that for Boolean propositions S1 and S2, we have WSl v Sd = m=(Ws l)JU2)) c-0 but only lI(S, A S2) I min(n(S&n(S2)) (10) in the general case (equality holds when S1 and S2 are logically independent). Indeed if S2 = +, II(S 1 A S2) = II(l) = 0, while min(II (S),lYl(TS)) = 0 only if the information is sufficiently complete for having either lI(-S) = 0 (S is true) or II(S) = 0 (S is false). If nothing is known about S, we have l-I(S) = I&S) = 1. By duality, a necessity measure N is associated to n according to the relation (which can be viewed as a graded version of the relation between what is necessary and what is possible in modal logic) N(S) = 1 - l&S) (11) which states that S is all the more necessarily true as IS has a low possibility to be true. It entails NV1 A 53 = min(N(S l)JW;?)) (12) and NC$ v S,> 2 mMNS1)NS2)). (13) Observe also that neither n , nor N, are fully compositional with respect to A, v and l. Possibilities are only compositional with respect to disjunction, necessities with respect to conjunction. The equalities (9), (11) and (12) should not be confused with (5), (6) and (4) respec- tively. In (9), (ll), (12) we deal with Boolean propositions pervaded with uncertainty due to incomplete information, while (4)-(5)-(6) pertain to non-Boolean propositions whose truth is a matter of degree (the information being assumed to be complete). This distinction is a crucial prerequisite in any discussion about fuzzy sets and possibility theory and their use in automated reasoning. Possibility measures have been shown (Dubois, 1986; Dubois & Prade, 1991) to be the numerical counterpart of so-called qualitative possibility relations 2 (where S 12 S2 reads “S1 is at least as possible as Ss”), in the sense that Vfl, 3 an ordering 2 such that t/S +‘S2, n(S,) 2 I-&) w S1 2 S2- The ordering 2 is supposed to be reflexive, complete (Sl 2 S2 or S2 2 Sl), transitive, non-trivial (T > I), such that VS, T 2 S (certainty of tautology) and to satisfy the characteristic axiom VS1, if S2 2 S3 then S1 v S2 2 S1 u S3. For qualitative necessity the above axiom is changed, for the corresponding ordering, by substituting n to u. This shows the qualitative nature of possibility and necessity measures. The case d of Section 2 which combines the case of fuzzy statements and of incomplete information can be also handled in the possibilistic framework. Let PD be the 152 Automated Reasoning membership function of the fuzzy set representing the available information and PS be the one representing the fuzzy statement. The degree of truth ZD(S) is then itself a fuzzy set of [O,l], which can be interpreted as a fuzzy truth-value, whose membership function is defined by ~D(S)(v)=supd~~~(~~ 1 c1s(d)=v); kD(s)(v>=o if~$-l@~=o i.e., k,(s)(v) is the grade of possibility that the degree of truth of S is equal to v knowing that the state of facts is restricted by D. The fuzzy truth value ED can be approximated by means of two numbers n(S) and N(S), which extend (8) and its dual to the case of a fuzzy statement S (Dubois & Prade, 1985), namely with II: = i&D I’M> = supd mMwS(O MD N(S) = 1 - n(G) = infd maxus( 1 - n(d)). Indeed n(S) and N(S) can be viewed as the degrees of possibility and necessity that S is “true”, if we interpret “true” by extending its definition from (0,l) (i.e., I+,&) = 1, ~~~(0) = 0) to WI by letting ~~~(9 = v, V v E [O,l]. We then have in any case rm = sup, mirU-&v)* v) N(S) = infv max(1 - kD(s)(v), v). 4. Almost Preserving Compositionality As said above a measure of uncertainty defined on a Boolean algebra and taking its values in the interval [O,l] cannot be fully compositional with respect to all the logical connectives, just because we cannot equip [O,lJ with a structure of Boolean algebra. However we may try to preserve compositionality as far as possible. Recently Schwartz (1992) has proposed a logic of likelihood governed by the following laws, for all S, S 1, S2 g(ls) = ’ -gcs)’ gts 1” ‘2) = 1 ifSlvSz=T ma(g(Sl) g(S2)) if not l , t OifSlAS2=I min(g(S l),g(S2)) if not. Such a measure of likelihood g is as compositional as possible. Note that these likelihood set-functions are self- dual. Moreover only operations with a qualitative flavor are used to combine the likelihood degrees. Only a totally ordered set equipped with an order reversing involution is required as a likelihood scale. In the following we investigate what is the power of expressiveness of these measures of likelihood, in the finite case. Let Q = {ol, . . . . Wn) be the finite set of atoms of the Boolean algebra 2sz. Let g((Oi}) = gi E [O,l]. We have Vi, gi = l-g(sZ-{Oi))= l-maXj+igj=minj~i(l-gj). If 3i, gi = 1 then g(a - (Wi)) = 0 and then V j f i, gj = 0. Thus it corresponds to the deterministic case. Let US suppose that 3i, gi = a E (0,l). Then V j # i, gj I maXk$i gk = g(ln - (Oi)) s 1 - gi g I- CX. Let us suppose that a = gl 2 g2 2... 2 gn. Then 82 = 1 - g(sZ - (02)) = 1 - IYMXj,t2 gj = 1 - gl = 1 - a. Since gl is the maximal level, it follows that cc 2 l/2. Similarly we have: g3 = 1 - max(gl, g2, &Q, . . . . gn) = 1 -a, . . . . gn = 1 - a. Thus if gl < 1, we can only have l>g12g2=g3=...=gn=1-gl>O.Sowecanonly describe a pseudo-deterministic situation where 3i, gi = o21/2,andVj#i,gj = 1 - a 5 l/2. In particular, total uncertainty is described by Vi, gi = a = 1 - a = l/2. In this calculus, we only have at most four certainty levels corresponding respectively to the complete certainty of truth (l), the likelihood of truth (L), the unlikelihood of truth (UL = 1 - L), and the complete certainty of falsity. Especially this representation of uncertainty does not really need the unit interval since only a 4-element totally ordered set (0, UL, L, 1) is needed. Thus this proposal corresponds to the most elementary logic of likelihood which can be imagined: there exists one alternative 00 which, without being necessarily complete- ly certain, appears to be more likely than the others which are considered as having a smaller, undifferentiated level of likelihood. This seems to coincide with the “simplified English probabilistic logic” considered by Aleliunas (1990); this logic also distinguishes between the four levels: 0 (certainly false), unlikely, likely, 1 (certainly true). It is interesting to see whether likelihood measures induce a comparative probability ordering on events. Namely a comparative probability ordering 2 is such that 2 is complete and transitive, S 2 0, V S c Q, and 2 satisfies the additivity axiom (Fine, 1973): V’s 1, then S2>S3#S1US2>S1US3 (14 where S, > S2 means S 1 2 S2 and not (S2 2 S 1). Any non-degenerate function g classifies the events in a into 4 classes of level 1, L, UL and 0 respectively. Namely 300 such that the class of level L is {S f a, wo E S), the class of level UL is (S f 0, wo e S ) . The class of level 1 is (Q) and the one of level 0 is (0). Particularly we have, for S1 f S2, S1 > S2 if and only if S1 = LR or S2 = 0 or (WO E S1 and 00 g S2). Let us consider whether (14) holds: - ifs, = &I2 then S1 = 0 and (14) is trivial. From now on s, #0QI; - if S2 f Sz, S3 f 0 then assume S2 > S3, i.e., UO E S2, q e S3. Since S1 n S2 = 0, 00 G S1. Hence woe S1 u S3 and S1 u S2 > S1 u S3. Conversely assume &I f S 1 u S2 > S 1 u S3. Clearly S1 u S3 #0; we have wo E S1 u S2,oo G! Sl u S3. Automated Reasoning 153 Hence wo 4 Sl, and wg E S2 - S3. Hence S2 > S3. Assume now S1 u S2 = Q > S1 u S3 then since S 1 n (S2 u S3) = 0, it follows that S3 c S2. If coo E S2 - S3 then g(S1 u S2) = 1 > g(S1 u S3) = UL and g(S2) = L > g(S3) = UL. If wo E S3 we have g(S2) = g(S3) = L and g(S1 u S2) = 1 > g(S1 u S3) = L. Hence (14) fails when Sl u S2 = Sz. - when S3 = 0 then (14) fails too, if wo E S1 since then g(S2) > gC+ but g(S, u S,> = g(S, u S,> = L generally. As a consequence the likelihood measure almost satisfies the axioms of a comparative probability relation. It satisfies the following reasonable relaxation of addi- tivity: VS 1, S 2, S3 such that S1 u S2 f a, S1 n (S2 u S3) = 0, S3 f 0: S2 > S3 t--/ S1 u S2 > S1 u S3. This section gives an answer to the following question: how far can we go with a representation of uncertainty that tries to take advantage of truth-functionality as far as possible. It is shown here that, not only full truth-functionality is not possible, but retaining this property as much as mathematical consistency allows, leads to a very crude, almost deterministic model of uncertainty. 5. Concluding Remarks The intended purpose of this paper is to emphasize the distinction between the treatment of gradual (or vague) predicates in presence of complete information which can be handled in a fully truth functional multiple-valued way (this is for instance the case for most of the applications in fuzzy control), and the handling of uncertainty for propositions which are either true or false (and which more generally may also have intermediary degrees of truth). In this second case, possibility theory offers a qualitative way for handling uncertainty which can be cast in a logical formalism (see, e.g., Dubois, Lang and Prade, 1991). Possibility theory, as probability theory and any uncertainty calculus is not fully compositional with respect to all connectives. It is still possible to enforce an almost fully compositional calculus for uncertainty, only at the high price of an important loss of expressiveness. On the whole we agree with Elkan (1993) on the point that the truth-functional fuzzy logic is not adapted to a proper handling of uncertainty in knowledge-based system. But our agreement is not based on an alleged self- inconsistency of fuzzy logic leading to a collapse. It is based on the fact that fuzzy logic offers a calculus of truth- values not of degrees of uncertainty. Especially there is no treatment of uncertainty in fuzzy controllers. Elkan’s trivialization result kills truth-functional uncertainty handling systems, and certainly does not harm fuzzy logic nor the interpolation device at work in fuzzy controllers. References Aleliunas, R. 1990. A summary of a new normative theory of probabilistic logic. In Uncertainty in Al, Vol. 4 (R.D. Shachter et al., eds.), 199-206. North-Holland. Bellman, R.E.; and Giertz, M. 1973. On the analytic formalism of the theory of fuzzy sets. Information Science 5: 149- 157. Buchanan, B.G.; and Shortliffe, E.H. 1984. Rule-Based Expert Systems. Readings, MA: Addison-Wesley. De Finetti, B. 1936. La logique de la probabilite. In Actes du Congres Inter. de Philosophie Scient@que, Paris, 1935, IVl-IV9. Hermann et Cie Editions, 1936. Dubois, D. 1986. Belief structures, possibility theory and decomposable confidence measures on finite sets. Comput. Artif Intell. (Bratislava) 5(5):403-416. Dubois, D.; Lang, J.; and Prade, H. 1994. Possibilistic Logic. In Handbook of Logic in AI and Logic Programming, Vol. 3 (D.M. Gabbay et al., eds.), 439- 5 13. Oxford University Press. Dubois, D.; and Prade, H. 1980. New results about properties and semantics of fuzzy set-theoretic operators. In Fuzzy Sets (P.P. Wang, SK. Chang, eds.), 59-75. Plenum. Dubois, D.; and Prade, H. 1985. Evidence measures based on fuzzy information. Automatica 31:547-562. Dubois, D.; and Prade, H. 1988a. Possibility Theory. New York: Plenum Press. Dubois, D.; and Prade, H. 1988b. An introduction to possibilistic and fuzzy logics (with discussions). In Non Standard Logics for Automated Reasoning (p. Smets et al., eds.), 287-315 & 321-326. Academic Press. Dubois, D.; and Prade, H. 1991. Epistemic entrenchment and possibilistic logic. Artificial Intelligence 50:223-239. Elkan, Ch. 1993. The paradoxical success of fuzzy logic. In Proc. AAAl’93, Washington, DC, July 11-15, 698-703. Fine, T.L. 1973. Theories of Probability. New York: Academic Press. Gadenfors, P. 1988. Knowledge in Flux. MIT Press. Nilsson, N.J. 1986. Probabilistic logic. Artificial Intelligence 28171-87. Schwartz, D.G. 1992. A min-max semantics for fuzzy likelihood. In Proc. 1st IEEE Inter. Conf. on Fuzzy Systems, San Diego, CA, March 8-12, 1393-1398. Weston, T. 1987. Approximate truth. J. Philos. Logic 16:203-227. Zadeh, L.A. 1965. Fuzzy sets. Infor. & Cont. 8:338-353. Zadeh, L.A. 1978. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1:3-28. Zadeh, L.A. 1979. A theory of approximate reasoning. In Machine Intelligence, Vol. 9 (J.E. Hayes, D. Michie, and L.I. Mikulich, eds.), 149-194. New York: Elsevier. Zadeh, L.A. 1982. Test score semantics for natural languages and meaning representation via PRUF. In Empirical Semantics, Vol. I (B.B. Rieger, ed.), 281-349. Bochum: Brockmeyer. 154 Automated Reasoning | 1994 | 3 |
1,652 | Neural Programming Language Hava T. Siegelmann Department of Computer Science Bar-Ilan University, Ramat-Gan 52900, Israel E-mail: hava@bimacs.cs.biu.ac.il Abstract Analog recurrent neural networks have attracted much attention lately as powerful tools of auto- matic learning. We formally define a high level language, called NEural Langage, which is rich enough to express any computer algorithm or rule- based system. We show how to compile a NEL program to a network which computes exactly as the original program and requires the same compu- tation time. We suggest this language along with its compiler as the ultimate bridge from symbolic to analog computation, and propose its outcome as an initial network for learning. * 1 Introduction Classical approaches of Computer Science and Ar- tificial Intelligence are based on understanding and explaining key phenomena in a discrete, symbolic manner. A list of rules or an algorithm is then developed and given to the computer to execute. These approaches have the limitations of human understanding and analysis power. An alternative approach to elicit knowledge and express it by symbols is the neural network mod- eling. Neural networks are trainable dynamical systems which learn by observing a training set of input-output pairs. They estimate functions with- out a mathematical model of which the output is assumed to depend on the input. The choice between the above two approaches depends on the particular application. For exam- ple, the first approach is a better fit for controlling simple engines; in the complex-task of generating a functional electric stimulation (FES) in locomotion of subjects with incomplete spinal cord injury, the classical methodology yields limited functionality, while the learning approach generates far better re- sults (Armstrong et al. 1993). The pure neural net- work approach, although rich and adaptable, may lose simple hints that are easily tractable by a hu- man expert (and thus are provided in “hand-crafted *This research was partidy supported by US Air Force Grant AFOSR-91-0343 rules”) but are hard to deduce from a sample set. In the functional electric stimulator, for example, a list of rules is thus preferred over adaptable ap- proaches for particular simple functions, while the adaptable approach is still generally preferred. An- other drawback of the nets is that they suffer from sensitivity of the convergence rate to initial state. The two approaches, symbolic algorithms and adaptive analog nets, are suggested in this work to be interleaved in a manner that takes the best of both models. This is based on very recent the- oretical findings in the area of artificial neural net- works: that the computational power of such nets is universal (Siegelmann & Sontag 1991). We pro- vide a novel method for translating algorithms (or rules) expressed in a Pascal-like programming lan- guage into a corresponding neural networks. This research can be thought of a basis for acquiring a function estimator in any area of expertise, using the following four step paradigm. 1. Knowledge will be elicited from experts in the field, and a program (or a rule-based system) will be written in a high level language. In our exam- ple of functional electric stimulator, the physician deduces rules from patterns recorded in able sub- jects as a first approximation for locomotion of paralyzes. 2. The program will be compiled into an equivalent neural net of analog neurons. 3. The applicability of the network for adapting and generalizing will be raised: nodes and edges of low computational significance will be added to yield a homogeneous architecture; the net may be pruned, and the activation function smoothed UP* 4. The network will be provided with a sample data of input-output pairs, and will adapt itself to comply with them, thus, tuning and fixing the original expert’s knowledge. The fields of knowledge engineering and pro- gramming will cover the first step. Learning al- gorithms of recurrent neural nets will cover the Neural Networks 877 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. 878 fourth step. For various learning methods see (Hertz, Krogh, & Palmer 1991). Our contribution is the methodology for the second step; the one that translates a computer program into a recur- rent network. Our requirement of the translation are strict. The translation should be fast, and the network should simulate the program without slow- ing down the computation. Note that the network itself should consist of analog neurons only and do not allow for any threshold (or other discontinuous) neuron, so that to better fit‘ methods of adaptatioi and learning. The third step is recommended for a practical reason: when a network adapts to per- form very accurately according to a training set, it tends to be “overfitting”, that is, to loose the capa- bility of generalizing well on new data. Because the network which is built at the second stage imitates a particular algorithm, its architecture and param- eter values overfit the algorithm and may have the overfitting problem. Nodes and edges are added to prevent this problem. At this stage, other consid- erations may be taken, e.g., achieving the effective number of parameters (Moody 1992) by pruning the network. Our approach of building an initial network from expert knowledge can be desirable when a partic- ular behavior is mandatory, e.g. safety conditions or security policy. In this case, the mandatory be- havior is coded into the network prior to learning, and we force parts of the network to remain fixed during the adaptation process, see for example the distal learning paradigm (Jordan 1992). 1.1 The Network Model We focus on recurrent neural networks which con- sist of a finite number of neurons. In these net- works, each processor’s tion of the type state is updated by an equa- xi(t + l,=& UijXj(f) + &j”,(l) + Cd) (1) j=l j=l where xi are the processors (i = 1,. . . , N), u are the I- external input, 6, b, c are constants, N is the num- ber of processors, and M is the number of external input signals. The function d is the simplest pos- sible “sigmoid,” namely the saturated-linear func- tion: a(x) := x { 0 ifa:< ifO<x<l (2) 1 ifx>l. When learning is desirable, the CT will be substi- tuted (during the third step) by a fully differen- tiable sigmoidal function. (Note that the precision of the neurons is not limited; thus our model de- scribes an analog rather than a digital machine.) As part, of the description, we assume that we have singled out a subset of the N processors, say Neural Networks xi,, - * -, xir ; these are the 1 output processors, and they are used to communicate the outputs of the network to the environment. Thus a net is specified by the data (aij, bij, ci) together with a subset of its nodes. 1.2 The Computational Power Some efforts have been directed towards practi- cal implementations of the applications, including those in the areas of pattern and speech recog- nitions, robot control, time series prediction, and more-see (Hertz, Krogh, & Palmer 1991). Only recently, rigorous foundations to the recurrent neu- ral network model were developed, see (Siegel- mann & Sontag 1991; 19948; Balc&zar et al. 1993; Siegelmann & Sontag 1994a). (See (Kilian & Siegel- mann 1993) for a related model with different acti- vation functions.) The computational power of the recurrent network (with finite number N of neurons and analog activations values) depends on the type of numbers utilized as weights (i.e. the constants a, h c.) If the weights are integers, the neurons may as- sume binary activation values only. Thus, the network computes a regular language. If the weights are rational numbers, the net- work is equivalent in power to a Turing Machine (Siegelmann & Sontag 1991). In particular, given any function 4 computed by a Turing Machine M in time T, one can construct a network n/ that computes the function 4 in exactly time T. That is, there is no slow down in the computation (Siegelmann & Sontag 199413). Furthermore, the size of the network is independent of the compu- tation time T. A corollary is the existence of a universal network consisting of 886 neurons and simple rational weights that computes all recur- sive functions. When weights are general real numbers (speci- fiable with unbounded precision), the network turns out to have super- Turing capabilities. How- ever, it is sensitive to resource constrains and thus is not a tautology. The exact characteri- zation of the computational class associated with such networks is disclosed in (Siegelmann & Son- tag 1994a).. I.3 Previous Related Work Previous work in inserting apriori knowledge to nets was shown to make the process of training faster for both feedforward, e.g. (Abu-Mostafa 1990; Al-Mashouq & Reed 1991; Berenji 1991; Giles & Maxwell 1987; Perantonis & Lisboa 1992; Pratt 1992; Suddarth & Holden 1991; Towell, Craven, & Shavlik 1990)) and recurrent networks, e.g. (Fras- coni et al. 1993; Omlin & Giles 1992). In all cases studied, the rules were very simple, that is, only regular rules of simple finite automata. We, on the other hand, insert rules that stem at any computer algorithm and not finite state automata only. Some work dealt with inserting rules with the em- phasize of correcting them, e.g.. (Fu 1989; Ginsberg 1988; Omlin & Giles 1993; Oursten & Mooney 1990; Pazzani 1989). The paper (Towell, Shavlik, & No- ordewier 1990) faced an expert system based on propositional calculus, and suggested to transform the original propositional domain theory into a net- work. -The connection weights were elegantly ad- justed in accordance with the observed examples using standard backpropagation techniques. We provide a general technique to translate first order logic (not only propositional) or any general algorithm (not only finite automata) to recurrent nets, rather than feedforward-acyclic architectures, which computationally are very limited (i.e. the computation ends in constant number of steps). We, -however, do not provide yet an algorithm- for tuning and correcting the encoded rules. This task is one-of the future directions of our work. 1.4 Programming Networks Given an algorithm, how does one construct a net- work that executes it? We demonstrate such a con- struction by an example. Example 1.1 Let M and N be values in [0, l] and let B be a Boolean expression. The conditional statement If(B) thenx=M else x = N can be executed by the following network: x1(t) = a(M+B-1) 4) = a(N -B) 23(t + 1) = a(x1(t> + x2(t)) * The neuron x1 attains the value a(M) when B = 1. As Q is the linear-saturated function of Equation 2, a~-lr is assumed to lie in the range [0, 11, xl(t) = = M . When B = 0, xl(t) = a(M - 1) = 0. The neuron 22 computes a( N - 1) = 0 for B = 1, and a(N) = N for B = 0. Summing the above two values into x3 results in a(M + 0) = M for B = 1, ~(0 + N) = N for B = 0 as desired. To synchronize the update, an “If” statement re- quires two sub-statement counters: one for the first update level, c 1, and one for the second update, ~2. The full update for the “if statement” is thus: xf = a(M + B + cl - 2) 2: = a(N - B + cl - 1) X3+ = a(x1 + x2 + cc - 1) ) The update equations of the counters are excluded. cl In general, tasks may be composed of a large num- ber of interrelated subtasks. The entire task may thus be highly complex, and designing an appropri- ate network from scratch becomes infeasible. We introduce a high level language (NEural Langage) for automatic construction of recurrent nets. One could compare the relationship between coding net- works directly and writing in NEL with the rela- tionship between coding in a machine language and programming in a high level language. 1.5 The Organization of The Paper The rest of this paper is organized into three sec- tions: In Section 2, we provide a brief syntactic description of the language; in Section 3 we show how to compile a subset of NEL into a network; and in Section 4 we conclude the NEL compiler. 2 Syntax Of NEL NEL is a procedural, parallel language. It al- lows for the subprograms procedure and function. A sequence of commands may either be executed sequentially (Begin, End) or in parallel (Parbe- gin, Parend). There is a wide range of possible data types for constants and variables in NEL, including the simple types: Boolean, character, scalar type, integer, real, and counter (i.e., an un- bounded natural number or 0); and the compound types: lists (with the operations defined in LISP), stacks, sets. records and arrays. For each data type, there are a few associated predefined func- tions, e.g. Isempty(stack), In(element, set), and Iszero( counter). The language is strongly typed in the sense that applying a function that is defined on a particular data type to a different data type may yield an error. Expressions are defined on the different data types. Examples of expressions are: Neural Networks 879 1. Zl C~Q for constants c and either real or inte- ger values of the variables xi. 2. (B1 And &) Or (x > a) for Boolean values B1, B2 and an integer value x. 3. Pred and Succ of an element e of a finite ordered type T returns another element of the same type. 4. Chr operates on an integer argument and returns a character. Statements of NEL include atomic statements (e.g., assignments, procedure calls, I/O state- ments), sequential compound statements (Begin, End), parallel compound statements (Pm-begin, Parend), flow control statements which include both conditional (e.g., If-then, If-then-else, case, and cond) and repetition statements (such as while and repeat). Full syntax of NEL is provided in (Siegelmann 1993). 3 Compiling NEL We next overview the compiler which translates programs written in the language NEL into neu- ral networks. A network operates generally in the following manner: there are N neurons; at each tick of the clock, all neurons are updated with new values. Thus, a network step consists of a parallel execution of N assignments. When simulating the program on a network, some of its neurons represent variables, some rep- resent the program commands, and, practically, about half of the neurons in the network constitute the program counters. More specifically, each state- ment is associated with a special neuron, called the “statement counter” neuron. These neurons take Boolean (i.e., binary) values only. When a state- ment counter neuron is True, the statement is exe- cuted. Note that several statement counters may assume the value True simultaneously. Full dis- cussion on controlling the counters is provided in (Siegelmann 1993). Here, we describe the compilation of a small sub- set of NEL statements into a network. The four most basic commands are the parallel block, the serial block, the conditional if statement, and the got0 statement. Other flow control statements - such as Case, Cond, While, Repeat, and Dolist- can be viewed as a combination of the above four. We, thus, overview how to compile the four build- ing blocks: 1. A parallel block consists of the commands en- closed by ParBegin and Parend. Each of these commands is associated with a statement counter. All these counters are set simultane- ously upon reaching the Parbegin. A concluding mechanism is required for synchronization. This mechanism keeps track of the termination of the 880 Neural Networks . The compilation of a simple if statement was pro- vided in Example 1.1. We compile a general if statement If(B) then stat1 else stat2 bY Parbegin If(B) then pc-stat1 = 1 ; If (l(B)) then pc-stat2 = 1 Parend A Goto statement is implemented simply by a change in the neurons simulating the statement counters of the program. Next, we consider a subset of the data types. Each variable, except for records and arrays, is rep- resented via one neuron in the network. various commands, and announces finishing upon termination of them all. Only then, the parallel block is concluded with the Parend. Details are provided in (Siegelmann 1993). A serial block consists of the commands between the Begin and End. This involves an extensive use of counters. Boolean values are represented via the numbers (0, 1). The logical operations are: Operation Network’s emulation Not(x) u l-x Or(xl, x2) +1+ x2) (3) And(xl, x2) a(~1 + 22 - 1) Relational operations are defined in a straight- forward manner: x > y is a(x - y), x 1 y is a(x - y + l), and x # y is xl(t) = CT(X - y), x2(t) = a(y - x) and xs(t + 1) = a(xr + x2). List of T. Assume, for simplicity, that T has only two elements T={O, 1); later we generalize T to arbitrary cardinality. Given a list of elements WlW2 - - *, we regard it as a string w = wlw2 . . .wta. We wish to represent this string as a number in the range [0, 11, so that to be held in a neuron. If we were to represent the string as a number EL 9 3 one would not be able to differenti- ate between the string “P,, and “p. 0”) where ‘.’ denotes the concatenation operator. Worse than that, the continuity of the activation function u makes it impossible to retrieve the most signifi- cant bit (in radix 2) of a list in a constant amount of time. (For example, the values .100000000000 and .Oll 111111111111 are almost indistinguish- able by a net.) We encode the list by n 2w.i + 1 xl a’= 1 4i * (For examples, the list w = 1011 is encoded by the number Q = .3133+) This number ranges in [0, l), but not every value in [0, 1) appears. If the list started with the value 1, then the associated number has a value of at least 9, and if it started with 0, the value is in the range [$, a). The empty list is encoded into the value 0. The next element in the list restricts the possible value further. The set of possible values is not continuous and has “holes”. Such a set of values “with holes” is a Cantor set. Its self-similar structure means that bit shifts preserve the “holes.” The advantage of this approach is that there is never a need to distinguish among two very close numbers in order to read the most significant digit in the base-4 representation. We next demonstrate the usefulness of our encoding of the binary lists. 1. CAR(w), Reading the First Element: The value of q is at least 4 when the Car of the list is 1, and at most 3 otherwise. The linear operation 4q - 2 transfers q to at least 1 when the Car element is 1, and to a non- positive value otherwise. Thus, the function Car (q) = a(4q - 2) provides the value of the Car element. 2. CDR(w),’ Removing the Left Element: Cdr a list, transfers the list w = 1011 to 011, or the encoding from q = .31334 to .1334. When the Car element is known, the opera- tion Cdr (q) = 4q - (2 Car (q) + 1) (or equiv- alently a(4q - (2 Car (q) + 1))) has the effect of CDRing the list. 3. CONS(e,w) Pushing a New Element to the Left of w: Pushing 0 to the left of the list W = 1011 changes the value into w = 01011. In terms of the encoding, q = .31334 is transferred into q = .131334. That is, the suffix remains the same and the new element e E (0, 1) is entered into the most significant location. This is easily done by the operation $ + 9 (which is equivalent to a($ + y) given that q E PA w 4. IsNull( The predicate IsNull indicates whether the list 20 is empty or not, which means in terms of the encoding, whether q = 0 or q 2 .14. This can be decided by the opera- tion IsNull (q) = a(4q) . Assume T has a general cardinality, n. The op- erations Car(w), Cdr(w), Cons(e,w) , and the predicate IsNull are implemented by: a($+~(a(2nq-2)+a(2nq-4)+...+a(2nq- (2n - 2fi)), u((2nq - 1 - 2(u(2nq - 2) + u(2nq - 4)+ -** + u(2nq - (293 - ‘J))))), a(& + e), and a(1 - 2nq) , respectively. VB Stacks are represented similarly to lists. Here Top substitutes Car, Pop substitutes Cdr, Push substitutes Cons, and the predicate Empty sub- stitutes IsNull. Scalars are implemented using the same idea of gaps as with lists. Assume a scalar type with n elements (0, 1, . . .(n - 1)). The ith element is represented as scalar (i, n) E %$ . Order oper- ations are implemented as follows: Operation Network‘s emulation 11 C4) A counter with the value n is represented as (l- 2-n), that is counter(n) c-, . u n (5) The operations on counters Inc, Dee, and the predicate IsZero are implemented by a( 4 (x+ 1)) 7 a(22 - 1) , and a( 1 - 2x) , respectively. 4 Conclusions In conclusions, we can prove the next theorem. Theorem 1 There is a compiler that translates each program in the language NEL into a network. The constants (weights) that appear in the network are the same as those of the program, plus several rational small numbers. Furthermore, the size of the network is O(length) and its running time is O(execution measure). Here, length is the static length of the program, i.e. the number of tokens listed in the source code, and the execution measure is its dynamic length, i.e., the number of atomic commands executed for a given input. We may furthermore conclude from previous work described in subsection 1.2 and from the above the- orem that all computer algorithms are expressible in NEL using rational constants only, while NEL programs that use real weights are stronger than any digital algorithm. Acknowledgment I wish to thank Eduardo Sontag and Jude Shavlik for useful comments. References Abu-Mostafa, Y. 1990. Learning from hints in neural networks. Journal of Complexity 6:192. Al-Mashouq, K., and Reed, I. 1991. Including hints in training neural nets. Neural Computation 3(3):418-427. Neural Networks 886 Armstrong, W.; Stein, R.; Kostov, A.; Thomas, M.; Baudin, P.; Gervais, P.; and Popvic, D. 1993. Applications of adaptive logic networks and dy- namics to study and control of hu man move- ment. 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Training second- order recurrent neural networks using hints. In Sleeman, D., and Edwards, P., eds., Proceedings of the Ninth International Conference on Machine Learning, 363-368. San Mateo, CA: Morgan Kauf- mann Publishers. Omlin, C., and Giles, C. 1993. Rule revision with recurrent neural networks. IEEE Transactions on Knowledge and publication. Data Engineering. accepted for Oursten, D., and Mooney, R. 1990. Changing rules: A comprehensive approach to theory re- finement. In Proceedings of the Eighth National Conference on Artificial Intelligence, 815. Pazzani, M. 1989. Detecting and correcting er- rors of omission after explanation-based learning. In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, 713. Perantonis, S., and Lisboa, P. 1992. Translation, rotation, and scale invariant pattern recognition by higher-order neural networks and moment clas- sifiers. IEEE Transactions on Neural Networks 3(2):241. Pratt, L. 1992. Non-literal transfer of informa- tion among inductive learners. In Mammone, R., and Zeevi, Y., eds., Neural Networks: Theory and Applications II. Academic Press. Siegelmann, H. T., and Sontag, E. D. 1991. Turing computability with neural nets. Appl. Math. Lett. 4(6):77-80. Siegelmann, H. T., and Sontag, E. D. 1994a. Ana- log computation via neural networks. Theoretical Computer Science. to appear. A preliminary ver- sion in: The second Israel Symposium on Theory of Computing and Systems, Natanya, Israel, June, 1993. Siegelmann, H. T., and Sontag, E. D. 1994b. On computational power of neural networks. J. Comp. Syst. Sci. previous version appeared in Proc. Fifth ACM Workshop on Computational Learning Theory, pages 440-449, Pittsburgh, July 1992. Siegelmann, H. T. 1993. Foundations of Recur- rent Neural Networks. Ph.D. Dissertation, Rut- gers University. Suddarth, S., and Holden, A. 1991. Symbolic neural systems and the use of hints for developing complex systems. 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1,653 | Gerhard Widmer Department of Medical Cybernetics and Artificial Intelligence, University of Vienna, and Austrian Research Institute for Artificial Intelligence, Schottengasse 3, A-1010 Vienna, Austria gerhard@ai.univie.ac.at Abstract The paper presents interdisciplinary research in the intersection of AI (machine learning) and Art (mu- sic). We describe an implemented system that learns expressive interpretation of music pieces from perfor- mances by human musicians. The problem, shown to be very difficult in the introduction, is solved by com- bining insights from music theory with a new machine learning algorithm. Theoretically founded knowledge about music perception is used to transform the orig- inal learning problem to a more abstract level where relevant regularities become apparent. Experiments with performances of Chopin waltzes are presented; the results indicate musical understanding and the ability to learn a complex task from very little train- ing data. As the system’s domain knowledge is based on two established theories of tonal music, the results also have interesting implications for music theory. Introduction Suppose you were confronted with the following task: you are shown a few diagrams like the one in figure 1, consisting of a sequence of symbols and a graph on top of these which associates a precise numeric value with each symbol. You are then given a new sequence of symbols (see bottom half of fig. 1) and asked to draw the ‘correct’ corresponding graph, or at least a ‘sensible’ one. Impossible, you think? Indeed, in this form the problem is extremely hard. It is radically un- derconstrained, it is not at all clear what the relevant context is (that a single symbol itself does not deter- mine the associated numeric value is clear because the same symbol is associated with different values in fig. l), and the problem is exacerbated by the fact that the examples are extremely noisy: the same example, if presented twice, will never look exactly the same. This paper will explain why people are nevertheless capable of solving this problem and will present a com- puter program that effectively learns this task. The *This research was sponsored in part by the Austrian Fonds zur Fikderung der wissenschaftlichen Forschung (FWF). Financial support for the Austrian Research Insti- tute for Artificial Intelligence is provided by the Austrian Federal Ministry for Science and Research. 114 The Arts 1.4, I 0.6 t *o*u*rrv q -._ ??? ve *ov * l 4 v l *at-7 f& *c;cs Figure 1: A training example and a new problem. problem, as the next section will reveal, comes from the domain of tonal music, and it will be solved by combining music-theoretic insights and theories with a hybrid machine learning algorithm. The result is an operational system that learns to solve a complex task from few training examples and produces artistically interesting (if not genuinely original) results. The main points we would like the reader to take home from this are on a general methodological level. This is an in- terdisciplinary project, and as such it has implications for both AI/machine learning and musicology. From the point of view of machine learning, the project demonstrates an alternative (though not novel) approach to knowledge-intensive learning. Instead of learning directly from the input data and using the available domain knowledge to guide the induction pro- cess, as it is done in many knowledge-based learning systems-e.g., FOCL (Pazzani & Kibler 1992)-we use the domain knowledge (music theory) to restruc- ture and transform the raw input data, to define more abstract target concepts, and to lift the entire problem to a more abstract level where relevant structures and regularities become apparent. From the point of view of musicology, the interest- ing result is not only that expressive interpretation can indeed be learned by a machine (at least to a certain degree). The project also indicates that AI and in particular machine learning can provide useful techniques for the empirical validation of general mu- sic theories. Our system is based on two well-known From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Figure 2: The problem as perceived by a human learner theories of tonal music (Lerdahl & Jackendoff 1983; Narmour 1977), and an analysis of the learning results provides empirical evidence for the relevance and ade- quacy of the constructs postulated by these theories. A closer look at the To return to the abstract problem in the previous sec- tion, why is it that people are able to tackle it success- fully? There are two simple reasons: (1) the problem is presented to them in a different form, and (2) they possess a lot of knowledge that they bring to bear on the learning task (mostly unconsciously). To unveil the secret, the people learning this task are music stu- dents learning to play some instrument, and to them the problem presents itself roughly as shown in fig. 2. The meaningless symbols from fig. 1 are now the notes of a melody (incidentally, the beginning of Chopin’s Waltz Op.69 no.2), and the graph on top plots the rel- ative loudness with which each note has been played by a performer. What students learn from such ex- amples is general principles of expressive performance: they learn to play pieces of music in an expressive way by continuously varying loudness or tempo, and they learn that by looking at the score as written and simul- taneously listening to real performances of the piece. That is, the graph is heard rather than seen. Generally, expressive interpretation is the art of ‘shaping’ a piece of music by varying certain musical parameters during playing, e.g., speeding up or slowing down, growing louder or softer, placing micro-pauses between events, etc. In this project, we concentrate on the two most important expression dimensions, dynam- ics (variations of loudness) and rubato (variations of lo- cal tempo). The relevant musical terms are crescendo vs. diminuendo (increase vs. decrease in loudness) and accelerando vs. ritardando (speeding up vs. slowing down), respectively. Our program will be shown the melodies of pieces as written and recordings of these melodies as played expressively by a human pianist. From that it will have to learn general principles of expressive interpretation. Why should the learning problem be easier when presented in the form of fig. 2 rather than fig. l? The difference between the two representations is that the latter offers us an interpretation framework for the symbols; we recognize notes, we recognize patterns (e.g., measures, ascending or descending lines, etc.), we know that the note symbols encode attributes like duration, tone height, etc. When listening to the piece, we hear more than just single, unrelated notes-we hear the rhythmic beat, we hear groups that belong together, we hear melodic, rhythmic, and other pat- terns, and we associate the rise and fall of loudness with these groups and patterns. In short, we have ad- ditional knowledge about the task, which helps us to interpret the input. Our learning program will also need such knowledge if it is to effectively learn expressive interpretation from examples. Music theory can tell us more precisely what the relevant knowledge might be. hat music theory tells us Expressive performance has only fairly recently be- come a topic of central interest for cognitive musicol- ogy. There is no general theory of expression, but two assumptions are widely agreed upon among theorists, and these form the basis of our approach: Expression is not arbitrary, but highly correlated with the structure of music as it is perceived by per- formers and listeners. In fact, expression is a means for the performer to emphasize certain structures and maybe de-emphasize others, thus conducing the listener to ‘hearing’ the piece as the performer un- derstands it. Expression is a multi-level phenomenon. More pre- cisely, musical structure can be perceived at vari- ous levels, local and global, and each such structure may require or be associated with its own expres- sive shape. Structures and expressive shapes may be nested hierarchically, but they can also overlap, reinforce each other, or conflict. The notion of musical structure is fundamental. It is a fact that listeners do not perceive a presented piece of music as a simple sequence of unrelated events, but that they immediately and automatically interpret it in structural terms. For instance, they segment the flow of events into ‘chunks’ (motives, groups, phrases, etc.); they intuitively hear the metrical structure of the music, i.e., identify a regular alternation of strong and weak beats and know where to tap their foot. Linearly ascending or descending melodic lines are often heard as one group, and so are typical rhythmic figures and other combinations of notes. Many more structural dimensions can be identified, and it has been shown that acculturated listeners extract these structures in a highly consistent manner, and mostly without being aware of it. This is the (unconscious) musical ‘knowl- edge’ that listeners and musicians automatically bring to bear when listening to or playing a piece. What music theory tells us, then, is that the level of individual notes is not adequate, neither for un- derstanding expressive performances, nor for learning. Analyzing an expressive performance without struc- tural understanding would mean trying to make sense Music / Audition 115 of figure 1 without being able to interpret the symbols. Expression decisions are not a function of single notes, but usually refer to larger-scale structures (e.g., ‘em- phasize this phrase by slowing down towards the end’). That is the level on which the decision rules should be represented; it is also the level on which musicians would discuss a performance. The design of our system has been guided by these insights. We have selected two well-known theories of tonal music- Lerdahl & Jackendoff’s (1983) Gen- erative Theory of Tonal Music and Narmour’s (1977) Implication-Realization Model-as the conceptual ba- sis. Both theories postulate certain types of structures that are claimed to be perceivable by human listeners. These types of structures provide the abstract vocab- ulary with which the system will describe the music. As the structures are of widely varying scope-some consist of a few notes only, others may span several measures -and as expressive patterns will be linked to musical structures, the system will learn to recognize and apply expression at multiple levels. From theoretical insights to a strategy The raw training examples as they are presented to the system consist of a sequence of notes (the melody of a piece) with associated numeric values that specify the exact loudness and tempo (actual vs. notated du- ration), respectively, applied to each note by the per- former. However, as observed above, the note level is not adequate. We have thus implemented a trans- formation strategy. The system is equipped with a preprocessing component that embodies its knowledge about structural music perception. It takes the raw training examples and transforms them into a more ab- stract representation that expresses roughly the types of structures human listeners might hear in the music. In this step also the target concepts for the learner are transformed to the appropriate level of granularity by identifying relevant chunks and associating them with higher-level patterns in the expression (dynamics and tempo) curves. Learning then proceeds at this abstrac- tion level, and the resulting expression rules are also formulated at the structure level. Likewise, when given a new piece to play, the system will first analyze it and transform it into an abstract form and then apply the learned rules to produce an expressive interpretation. Transforming the problem The problem transformation step proceeds in two stages. The system first performs a musical analysis of the given melody. A set of analysis routines, based on selected parts of the theories by Lerdahl and Jack- endoff (1983) and Narmour (1977), identifies various structures in the melody that might be heard as units or chunks by a listener or musician. The result is a rich annotation of the melody with identified struc- tures. Fig. 3 exemplifies the result of this step with htwnonic reium # tilpttmlic gap dythmicgap ’ I t I ‘Figure 3: Structural interpretation of part of minuet. 01 /hasc./h3 .I : I Figure 4: Two of the expressive shapes found. an excerpt from a simple Bach minuet. The percep- tual chunks identified here are four measures heard as rhythmic units, three groups heard as melodic units or “phrases” on two different levels, two linearly ascend- ing melodic lines, two rhythmic patterns called rhyth- mic gap f;ZZs (a concept derived from Narmour’s the- ory), and a large-scale pattern labelled harmonic de- parture and return, which essentially marks the points where the melody moves from a stable to a less stable harmony and back again. It is evident from this ex- ample that the structures are of different scope, some completely contained within others, some overlapping. In the second step, the relevant abstract target con- cepts for the learner are identified. The system tries to find prototypical shapes in the given expression curves (dynamics and tempo) that can be associated with these structures. Prototypical shapes are rough trends that can be identified in the curve. The system distin- guishes five kinds of shapes: evenlevel (no recogniz- able rising or falling tendency of the curve in the time span covered by the structure), ascending (an ascend- ing tendency from the beginning to the end of the time span), descending, ascdesc (first ascending up to a certain point, then descending), and desc-asc. The system selects those shapes that minimize the devia- tion between the actual curve and an idealized shape defined by straight lines. The result of this analysis step are pairs <musical structure, expressive shape> that will be given to the learner as training examples. Fig. 4 illustrates this step for the dynamics curve as- sociated with the Bach example (derived from a perfor-- mance by the author). We look at two of the structures found in fig. 3: the ascending melodic line in measures l-2 has been associated with the shape ascending, as the curve shows a clear ascending (crescendo) tendency in this part of the recording. And the ‘rhythmic gap fill’ pattern in measures 3-4 has been played with a desc-asc (decrescendo - crescendo) shape. 116 The Arts I 1 L lfncwk3dga-based-c learner Instance-based numeric Lsanm Figure 5: Schema of learning algorithm IBL-SMART. Learning expression rules: IBL-SMART The results of the transformation phase are passed on to a learning component. Each pair <musical structure, expressive shape> is a training example. Each such example is further described by a quanti- tative characterization of the shape (the precise loud- ness/tempo values (relative to the average loudness and tempo of the piece) of the curve at the extreme points of the shape) and a description, in terms of music-theoretic features, of the structure and the notes at its extreme points (e.g., note duration, harmonic function, metrical strength, . . . ). Some of these de- scriptors are symbolic (nominal), others numeric. In abstract terms, the problem is then to learn a numeric function: given the description of a musical structure in terms of symbolic and numeric features, the learned rules must decide (1) which shape to apply and (2) the precise numeric dimensions of the shape (e.g., at which loudness level to start, say, a crescendo line, and at which level to end it). The learning algorithm used in our system is IBL- SMART (Widmer 1993). IBL-SMART is a multistrategy learner in two respects: at the top level, it integrates symbolic and numeric learning; and the symbolic com- ponent integrates various plausible reasoning strategies so that it can utilize a given domain theory (possibly incomplete and imprecise/qualitative) to bias the in- duction process. The second aspect is not relevant here, as we have no explicit domain theory-the musical knowledge is used in the preprocessing stage. The integration of symbolic and numeric learning is what is required here, and that is realized in a quite straightforward way in IBL-SMART: the program consists of two components (see fig. 5), a symbolic rule learner and an instance- based numeric learner. The symbolic component is a non-incremental algorithm that learns DNF rules by growing an explicit discrimination or refinement tree in a top-down fashion. The basic search strategy is inspired by the ML-SMART framework (Bergadano & Giordana 1988): a best-first search, guided by cov- erage and simplicity criteria, is conducted until a set of hypotheses is found that covers a sufficient number of positive examples. In our case, the target concepts for the symbolic learner are the different expressive shapes, i.e., it learns to determine the appropriate gen- eral shape to be applied to a musical structure. The numeric component of IBL-SMART is an instance-based learner that in effect builds up numeric interpolation tables for each learned symbolic rule to predict precise numeric values. It stores the instances with their numeric attribute values and can predict the target values for some new situation by numeric interpolation over known instances. The connection between these two components is as follows: each rule (conjunctive hypothesis) learned by the symbolic com- ponent describes a subset of the instances; these are assumed to represent one particular subtype of the con- cept to be learned. All the instances covered by a rule are given to the instance-based learner to be stored to- gether in a separate instance space. Predicting the tar- get value for some new situation then involves match- ing the situation against the symbolic rules and us- ing only those numeric instance spaces for prediction whose associated rules are satisfied. The symbolic learner effectively partitions the space for the instance- based method, which then constructs highly special- ized numeric predictors. The basic idea is somewhat reminiscent of the concept of regression trees (Breiman et al. 1984). For a more detailed presentation of the algorithm, the reader is referred to (Widmer 1993). Applying learned rules to new problems When given the score of a new piece (melody) to play expressively, the system again first transforms it to the abstract structural level by performing its musi- cal analysis. For each of the musical structures found, the learned rules are consulted to suggest an appropri- ate expressive shape (for dynamics and rubato). The interpolation tables associated with the matching rules are used to compute the precise numeric details of the shape. Starting from an even shape for the entire piece (i.e., equal loudness and tempo for all notes), expres- sive shapes are applied to the piece in sorted order, from shortest to longest. That is, expression patterns associated with small, local structures are applied first, and more global forms are overlayed later. Expressive shapes are overlayed over already applied ones by aver- aging the respective dynamics and rubato values. The result is an expressive interpretation of the piece that pays equal regard to local and global expression pat- terns, thus combining micro- and macro-structures. Experimental This section briefly presents some results achieved with waltzes by Frederic Chopin. The training pieces were five rather short excerpts (about 20 measures each) from the three waltzes Op.64 no.2, Op.69 no.2 (see fig.2), and Op.70 no.3, played by the author on an electronic piano and recorded via MIDI. The results of learning were then tested by having the system play other excerpts from Chopin waltzes. Here, we can only show the results in graphic form. As an example, fig. 6 shows the system’s perfor- mance of the beginning of the waltz Op.18 after learn- ing from the five training pieces. The plots show Music / Audition 117 0.8 Figure 6: Chopin Waltz op.18, Eb major, as played by learner: dynamics (top) and tempo (bottom). the loudness (dynamics) and tempo variations, respec- tively. A value of 1 .O means average loudness or tempo, higher values mean that a note has been played louder or faster, respectively. The arrows have been added by the author to indicate various structural regularities in the performance. Note that while the written musical score contains some explicit expression marks added by the composer (or editor) - e.g., commands like crest, sf or p and graphical symbols calling for large- scale crescendo and decrescendo - the system was not aware of these; it was given the notes only. It is difficult to analyze the results in a quantitative way. One could compare the system’s performance of a piece with a human performance of the same piece and somehow measure the difference between the two curves. However, the results would be rather meaning- less. For one thing, there is no single correct way of playing a piece. And second, relative errors or devia- tions cannot simply be added: some notes and struc- tures are more important than others, and thus errors are more or less grave. In a qualitative analysis, the results look and sound musically convincing. The graphs suggest a clear un- derstanding of musical structure and a sensible shap- ing of these structures, both at micro and macro levels. At the macro level (arrows above the graphs), for in- stance, both the dynamics and the tempo curve mirror the four-phrase structure of the piece. In the dynamics dimension, the first and third phrase are played with a recognizable crescendo culminating at the end point of the phrases (the Bb at the beginning of measures 4 and 12). In the tempo dimension, phrases (at least the first 118 The Arts three) are shaped by giving them a roughly parabolic shape-speeding up at the beginning, slowing down to- wards the end. This agrees well with theories of rubato published in the music literature (Todd 1989). At lower levels, the most obvious phenomenon is the phrasing of the individual measures, which creates the distinct waltz ‘feel’: in the dynamics dimension, the first and metrically strongest note of each measure is emphasized in almost all cases by playing it louder than the rest of the measure, and additional melodic consid- erations (like rising or falling melodic lines) determine the fine structure of each measure. In the tempo di- mension, measures are shaped by playing the first note slightly longer than the following ones and then again slowing down towards the end of the measure. The most striking aspect is the close correspondence between the system’s variations and Chopin’s explicit marks in the score (which were not visible to the system!). The reader trained in reading music nota- tion may appreciate how the system’s dynamics curve closely parallels Chopin’s various crescendo and de- crescendo markings and also the p (piano) command in measure 5. Two notes were deemed particularly worthy of stress by Chopin and were explicitly anno- tated with sf ( f s orzato): the Bb’s at the beginning of the fourth and twelfth measures. Elegantly enough, our program came to the same conclusion and empha- sized them most extremely by playing them louder and longer than any other note in the piece; the correspond- ing places are marked by arrows with asterisks in fig. 6. Experiments with other Chopin waltzes produced re- sults of similar quality. Preliminary results with songs by Franz Schubert are also encouraging, but suggest that an overabundance of musical structures might de- grade the quality somewhat. This indicates the need for a more refined shape combining strategy. Summary and Discussion This paper has presented a system that learns to solve a complex musical task from a surprisingly small set of examples and produces artistically interesting results. The essence of the method is (1) a theory-based trans- formation of the learning problem to an appropriate abstraction level and (2) a hybrid symbolic/numeric learning algorithm that learns both symbolic decision rules and predictors of precise numeric values. What really made the problem solvable-and this is the main point we would like to make-is the interdis- ciplinary and principled approach: combining machine learning techniques with a solid analysis of the task domain and using existing theories of the domain as a sound basis. The result is a system that is of interest to both fields involved, machine learning and music. From the point of view of machine learning, using available domain knowledge to transform the learning problem to an abstraction level that makes hidden reg- ularities visible is a viable alternative to more ‘stan- dard’ knowledge-based learning, where learning pro- ceeds at the level of the original data, and the knowl- edge is used to bias induction towards plausible gen- eralizations. This approach has also been advocated by a number of other researchers, most notably (Flann & Dietterich 1989). That does not preclude the addi- tional use of domain knowledge for guiding the induc- tion process. Indeed, though the performances pro- duced by our system are musically sensible, the rules it constructs do not always correspond to our musi- cal intuition. To further guide the system towards in- terpretable rules we plan to supply it with a partial domain theory that specifies relevant dependencies be- tween various domain parameters. This will require no changes to the system itself, because IBL-SMART is capable of effectively taking advantage of incomplete and imprecise domain theories (Widmer 1993). For musicology, the project is of interest because its results lend empirical support to two quite recent gen- eral theories of tonal music. In particular, the role of Narmour’s music theory is strengthened by our results. Some music researchers claim that grouping (phrase) structure is the essential carrier of information for ex- pressive phrasing. An analysis of the results of our sys- tem’ however, suggests that melodic surface patterns derived from Narmour’s theory are equally important and determine or explain to a large extent the micro- structure of expression. We would generally propose our methodology (using established artistic or other theories as a basis for programs that learn from real data) as a fruitful empirical validation strategy. References Bergadano, F., and Giordana, A. 1988. A knowledge intensive approach to concept induction. In Proceed- ings of the Fifth International Conference on Machine Learning. Ann Arbor, MI. Breiman, L.; Friedman, J.; Olshen, R.; and C. Stone, C. 1984. Classification and Regression Trees. Bel- mont’ CA: Wadsworth. Flann, N., and Dietterich, T. 1989. A study of explanation-based methods for inductive learning. Machine Learning 4(2): 187-226. Lerdahl, F., and Jackendoff, R. 1983. A Generative Theory of Tonal Music. Cambridge, MA: MIT Press. Narmour, E. 1977. Beyond Schenkerism. Chicago University Press. Pazzani, M., and Kibler, D. 1992. The utility of knowledge in inductive learning. Machine Learning 9( 1):57-94. Todd, N. 1989. Towards a cognitive theory of ex- pression: The performance and perception of rubato. Contemporary Music Review 4:405-416. Widmer, G. 1993. Plausible explanations and instance-based learning in mixed symbolic/numeric domains. In Proceedings of the 2nd Intl. Workshop on Multistrategy Learning. Harper’s Ferry, W.VA. Music / Audition 119 | 1994 | 300 |
1,654 | Knowledge Representation for Video Marc Davis Interval Research Corporation 180 1 -C Page Mill Road Palo Alto, CA 94304 davis@interval.com Abstract Current computing systems are just beginning to enable the computational manipulation of temporal media like video and audio. Because of the opacity of these media they must be repre- sented in order to be manipulable according to their contents. Knowledge representation techniques have been implicitly de- signed for representing the physical world and its textual repre- sentations. Temporal media pose unique problems and opportu- nities for knowledge representation which challenge many of its assumptions about the structure and function of what is repre- sented. The semantics and syntax of temporal media require re- presentational designs which employ fundamentally different conceptions of space, time, identity, and action. In particular, the effect of the syntax of video sequences on the semantics of video shots demands a representational design which can clearly articu- late the differences between the context-dependent and context- independent semantics of video data. This paper outlines the the- oretical foundations for designing representations of video, dis- cusses Media Streams, an implemented system for video repre- sentation and retrieval, and critiques related efforts in this area. Introduction The central problem in the creation of robust and scalable systems for manipulating video information lies in representing video content. Currently, content providers possess large archives of film and video for which they lack sufficient tools for search and retrieval. For the types of applications that will be developed in the near future (interactive television, personalized news, video on demand, etc.) these archives will remain a largely untapped resource, unless we are able to access their con- tents. Without a way of accessing video information in terms of its content, a hundred hours of video is less useful than one. Given the current state of the art in machine vision and signal processing, we cannot now, and probably will not be able to for a long time, have machines “watch” and understand the content of digital video archives for us. Unlike text, for which we have developed sophisticated parsing and indexing technologies, and which is accessible to processing in various structured forms (ASCII, RTF, PostScript, SGML, HTML), video is still largely opaque. Some headway has been made in this area. Algorithms for the automatic annotation of scene breaks are becoming more robust and enhanced to handle special cases such as 120 The Arts fades (Zhang, Kankanhalli, & Smoliar 1993). Work on camera motion detection is close to enabling reliable auto- matic classification of pans and zooms (Teodosio 1992; Tonomura, Akutsu, Otsuji, & Sadakata 1993; Ueda, Miyatake, Sumino, & Nagasaka 1993). Researchers are also making progress in the automatic segmentation and tagging of audio data by means of parsing the audio track for pauses and voice intensities (Arons 1993), as well as specialized audio parsers for music, laughter, and other highly distinct acoustic phenomena (Hawley 1993). Advances in signal separation and speech recognition will also go a long way to automating the parsing of the con- tent of the audio track. Yet this information alone does not enable the creation of a sufficient representation of video content to support content-based retrieval and mani- pulation. Signal-based parsing and segmentation technolo- gies must be combined with representations of the higher level structure and function of video data in order to enable machines to make inferences about video content. Why is video representation an important research area for AI? Besides the pragmatic value of this work for the information and entertainment industries, its relevance extends to the enabling of a broad-based shift in the media of human communication and knowledge. We are cur- rently in a crucial phase of a second “Gutenberg shift” (McLuhan 1962) in which video is becoming a ubiquitous data type not only for viewing (i.e., reading) but for daily communication and composition (i.e., writing). This shift will only be possible when we can construct representa- tions of video which enable us to parse, index, browse, search, retrieve, manipulate, and (re)sequence video according to representations of its content. Video representation also requires the rethinking of traditional approaches to knowledge representation and story generation in AI. The generation problem has been framed as the problem of constructing a media indepen- dent engine for creating sequences of concepts or events which then guide synthesis processes in different media (usually text (Schank & Riesbeck 1981), occasionally graphics (Feiner & McKeown 1990; Kahn 1979)). With recorded video, the generation problem is recast as a representation and retrieval problem. The task, as in edit- ing together found footage, is a matter of creating media specific representations of video which facilitate the retrieval and resequencing of exiting content. This differ- ence in approach has fundamental ramifications for repre- From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. sentational design. It is not merely a matter of adapting media independent representations to the specific proper- ties of video, but of designing representations whose basic ontology and inference mechanisms capture the specific semantic and syntactic properties of video. Therefore, the task which confronts artificial intelli- gence researchers in this area is to gather insights from disciplines that have studied the structure and function of video data and to use these insights in the design of new representations for video which are adequate to the task of representing the medium. Film analysis and theory have developed a useful repertoire of analytical strategies for describing the semantics and syntax of video data. These insights inform the following theoretical discussion and representational design. epresenting Video Current paradigms of video representation are drawn from practices which arose primarily out of “single-use” video applications. In single-use applications, video is shot, annotated, and edited for a given movie, video, or television program. Representations are created for one given use of the video data. There do exist certain cases today, like network news archives, film archives, and stock footage houses, in which video is used multiple times, but the level of granularity of the representation and the semantics of the representations do not support a wide reusability of video content. The challenge is to create representations which support “multi-use” applications of video. These are applications in which video may be dy- namically resegmented, retrieved, and resequenced on the fly by a wide range of users other than those who originally created the data. Most attempts to represent video content utilize repre- sentations developed for other media. Most commercially used representations apply techniques used for represent- ing text (predominantly keywords or full text annotation); AI-influenced representations apply techniques developed for representing the physical world (Guha 1994; Guha & Lenat 1994; Lenat & Guha 1990) or for representing ab- stract, supposedly media-independent concepts (Schank 1993; Schank & Rieger 1974). All of these attempts ne- glect to consider that video as a data type may have unique properties which may themselves need to explicitly repre- sented and which may render techniques developed for other media inadequate. Stream-Based Representation of Temporal Media In designing a representation of video content we must think about the structure of what is being repre- sented. A video camera produces a temporal stream of image and sound data represented as a stream of frames played back at a certain rate-normally 30 frames per sec- ond. This stream of frames has higher level structures of organization commonly referred to as follows: a stream of frames recorded between the time in which the recording device is turned on and turned off is a shot; a temporal concatenation of shots is referred to as a sequence; and a sequence of shots all sharing the same spatial location is often referred to as a scene (Bordwell & Thompson 1990). In most representations of video content, a stream of video frames is segmented into units called clips whose boundaries often, but do not necessarily, coincide with shot or scene boundaries. Current tools for annotating video content used in film production, television produc- tion, and multimedia, add descriptors (often keywords) to clips. There is a significant problem with this approach. By taking an incoming video stream, segmenting it into various clips, and then representing the content of those clips, a clip-based representation imposes a fixed segmentation on the content of the video stream. To illus- trate this point, imagine a camera recording a sequence of 100 frames. Traditionally, one or more parts of the stream of frames is segmented into clips which are then respec- tively annotated by attaching descriptors. The clip is a fixed segmentation of the video stream that is separated from its context of origin and enforces only one segmentation of the original data. In a stream-based representation, the stream of frames is left intact and is represented by multi-layered annota- tions with precise time indexes (beginning and ending points in the video stream). The result is that this repre- sentation makes annotation pay off-the richer the anno- tation, the more numerous the possible segmentations of the video stream. The Stream of 100 Frames of Video with 6 Annotations Resulting in 66 Possible Segmentations of the Stream Clips change from being fixed segmentations of the video stream, to being the results of retrieval queries based on annotations of the video stream. In short, in addressing the challenges of representing video what we need are representations which make clips, not representations of clips. Video Syntax and Semantics In attempting to create a representation of video con- tent, an understanding of the semantics and syntax of video information is a primary concern. For video, it is essential to clearly distinguish between context-dependent and context-independent semantics. Syntax, the sequenc- ing of individual video shots, creates new semantics which may not be present in any of the individual shots and Theater / Video 121 which may supersede or contravene their existing seman- tics. This is evidenced by a basic property of the medium which enables not only the repurposing of video data (the resequencing of video shots taken from their original con- texts and used to different ends in new contexts), but its basic syntactic functionality: the creation of meaningful sequences through concatenating visual and auditory re- presentations of discontinuous times and discontiguous spaces. Eisenstein described this property as montage (Eisenstein 1947). The early experimental evidence for effects of the syntax of shot combination on the semantics of individual shots was established by the Soviet cinematographer Lev Kuleshov early in this century (Isenhour 1975; Kuleshov 1974). The classic example of the “Kuleshov Effect” was evidenced by the following experiment. The following se- quence was shown to an audience: a long take in close-up of the Russian actor Mozhukin’s expressionlessly neutral face - cut - a bowl of steaming soup - cut - the same face of the actor - cut - a woman in a coffin - cut - the same face of the actor - cut - a child playing with a toy bear- cut - the same face of the actor. When audi- ence members were asked what they saw, they said, “Oh, he was hungry, then he was sad, then he was happy.” The same exact image of the actor’s face was used in each of the three short sequences. What the Kuleshov Effect re- veals is that the semantics of video information is highly determined by what comes before and what comes after any given shot. Because of the impact of the syntax of video se- quences on the semantics of video shots, any indexing or representational scheme for video content needs to explain how the semantics of video changes by resequencing and recombination. The challenge is then twofold: to describe what features or annotations survive recombination and to describe how the features which do not survive emerge from those which do. The challenge of representing the syntax dependent and syntax independent semantic features of video content has a deep similarity to a core problem in knowledge re- presentation: the frame problem (McCarthy & Hayes 1969). The important difference between approaches to solving the frame problem in AI and the demands of creat- ing a knowledge representation for video lies in the fact that video is itself a representation of the world with its own ontological properties and its own constraints on the construction and maintenance of continuity through the montage of shots. In a word, video has not only its own semantics and syntax, but its own “common sense” which previous approaches to common sense knowledge, tempo- ral, and action representation have yet to address. Ontological Issues in Video Space Through sequencing of shots video enables the con- struction of many types of spaces: representations of spaces which have real world correlates (real spaces); spaces which do not but could exist in the physical world (artificial spaces); and even spaces which cannot exist in the physical world as we commonly experience it (impossible spaces). In thinking about the first two classes of spaces which can be constructed cinematically (real and artificial spaces) an important distinction can be made among three types of spatial locations: the actual spatial location of the recording of the video; the spatial location which the viewer of the video infers when the video is viewed independent of any other shots; and the spatial lo- cation which the viewer of the video infers when it is viewed in a given sequence. For example, imagine a shot filmed in a dark alley in Paris on October 22, 1983, from 4: 15 am to 4: 17 am. The actual location of recording may be in a given street in a certain part of the city and could be expressed in terms of an exact longitude, latitude, and altitude. The shot we are imagining has no distinguishing features which mark it as a particular Parisian street or as a Parisian street at all. Independent of any sequence it appears as a “generic dark alley in a city.” With the use of a preceding establishing shot, for example an aerial view of New York City at night, the shot now has the inferable spatial location of “a dark alley in New York City.” Therefore, representations of the spatial location of a video must represent the differ- ence between a video’s actual recorded spatial location and its visually inferable ones. The geometry of video spaces and the objects within them also have unique properties. The location of objects within the video frame can be represented by a hybrid 2 dimensional and 3 dimensional representation. Since video spaces can be constructed and concatenated into ir- real geometries they have only a relational 3 dimensional- ity in which the geometry is best expressed in terms of relative as opposed to absolute positions. Therefore, 3 dimensional spatial relations are on the order of “in front of,” or “on top of,” etc. opposed to a given XYZ coordi- nate. Since the 3 dimensional world of the video is itself represented in a 2 dimensional projection, all objects in the 3 dimensional space of the recorded/constructed world have a location in the 2 dimensional plane of the screen. The 2 dimensional screen position of an object is a crucial aspect of its spatial representation and composition which is used by filmmakers to create both aesthetic order (in terms of balanced compositions as in photography) and cognitive order (in terms of the “rules” of Western film- making for the construction of space through action, chief among them being the “180 degree rule” which results is the well-known shot reverse shot of two person dialogue crosscutting). Identity Identity of persons and objects is complex in video. A considerable portion of the cinematic craft is devoted to the construction and maintenance of coherent identities for characters and locales. This is achieved thorough the dis- cipline of “continuity.” Continuity is the process whereby 122 The Arts salient details of a character’s and a locale’s appearance remain in continuity from shot to shot (i.e., remain con- stant when appropriate, change when appropriate). For example, if an actor is wearing a black hat in one shot and not in the next, if there is no inferable explanation for the absence of the hat “continuity” is said to have been bro- ken. The effort to maintain continuity is deeply related to the frame problem in AI. But because video is not the physical world, but a systematic representation of it, conti- nuity can be established and maintained by inferences not found in common sense reasoning. Interesting examples center on techniques for main- taining the continuity of the identity of a character in a narrative film. A character can literally be “assembled” out of the parts of other characters at various levels of granularity. Kuleshov is well known for constructing a woman character by editing together shots of different body parts of several different women. The identity of a character between shots may rely on any combination of: role (which is comprised of costume, action, and location) and actor. In a demo reel from the stock footage house Archive Films, scenes of several different actors are cut together to make up the central character of a business man traveling around on a busy workday (Archive Films 1992) . Continuity of identity can cut across roles and be established by the continuity of the actor. Shots of the same actor taken from various performances of different characters can be edited together to form one character. Imagine, for example, a story about a killer cyborg who goes to Mars which could be created by editing together several of Arnold Schwarzenegger’s films (The Terminator and Total Recall). Action The central problem for representing temporal media is the representation of dynamic events. For video in par- ticular, the challenge is to come up with techniques for representing and visualizing the complex structure of the actions of characters, objects, and cameras. A representa- tion of cinematic action for video retrieval and repurposing needs to focus on the granularity, reusability, and seman- tics of its units. In representing the action of bodies in space, the representation needs to support the hierarchical decomposition of its units both spatially and temporally. Spatial decomposition is supported by a representation that hierarchically orders the bodies and their parts which participate in an action. For example, in a complex action like driving an automobile, the arms, head, eyes, and legs all function independently. Human body motions may be further categorized in two ways: abstract physical motions and conventionalized physical motions. Abstract physical motions can be represented according to articulations and rotations of joints. There are, however, many commonly occurring, complex patterns of human motion which seem to have cross-cultural importance (e.g., walking, sitting, eating, talking, etc.). Conventionalized body motions compactly represent motions which may involve multiple abstract body motions. Temporal decomposition is enabled by a hierarchical organization of units such that longer sequences of action can be broken down into their temporal subabstractions all the way down to their atomic units. In the representational design of the CYC system, Lenat points out the need for more than a purely temporal representation of events that would include semantically relevant atomic units orga- nized into various temporal patterns (repeated cycles, scripts, etc.) (Lenat & Guha 1990). For example, the atomic unit of “walking” would be “taking a step” which repeats cyclically. An atomic unit of “opening a jar” would be “turning the lid” (which itself could theoretically be broken down into smaller units-but much of the chal- lenge of representing action is knowing what levels of granularity are useful). In video, however, actions and their units do not have a fixed semantics because their meaning can shift as the video is recut and inserted into new sequences. For exam- ple, a shot of two people shaking hands, if positioned at the beginning of a sequence depicting a business meeting, could represent “greeting,” if positioned at the end, the same shot could represent “agreeing.” Video brings to our attention the effects of context and order on the meaning of represented action. In addition, the prospect of repre senting video for a global media archive brings forward an issue which traditional knowledge representation has largely ignored: cultural variance. The shot of two people shaking hands may signify greeting or agreeing in some cultures, but in others it does not. How are we to annotate shots of people bowing, shaking hands, waving hello and good-bye? The list goes on. An answer to these issues is to represent the context- independent semantics of actions using physically-based description and to build up the representation of context- dependent semantics by creating a network of analogies between similar concrete action sequences which are themselves represented by physically-based descriptions. Time The representation of time in video requires the same distinction made for representing space: the difference be- tween actual recorded time and the two types of visually inferable time. A further important distinction in narrative video must be made between three different types of temporal duration (Bordwell & Thompson 1990): . story duration (the duration of the events of the entire story as opposed to the particular story events selected for presentation in the video); 0 plot duration (the duration of the particular events presented in the video); . screen duration (the duration of the actual video as screened) The full representation of these three types of duration is an open research problem. Theater / Video 123 Media Streams: A Research Prototype for Video Representation and Retrieval Media Streams Overview Over the past three years, members of the MIT Media Laboratory’s Machine Understanding Group (Marc Davis with the assistance of Brian Williams and Golan Levin under the direction of Prof. Kenneth Haase) have been building a prototype for the representation and retrieval of video data. This system is called Media Streams (Davis 1993a; Davis 1993b). Media Streams is written in Macintosh Common Lisp and FRAMER (Haase 1993a), a persistent framework for media annotation and description that supports cross-platform knowledge representation and database functionality. Media Streams runs on an Apple Macintosh Quadra 950 with three high resolution, acceler- ated 24-bit color displays and uses Apple’s QuickTime digital video format. Media Streams makes use of all the insights outlined above about knowledge representation for video. With an iconic visual language designed for video representation, users create stream-based representations of video content. Media Streams utilizes a hierarchically structured seman- tic space of iconic primitives which are combined to form compound descriptors which are then used to create multi- layered, temporally indexed annotations of video content. These iconic primitives are grouped into descriptive cate- gories designed for video representation and are structured to deal with the special semantic and syntactic properties of video data. The categories include: space, time, weather, characters, objects, character actions, object ac- tions, relative position, screen position, recording medium, cinematography, shot transitions, and subjective thoughts about the material. Media Streams’ interface addresses two fundamental issues in video annotation and retrieval: creating and browsing the space of descriptors to be used in annotation and retrieval; and annotating, browsing, and retrieving video shots and sequences. Consequently, the system has two main interface components: the Icon Space (Fig. 1) and the Media Time Line (Fig. 2). The Icon Space is the interface for the selection and compounding of the iconic descriptors in Media Streams. To date there are approximately 3000 iconic primitives. Through compounding, the base set of primitives can pro- duce millions of unique expressions. In the Icon Space, users can create palettes of iconic descriptors for use in annotation and search. By querying the space of descrip- tors, users can dynamically group related iconic descrip- tors on-the-fly. These icon palettes enable users to reuse the descriptive effort of others. When annotating video, users can make use of related icons that other users have already created and used to annotate similar pieces of video. What enables the user to navigate and make use of a large number of primitives is the way the Icon Space or- ganizes icons into cascading icon hierarchies. The Icon Space has two significant forms of organization for man- aging navigational and descriptive complexity: a cascading hierarchy with increasing specificity of primitives on subordinate levels; and compounding of hierarchically organized primitives across multiple axes of description. The Media Time Line is the core browser and viewer of Media Streams (Fig. 2). It enables users to visualize video at multiple timescales simultaneously, to read and write multi-layered iconic annotations, and provides one consistent interface for annotation, browsing, query, and editing of video and audio data. Media Streams Representational Structures The underlying representation of video in Media Streams combines two distinct representations: a semanti- cally structured generalization space of atemporal categor- ical descriptors; and an episodically structured relational space of temporal analogical descriptions. The atemporal semantic representation underlies the icon hierarchies in the Icon Space. The temporal episodic representation is built up when iconic descriptors are used to create annota- tions on Media Time Lines which establish specific rela- tionships between these descriptions through combination and temporal order. The semantic/episodic distinction was originated by researchers in human memory (Baddeley 1984; Tulving 1993) and made computational by Schank’s work in dynamic memory (Schank 1982). Semantic memory can be thought of as the categorical or definitional part of hu- man memory: remembering what a thing is and what class or category it belongs to. Episodic memory can be thought of as the representation of a sequence of events, an episode. Semantic and episodic memory structures enable us to create a mixed representational system which can answer the fundamental problem of video retrieval sys- tems: how do we determine the similarity of descriptors, of descriptions, of shots, and of sequences? Similarity needs to be context-sensitive and compare not just descriptors, but relations between them. The determination of similar- ity holds the key to retrieval, and due to the properties of video as a medium (especially its semantic and syntactic features discussed above) the semantic and episodic mem- ory systems must work together using different similarity metrics in order to retrieve video based on its unique features. Media Streams Retrieval Algorithms Media Streams employs two different types of re- trieval algorithms: atemporal semantically based retrieval of icons and video segments; and temporal analogically based retrieval of video segments and sequences. Both re- trieval strategies can use each other and be interleaved. These algorithms can be further distinguished by the objects they operate on and the criteria of similarity they employ. All retrieval algorithms operate on descriptors and relations between them. At the simplest level, re- trieval can be based on the identity of components. A more semantically based retrieval utilizes the hierarchical tree structure of the Icon Space to match components 124 The Arts Theater / Video 125 based on generalization or specialization. The most so- phisticated retrieval is that which takes into account the semantic and syntactic structure of temporally-indexed de- scriptions and the relations between them and thereby matches based on analogical similarity. These retrieval algorithms are based on work done by Professor Kenneth Haase (Haase 1993b). His analogical matching system called “Mnemosyne” (after the Greek goddess of memory who was also the mother of the nine muses) is a radically memory-based representational system in which analogical matching forms the core representation. The challenge which this memory-based representation addresses is the inflexibility and brittleness of most semantic or categorical representations. In knowl- edge representations where a fixed hierarchical semantic structure is not sufficient to allow flexibility of the repre- sentation, an episodic memory structure is needed so that the semantics of the descriptors used in the semantic memory is, in effect, contextualized by a network of dif- ferences and similarities between concrete examples of the descriptors’ use. Media Streams extends this work by combining semantic and episodic representational systems in order to facilitate context-independent and context-de- pendent representation and retrieval of video. Media Streams also adds the ability to represent and match on temporal relations. This extension is based on earlier work in temporal representation (Allen 1985). Here is an example to illustrate how Media Streams’ representational structures and retrieval algorithms work. Imagine we want to find a video shot of John and Joe shaking hands in Boston. A query which used only se- mantic memory would find shots of John and Joe shaking hands in Boston, of other men shaking hands somewhere in Massachusetts, of people of unspecified gender shaking hands somewhere in the United States, etc. A query which used episodic and semantic memory would find shots of John and Joe shaking hands in Boston as well as shots of Hirotada and Takafumi bowing to one another in Tokyo, and so forth. Related Work The CUC Project: Representing the World The goal of the CYC project is to overcome the brit- tleness and domain-specificity of all previous attempts at representing our common-sense knowledge about the world (Lenat & Guha 1990). Since 1984 the CYC project has done extensive work in creating representations of ob- jects, actions, and events. Recently the CYC project has begin to apply its large semantic knowledge base to the representation and retrieval of still images and video. Surprisingly, these attempts fall prey to exactly the same criticism which Lenat himself levied against efforts to represent the physical world by natural language. Lenat argued that natural language was an inadequate represen- tational system for representing knowledge about the world because it is not a designed representation (Lenat & Guha 1990). In other words, natural language is not de- signed in such a way so as to capture the salient features of the world which are amenable to computational represen- tation. Nevertheless, the CYC project makes a method- ological error in its efforts to represent stills and video: it applies its representation language (which is a representa- tion of the world) to video without redesigning it for the representation of video. What Media Streams does in con- trast is create a representation language for video, in other words, a representation of a representation of the world. According to Guha, CYC represents video as “information bearing objects with propositional content.” Guha admits that this approach may break down due to the particular context-dependent and context-independent semantics of video data (Guha 1994). With video, editing and rese- quencing may change the given “propositional content” of any “information bearing object.” Schank: Conceptual Dependency and Case Based Reasoning Conceptual dependency reduced all of human action into a small set of composable primitives (Schank & Rieger 1974). This work has a certain appeal for its rigor and simplicity, yet it has an apparent deficit for application to video representation: the semantics of human action within video are not fixed and change on recombination. The challenge is not to reduce all video actions to unam- biguous media-independent primitives, but to articulate a semantics of action which is conditioned by the properties of the medium. Traditional case-based reasoning relies on the index- ing of cases under predetermined abstractions. This ap- proach presents two problems for video representation: the indexing must, as stated above, articulate the difference between context dependent and context independent as- pects of video content; and then use this distinction in its indexing to support the reindexing of cases when video elements are resequenced. Schank and his students have recently applied their efforts to video representation. They are conducting a large scale project to develop a video database for interac- tive corporate training applications. In this work, video is represented as if it were just text, or a fortiori, ideas. The video data is treated as if it were fully transparent and one need only represent the ideas behind it in order to fully represent its contents. Schank does concede that this ap- proach is designed for the needs of his current project and that it may prove inadequate for representing video which will be resegmented and/or repurposed (Schank 1993). loch: AI and Video Representation The mots promising prior work done in knowledge representation for video is the research of Gilles Bloch (Bloch 1987). In his short unpublished paper he outlines the issues involved in applying Schank’s conceptual de- pendency representation to video segments. He also dis- cusses using No&l Burch’s categories for transitions, and mentions the importance of gaze vectors in video (Burch 126 The Arts 1969). His prototype system supposedly was able to con- struct simple video sequences using Schankian scripts. His work did not address the issue of how these represen- tations are written (annotation) or read (browsing) and the extent to which they supported repurposability and reseg- mentation of the content is unclear. Unfortunately, Bloch’s untimely death cut off this fruitful early path of re- search in applying artificial intelligence techniques to the problems of video representation. Conclusion and Future This paper is a first attempt to articulate the challenge of creating robust representations of video within artificial intelligence which will support the description, retrieval, and resequencing of video according to its content. Work in the representation of video content requires a fundamen- tal analysis of the structure and function of video. The im- plications of this analysis for designing representations of video content are a coming to terms with the unique se- mantic, syntactic, and ontological properties of the repre- sentational system of video. Media Streams is a research effort in video annotation and retrieval which has begun to develop these types of representations. Much research re- mains to be done especially in the area of the representa- tion of time, transitions, and the higher level structures of sequences, scenes, and stories. Acknowledgments The research discussed above was conducted at the MIT Media Laboratory and Interval Research Corporation. The support of the Laboratory and its sponsors is grate- fully acknowledged. I want to thank Brian Williams and Golan Levin for their continually awe-inspiring efforts and my advisor, Prof. Kenneth Haase, for his insight, inspira- tion, and support. Thanks also to Warren Sack, David Levitt, and Wendy Buffett for editorial and moral support. eferences Allen, J. F. 1985. Maintaining Knowledge about Temporal Intervals. In R. J. Brachman & H. J. Levesque Eds., Readings In Knowledge Representation pp. 510-521. San Mateo, California: Morgan Kaufmann Publishers, Inc. Archive Films. 1992. Archive Films Demo Reel. New York: Archive Films. Arons, B. 1993. Interactively Skimming Recorded Speech. Ph.D., Massachusetts Institute of Technology. Baddeley, A. D. 1984. Memory Theory and Memory Therapy. In B. A. Wilson & N. Moffat Eds., Clinical Management of Memory Problems. 5-27. Rockville, Maryland: Aspen Systems Corporation. Bloch, G. R. 1987. From Concepts to Film Sequences. Unpublished Document. Yale University Department of Computer Science. Bordwell, D., & Thompson, K. 1990. Film Art - An Introduction third ed. McGraw-Hill Publishing Company. Burch, N. 1969. Theory of Film Practice Helen R. Lane, Trans.. Princeton: Princeton University Press. Davis, M. 1993a. Media Streams: An Iconic Visual Language for Video Annotation. In Proceedings of the 1993 IEEE Symposium on Visual Languages. 196-202. Bergen, Norway: IEEE Computer Society Press. Davis, M. 1993b. Media Streams: An Iconic Visual Language for Video Annotation. Telektronikk 4.93: 59-7 1. Eisenstein, S. M. 1947. The Film Sense Jay Leyda, Trans. San Diego: Harcourt Brace Jovanovich, Publishers. Feiner, S. K., & McKeown, K. R. 1990. Generating Coordinated Multimedia Explanations. In Proceedings of the Sixth IEEE Conference on Artificial Intelligence Applications. Santa Barbara: IEEE Press. Guha, R. V. 1994. Personal Communication. Guha, R. V., & Lenat, D. B. 1994. Enabling Agents to Work Together. Communications of the ACM Forthcoming. Haase, K. 1993a. FRAMER: A Persistent Portable Representation Library. Internal Document. MIT Media Laboratory. Haase, K. 1993b. Integrating Analogical and Case-Based Reasoning in a Dynamic Memory. Internal Document. MIT Media Laboratory. Hawley, M. 1993. Structure out of Sound. Ph.D., Massachusetts Insitute of Technology. Isenhour, J. P. 1975. The Effects of Context and Order in Film Editing. AV Communications Review 23( 1): 69-80. Kahn, K. 1979. Creation of Computer Animations from Story Descriptions. Technical Report. No. 540. Massachusetts Institute of Technology Artificial Intelligence Laboratory. Kuleshov, L. 1974. Kuleshov on Film: Writings by Lev Kuleshov Ronald Levaco, Trans. Berkeley: University of California Press. Lenat, D. B., & Guha, R. V. 1990. Building Large Knowledge- Based Systems: Representation and Inference in the Cyc Project. Reading, Massachusetts: Addison-Wesley Publishing Company, Inc. McCarthy, J., & Hayes, P. 1969. Some Philosophical Problems from the Standpoint of Artificial Intelligence. In Machine Intelligence 4 . Endinburgh: Endinburgh University Press. McLuhan, M. 1962. The Gutenberg Galaxy: The Making of Typographic Man. Toronto: University of Toronto Press. Schank, R. C. 1982. Dynamic Memory: A Theory of Reminding and Learning in Computers and People. Cambridge: Cambridge University Press. Schank, R. C. 1993. Personal Communication. Schank, R. C., & Rieger III, C. J. 1974. Inference and the Computer Understanding of Natural Language. Artificial Intelligence 5(4): 373-412. Schank, R. C., & Riesbeck, C. 1981. Inside Computer Understanding: Five Programs Plus Miniatures. Hillsdale, New Jersey: Lawrence Erlbaum Associates. Teodosio, L. 1992. Salient Stills. M.S.V.S., Massachusetts Institute of Technology Media Laboratory. Tonomura, Y., Akutsu, A., Otsuji, K., & Sadakata, T. 1993. VideoMAP and VideoSpaceIcon: Tools for Anatomizing Content. In Proceedings of INTERCHI’93. 131-136. Amsterdam, The Netherlands: ACM Press. Tulving, E. 1993. What is Episodic Memory? Current Directions in Psychological Science 2(3): 67-70. Ueda, H., Miyatake, T., Sumino, S., & Nagasaka, A. 1993. Automatic Structure Visualization for Video Editing. In Proceedings of INTERCHIP3. 137-141. Amsterdam, The Netherlands: ACM Press. Zhang, H., Kankanhalli, A., & Smoliar, S. W. 1993. Automatic Partitioning of Full-Motion Video. Multimedia Systems 1: 10-28. Theater / Video 127 | 1994 | 301 |
1,655 | Semi-Autonomous Animated Actors Steve Strassmand Apple Computer, Inc. One Main St., Cambridge, MA 02 I42 straz@apple.com Abstract This paper describes an interdisciplinary experiment in controlling semi-autonomous animated human forms with natural language input. These computer-gener- ated characters resemble traditional stage actors, in that they are more autonomous than traditional hand-guided animated characters, and less autonomous than fully improvisational agents. We introduce the desktop tkeatev metaphor, reserving for users the creative role of a theatrical writer or director. I. introduction Much animation research has been devoted to the two extreme ends of the scale of autonomous behavior. In traditional animation, a character’s behavior is fully guided by the artist [Thomas 811, [Jones 891. This approach can achieve astounding results, but only through comparably astounding investments of both skill and labor. At the other extreme, agent- or simulation-based techniques [Johnson 911, [Bates et al 921, [Loyal1 et al 931 give rise to fully autonomous characters, improvising behavior in real-time with little creative input required from the user once the initial conditions are set up. This paper describes a system called Divadlo2, for controlling semi-autonomous characters, whose improvisational skills lie somewhere in the middle of the autonomy spectrum. Like tradi- tional stage actors, their behavior is largely con- strained by an external source (the script and stage directions, provided by the user). Such a system might be called a desktop tkeater3, system since it reserves for users the creative role of a theatrical writer or director. This gives the user *This paper describes work done at the MIT Media Labo- ratory, Cambridge, Mass., completed in 1991. It was sup- ported in part by an equipment grant from Hewlett-Packard Corporation, and research grants from Toshiba and the Nichidai Fund. *Diuudlo is Czech for “theater,” as robot is derived from the Czech word for “worker”. I.28 The Arts the potential to realize specific creative ideas with significantly less effort than traditional anima- tion techniques. In typical usage (Figure la-b), a user enters natural language commands, either as individual sentences or as paragraphs, describing a scene. Statements describing initial conditions take im- mediate effect. As characters and objects are in- troduced, positioned, and otherwise specified, the graphics display is updated in real time. State- ments describing actions or transformations of non-zero duration are accumulated in parallel and/or serial combinations into a plan, which is refined and rendered into an animation. This last step is performed offline, not interactively, due to performance limitations in the graphics sub- system. This system was inspired in part by the vision of an interactive fantasy system [Laurel 861, and in part by SHRDLU [Winograd 721, in which a semi-autono- mous agent manipulated simulated blocks and pyra- mids in a 3d environment in response to a natural language dialog with the user. Other efforts at story animation generally output 2d forms [Kahn 791, [Takashima 871, avoiding the many problems of 3d representation and control. We are aware of only one other group [Badler et al 911 which has assembled a significant architecture to enable natural language con- trol of animated 3d human forms. Perhaps the most challenging aspect of building such a system was the need to integrate specialized information for natural language, 3d graphics, plan- ning, and robotics. Rather than focusing on developing any one particular theory or subsystem, we observed that the parts interact in combination to produce both synergies and compromises in design and perfor- mance. 3This is by analogy to “desktop publishing” systems, which reduce the skills and labor needed for document publishing while reserving the creative aspects for users. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Figure I a: A transcript of user interaction 2. i Knowledge base p> New scene. Creating a new scene: SCENE.1 p> The characters in this scene are John and Mary. Adding actors to the scene: (JOHN MARY) p> John’s shirt is green. OK. p> He's left-handed. OK. p> There's a desk at stage left. Introducing a new object: DESK.1 p> It's facing center stage. OK. (more stage layout directions)... $-In this scene, John gets angry. New action: BECOME.1 p> He offers the book to Mary rudely, but she refuses it. New actions: (OFFER.1 REFUSE.11 p> He slams it down on the table. New action: SLAM.1 p> Mary cries while John glares at her. New action: (CRY.1 GLARE.11 Figure I b: The scene specified in figure la, above Figure 2: System overview Knowledge base User _ input Renderer + Ammat!on Figure 2 shows an overview of the system’s struc- ture. A parser (and simple generator) handles input from the user, and a graphics subsystem generates and records the output animations. A knowledge base is used to maintain a library of potentially useful objects and actions, as well as knowledge about objects and actions instantiated in the current scene. Knowledge about scripts, plans, goals, resources, and robotic mo- tor skills is used to refine the user-specified plan into a detailed animation script. At the center of the system is a frame-like knowledge base implemented in ARLOtje [Haase 901. Units in ARLOtje are organized into class hierarchies, and each unit is distinguished by the values stored in slots it possesses or inherits from other units. By using one representation scheme for all these different compo- nents, the task of sharing knowledge among them is greatly simplified. For example, the unit representing the notion of a chair contains linguistic information (“chair” is a noun), physical information (the shape and color of a chair), and functional information for reason- ing (chairs are for sitting on). The knowledge base includes: a A grammar and lexicon, grounded in the object, pose, and script library, for use by the natural lan- guage parser and generator. 0 A semantic network describing characters, objects and their attributes, including: l Quantitative 3d geometrical knowledge: shapes, positions, orientations, and hierarchical relation- ships among objects. . Quantitative color, shading, and texture informa- tion about each object for use by the graphics subsystem in rendering. l Qualitative information about object attributes, in- ferred from quantitative information. This allows the parser to disambiguate references like “the downstage chair” or “the blue book”. This also greatly facilitates resource planning, such as iden- tifying unoccupied chairs before sitting, or clear portions of table surfaces before placing objects. 0 Qualitative information about the actor’s status, such as its posture (sitting or leaning), emotional state, or immediate goals or constraints. 0 Poses; partial specifications of typical body postures e Scripts describing actions, including preconditions, postconditions and other constraints. These include: . A repertoire of high-level tasks for specification by the user. l A repertoire of low-level motor skills, such as stand- ing or grasping. @ Rules describing partial rewriting of plans when certain patterns are detected in them. Theater / Video 129 In addition, the units are surrounded by utility func- tions containing heuristic rules which capture special- purpose knowledge. These largely reside in or are invoked by demons on a unit’s slots, and are used to constrain or compute values as they are needed. 2.2 Object representation The “actors” in this system are derived from one of two (one male, one female) fully articulated human forms, rendered in 3d. Each figure is a tree of 44 rigid polyhedra (about 2000 polygons), connected by joints of one or more degrees of freedom. While this is still more doll-like than realistic, it is enough detail to simulate posture down to individual knuckles on the hand. A specific actor can be instanced and given customized body dimensions, clothing, body, or hair color. Symbolic annotations are used to correlate polyhe- dra and their attributes to units in the knowledge base. For example, asserting that a character is wearing tennis sneakers would cause certain polygons to be colored white. This sort of knowledge-enhanced mod- eling, by integrating symbolic and traditional anima- tion data, greatly reduces the effort required to popu- late a scene with models. In addition to actors, the system has a stock of about 30 kinds of props, including furniture, office equip- ment, plumbing fixtures, and appliances, all of which come in a variety of decorator colors. Knowledge about each prop includes shape, lexicon entries, attribute- based variants (such as numerical values for “large” and “small” in the case of boxes), and constraints on positioning and usage. Light sources and camera angles are also available for creation and manipulation through natural language commands. To get a handle on controlling the human form, we use a data structure called a pose to represent partial configurations. A pose is a tree whose nodes are coor- dinate transformation matrices with symbolic annota- tions. For example, an “ok” hand gesture is a pose capturing the tree of joint rotations on one hand (rooted at the wrist), with the thumb and forefinger forming a circle. A “salute” is a pose which captures the entire body’s skeletal tree in a military salute. Recalling, combining, or simple interpolation of such poses greatly enriches the repertoire of possible movement. Thus, a character can salute and then bring the hand forward to give an “ok” gesture. Poses turn out to be convenient for describing inani- mate, articulated objects as well. Refrigerators can be open or shut and chairs can be reclined by applying appropriate poses to them. 2. inguistic knowle Divadlo’s parser is derived from BUP, a bottom-up parser for augmented phrase-structured grammars [Finin 851. The lexicon is grounded in several hundred units in the knowledge base, including the instantiable objects and behaviors, as well as units for attributes such as adjectives and adverbs. The parser supports resolution of pronouns, many common contractions, prefixes and suffixes, verb con- jugation, and input of arbitrary number and string constants. Pronouns are resolved using a few simple heuristics such as gender or most-recent reference. The grammar consists of about a hundred rules. In general, input falls into three broad categories: queries, commands, and statements. The system is non-modal; any kind of input can be entered at any time, and multiple inputs can be concatenated into a paragraph for block execution. 2.3. I Queries Queries allow the user to interrogate the system with questions like “Where’s the chair?“, “Who is eating the pie?“, or “Is John left-handed?” As each query is parsed, the knowledge base is searched and a simple generator is used to create the answer. There are 8 categories of queries (corresponding to who, what, where, etc.), each with its own ad hoc rules for generating database searches and generating English responses. In response to a question like “Where’s the chair?“, Divadlo prints something like "T h e red c h a i r i s i n f r o n t of t h e d e s k", which is arguably better for end- users than something like "CHAIR. 1 AT- LOCATION ( 45 .3 3.7 >” The system takes advantage of the fact that both numerical and symbolic information is stored. Since, in this hypothetical case, the chair was not moved sinceitwasoriginallyplaced (AT-LOCATION (FRONT- 0 F D ES K .3 > >, this attribute is still available for use. If the chair had been moved to an arbitrary location with no symbolic significance, the generator might infer another descriptive phrase from the coordinates, such as “The red chair is downstage.” 2.3.2 Commands The user issues commands to Divadlo in order to give control information outside the narrative of the scene being constructed. These include commands for con- trolling the graphics subsystem (“Record”), inspecting objects in the knowledge base (“Inspect the chair”), or terminating the program (“Quit”). 2.3.3 Statements Most input forms are statements, which describe the scene. While commands are all imperatives, statements 130 The Arts are distinguished by a simple trick: they are all third- person declaratives. A statement in present continu- ous tense, e.g. “John is sitting on the chair,” is taken as an initial condition and is executed immediately, just as a stage direction in a script would be. A statement in present simple tense, e.g. “John sits on the chair,” is taken as an action to be executed during the scene (see below). Actions are units that represent processes that occur over time. This includes elements of an actor’s behav- ior, a continuous change to internal or mental states, or environmental changes. The expressive nature of a character’s behavior is largely expressed by the choice of actions to portray a given task, or by the values of animation control parameters which modulate task execution. Since Divadlo cannot animate in real time, actions derived from user statements are added to a single global plan, from which an animation is eventually compiled and rendered in a batch operation. By de- fault, each new action specified in a statement is ap- pended to the scene’s plan, or script, in serial order. Parallel actions can be specified with compound state- ments such as “While action,, action ” or “&i~n, as action,.” A special kind of parallel act&n, whose dura- tion spans the entire scene, can be specified with a form like “In this scene, action,.” Since it is assumed that the user provides relatively concrete instructions, no attempt is made to perform sophisticated problem-solving, e.g. “James Bond then rescues all the prisoners.” It suffices to traverse the global plan top-down, expanding actions into succes- sively finer detail. This is described in section 3, below. 2.4. I Motor skills The lowest level unit that actually implements an action is a motor skill [Zeltzer 821. A motor-skill action has a S K I L L - C 0 D I N G attribute which contains a lisp function which actually does the “dirty work” of posi- tioning the joints and limbs of the actor over time. To implement this function, a variety of techniques are used, appropriate to the skill. Some of these are surveyed in [Calvert 911. The simplest skills, like WA V E - H E L LO, are interpolations of stored poses (or keyframes), specifying joint angles on the actor’s arm. Divadlo has a set of tools that supports a variety of keyframing techniques, including linear and spline interpolation, several different representations for joing rotation and displacement, and smooth merging of multiple, par- tially specified keyframes (e.g. allowing an actor to snap its fingers while waving hello). Skills may also use more advanced techniques, like inverse kinematics, which is used by skills like R E A C H, which places the actor’s hand at a given point in space. Walking uses a special hybrid algorithm similar to the one used in [Sims 871. Full dynamical modeling is not yet supported in Divadlo, though many others have demonstrated dynamics-based control models for ani- mated human forms [Girard and Maciejewski 851 [Badler et al 931. Figure 3 shows a typical motor skill for sitting, which uses a combination of inverse kinematics (to keep the feet placed on the floor and guide the actor’s posterior to the chair’s seat) and key framing (to rotate the hands naturally). Figure 3: A typical motor skill for sitting Theater / Video 131 Figure 4: A typical script describing sitting (defscript sit ((agent (find-plausible-agent this-action)) (chair (find-plausible-chair this-action)) (current-occupant (get-value (my chair) 'occupant))) (already-sitting :doc ("No 'need to SIT, - -a is already sitting down." (my agent)) :test (equalp (my agent) (my current occupant)) :script (delete-action this-action)) (already-occupied :doc ("-a currently occupied by -a, evacuate it." (my chair) (my current-occupant)) :test (and (not (null (my current-occupant))) (not (equal (my current-occupant) (my agent)))) :effects '((occupant ,(my chair) (my agent)) (posture ,(my current-Occupant) standing) (posture ,(my agent) sitting)) :script (create-subtasks this-action '(serial (stand (agent (my current-occupant))) (go (agent (m;/ current-occupant) (to ,(mike-suggestion '(pick-random-place-nearby ,(my-chair))))) (sit (agent , (my agent))) (chair ,(my chair)))))) (far-away :doc ("-a is too far away from -a, must move closer" (my agent) (my chair)) :test (not (ready-to-sit ? (my agent) (my chair))) :effects '((occupant ,(my chair) ,(my agent)) (position ,(my agent) (get-value (my chair) 'position) (posture ,imy agent) (sitting ,(my chair)))) :script (create-subtasks this-action '(serial (go (agent (my agent)) (to ,(piace-in-front-of (my chair)))) (sit (chair ,(my chair)))))) (normal-case :doc ("-a sits on -a" (my agent) (my chair)) :test t :effects '((occupant (my chair) (my agent)) (posture ,?my agent) (iitting ,(my chair)))) :script (create-subtasks this-action '(sit-motor-skill (agent ,(my agent)) (chair ,(my chair)))))) 2.4.2 Scripts The expansion of higher-level actions are are gov- erned by a script [Schank & Abelson 771, associated with each general class of actions. These serve as tem- plates for the action instances, which are knowledge units placed on the global plan to represent concrete details of the performance. A script has two parts; the resources which indicate parameters which must be known before any further reasoning can be done, and the cases, which describe various ways to carry out the action. For example, Figure 4 shows a typical script describing the action SIT. The first element of the D E FS C R I PT form, after the action’s name, S I T, is a list of resources, which in this case are agent, chair, and current-occupant. Each in- stance of an action attempts to bind specific values for these resources before continuing with the expansion. For example, if the sentence “John sits on the red chair” instantiates the action S I T .3, and if nobody is sitting on that red chair at that point in the plan, the resources can be filled in as follows: AGENT + JOHN, CHAIR + DESK-CHAIR.l,CURRENT-OCCUPANT+NIL. Often, the value of a resource may not be immedi- ately computable with the currently available informa- tion, in which case it is deferred for later analysis (see below). For convenience, helper functions like find- plausible-agent and find-plausible-target are some- times used to help identify resource bindings. These capture specific knowledge by following a few simple heuristics, just as looking for for the object and subject of the sentence, respectively. They also constrain the search, for example, by making sure the A G E NT is an animate object. The remainder of the script describes one or more cases, describing different possible conditions which may affect the performance of that action. Each case includes 132 The Arts e nume - the name of this case 0 documentation - a descriptive the planner’s progress form for use in tracing @ test - a predicate indicating whether this case is applicable 0 effects - assertions summarizing performing this case the consequences of e script - actions to take in order to implements this case The example above shows several cases that might arise for an actor instructed to sit down. It may already be sitting, there may be someone else in the target chair, or the target chair may be far enough away to require the subtask of approaching it. The last case is the “normal” case, in which it is assumed that all precon- ditions have been satisfied, and the appropriate motor skill can be directly invoked. Divadlo uses a relatively simple planner, always operating on a concrete, global plan, with no back- tracking. As previously mentioned, most stage direc- tions are straightforward. The system’s main task is to expand high-level tasks into appropriate subtasks, and to infer and provide concrete animation control pa- rameters to the motor skills. Plan expansion occurs in two passes on each itera- tion: in the first, a pending action is selected and expanded - the most common operations are substi- tution (replacing with a more specific task), insertion (to satisfy preconditions or postconditions), or dele- tion (of superfluous actions). The second pass allows opportunistic modifications to the plan, by applying rewrite rules triggered by matching patterns and per- form arbitrary operations on the plan elements. Ex- amples include: 0 consolidation, such as replacing RU N and K I C K - 6 A L L withaspecial.izedversionRUN-WHILE-KICKING-BALL. 0 inserting or removing delays to break up coinci- dences or improve synchronization between related actions. e altering resource parameters of actions, e.g. chang- ing the way an actor performs a task after repeating it thrice, to avoid seeming too repetitious. 0 insertion of opportunistic behavior, such as having a sick character occasionally sneeze while performing other tasks. Some limited lookahead is provided by a mecha- nism for deferred choices, inspired by a similar feature in AN1 [Kahn 791. In computing resource values before expanding a script, insufficient or ambiguous informa- tion causes an explicit choice object to be created, which captures the dependencies and alternatives. Choices are placed on a queue to be resolved when the necessary information is available, or when continued deferral would halt further progress, in which case a peremptory decision is made. Divadlo is not a purely symbolic system, but neither is it purely a situated or “nouvelle” AI as categorized in [Brooks 901. We note that our goal is entertainment, not verisimilitude. Unlike robotics or physically-based ani- mation, a grounding in reality or high-fidelity simula- tion is not always necessary or even desirable from an artistic point of view. (This is fortunate, considering how difficult it is to build such systems, and how computationally demanding they are to run interac- tively). On the other hand, unlike purely symbolic systems, Divadlo’s objects are grounded in a simulated world with three continuous spatial and one temporal dimension, in which the generally accepted rules of gravity, collision avoidance, etc. must usually be fol- lowed. . We believe that somewhere between the vivid furni- ture of Virtual Reality (passive-reactive objects) and the teeming ant colonies of Artificial Life (fully autono- mous agents), there lies the relatively unexplored do- main of the semi-autonomous agent. We envision an entertainment system of the future, consisting of a troupe of virtual thespians ready to act out dramatic scenes of the user’s invention. In real life, actors get relatively explicit stage instruc- tions from writers and directors, and are rarely called upon to perform complex problem-solving. They are told where to stand, when to move, and are often given advice on how to modulate their motion. This creative control is part of the pleasure ofzuriting and directing, and our goal is to reserve it for the user. At the same time, a large category of users prefer to avoid fully-guided animation, which carries the obligation to provide too much control at too low a level of detail. The expertise of animators needs to be captured into useful action units so that “clip behaviors”, much like “clip art”, could be pragmatically recycled. Before this can be realized, hcwever, several dispar- ate components must be integrated into a practical infrastructure for these actors to inhabit. We have built an experimental system integrating natural language, knowledge representation, planning, robotics, and com- puter animation. 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Bryan and Bates, Joseph, Real-time Control of Animated Broad Agents, Proceedings of the 15th Annual Conference of the Cognitive Science Society, 1993. Minsky, Marvin, Society of Mind, Simon and Schuster, New York, 1985. Schank, R.C. and Abelson, R.P. Scripts, Plans, Goals, and Understanding, Lawrence Erlbaum Press, Hillsdale, NJ, 1977. Sims, Karl, Locomotion of Jointed Figures over Complex Terrain, MS Thesis, MIT Media Lab, June 1987. Strassmann, Steve, Desktop Theater: Automatic Genera- tion of Expressive Animation , Ph.D. thesis, MIT Media Lab, June, 1991. Takashima, Y., Shimazu, H., and Tomono, M., Stovy Driven Animation, CHI+GI ‘87 Proceedings, ACM SIGCHI, pp. 149-153,1987. Winograd, Terry, Understanding Natural Language, Cognitive Psychology Vol. 3, (1) 1972. Zeltzer, David, Motor ControZ Techniques for Figure Animation, IEEE Computer Graphics and Applica- tions 2(9):53-59,1982. 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1,656 | Multi-recurrent Networks for Traffic Forecastin Claudia Ulbricht Austrian Research Institute for Artificial Intelligence Schottengasse 3, A-1010 Vienna, Austria claudia@ai.univie.ac.at Abstract Recurrent neural networks solving the task of short- term traffic forecasting are presented in this report. They turned out to be very weII suited to this task, they even outperformed the best results obtained with conventional statistical methods. The outcome of a comparative study shows that multiple combinations of feedback can greatly enhance the network perfor- mance. Best results were obtained with the newly developed Multi-recurrent Network combining output, hidden, and input layer memories having self-recurrent feedback loops of different strengths. The outcome of this research wiIl be used for installing an actual tool at a highway check point. The investigated meth- ods provide short-term memories of different length which are not only needed for the given application, but which are of importance for numerous other real world tasks. Introduction Forecasting the number of cars passing a check point on a highway is important for warning the people working there of upcoming heavy traffic. It is needed to avoid congestion and to control the highway accesses. At the site under investigation, the number of cars has been estimated by looking at reference days having similar properties. This task has also been tackled with vari- ous traditional statistical methods taking into account also recent traffic flow. This report shows how bet- ter performance can be achieved with recurrent neural networks. The novel network architecture developed for this task shows the importance of designing appro- priate feedback links for time series prediction tasks. The combination of various types of feedback allows the formation of “memories” having different qualities. *This research was supported by a grant from the Aus- trian Industrial Research Promotion Fund, Project No. 2/282 as a part of the Esprit-II project Nr. 5433 “NEU- FODI” (Neural Networks for Forecasting and Diagnosis Applications) which was performed in cooperation with BIKIT (Belgium), Lyonnaise des Eaux Dumez (France), Elorduy y Sancho, and Labein (both Spain). The data sets were provided by COFIROUTE, a subsidiary of Lyonnaise des Eaux Dumez. Forecasting with Neural Networks Time series forecasting is relevant for numerous appli- cations in a wide range of areas. For instance, forecast- ing product demand in business or forecasting option prices in financial markets. Since estimates about fu- ture developments are important for decisions and ac- tions today, there is always a need for better forecasting techniques. A lot of research has been done in the field of time series forecasting, an area to which AI meth- ods can contribute a lot. In comparison to traditional statistical methods, neural networks offer a high flex- ibility concerning the types of functions that can be approximated adaptively during the training process. They are well suited to such function approximation tasks. After being trained to perform mappings for the examples in the training set, they can generalize to new examples. Delay Mechanisms Time series can only be handled by neural networks when some kind of delay mechanism is provided be- cause multiple input patterns together in their given order have to influence the output. Windows, time de- lays, and feedback are examples of such mechanisms. Networks that can handle time series require at least one delay mechanism, but better performance can be achieved by combining different mechanisms as, for in- stance, an input window and feedback. This way the strengths of several techniques can be exploited. An overview of such mechanisms is given in (Ulbricht et al. 1992). Non-recurrent Networks The most straightforward approach for handling time series is using an input window which holds a restricted part of the time series. The neural network analyzes this part of the time series before the window is shifted by one or more elements further in time. An example can be found in (Tom & Tenorio 1989). Such a win- dow can be modeled by collecting sequence elements arriving one after the other in some input memory un- til they can be used. Thus, the temporal dimension is reduced to zero by parallelizing sequence elements. Neural Networks 883 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. However, it is also possible to apply windows to several layers to repeat the windowing effect, as it is done in the TRACE model of speech perception (McClelland & Elman 1986). Such additional windows let the actual window size of the network grow. Time windows are also created in so-called time delay networks (see, for instance, (Wan 1990) or (Waibel 1988)). Signals origi- nally ordered in time arrive at a single unit in parallel at the same point in time. All these networks are non-recurrent networks with- out any feedback loops. They can only handle limited parts of time series at once. Moreover, invariance prob- lems can arise because such networks are not flexible regarding the length of time intervals. The capacity of the memory of networks employing only non-recurrent mechanisms is limited by the size of the windows or by the number of time delays. Recurrent Networks Types of Memories The memory of a network with feedback has no defini- tive temporal limitation. The advantage of such a memory has to be paid by incompleteness, though. Past inputs are not kept in their complete original form, but only in a processed format thereby extract- ing and memorizing only a few characteristics. How- ever, when using simple feedback loops the knowledge on past inputs and states decays rapidly. On the one hand, this effect seems to be very reasonable because the further back in time the less important events seem to be for the current situation. On the other hand, some past events can be very important. Both types of memories can be useful: flexible ones keeping recent events and rigid ones storing information over longer time periods. Another advantage of recurrent networks is that they allow the formation of states. If recurrent networks are updated like feedforward networks (with a single update per time step) they keep their general characteristics. Networks of this kind are also called “recurrent feedforward networks,” “simple recurrent networks,” or “partially recurrent networks” (Hertz, Krogh, & Palmer 1991). Various neural network architectures employing dif- ferent types of feedback can be found in literature. Output feedback is part of the network described in (Jordan 1986). The unit activations of the hidden layer are fed back in the network presented on page 184 in (Elman 1990). In the fully recurrent network de- scribed in (Smith & Zipser 1989) all information is fed back via a single feedback loop around the only layer. Storing the contents of the input layer for the next time step is equal to using input windows and does not introduce true recurrence. Finally, memory layers can also be fed back to themselves as it is also found in the network described in (Jordan 1986). This type of feedback has to be combined with some other feed- back. The flexibility of such a memory can be tuned by adjusting the influence of these feedback loops. As will be shown in this report, memories can take on any In this context, a memory is a layer receiving a copy of some other network layer. Its contents can later be fed forward to other layers - typically to the hidden layer. Such a memory layer stores information over time as unit activations. If the associated time delay is of length 1, the contents of the layer are stored for one time interval. Different types of delay connections for transferring the contents of a layer to a memory layer can be distinguished. They can be classified ac- cording to their properties in various ways. Feedback usually gets its name from the layer that is fed back as, for instance, “output feedback.” In the tested net- works, memory layers keep information of one or sev- eral of the following layers: the input layer, the hidden layer, the output layer, or one of the memory layers. Information is not necessarily stored by the memory layer the way it is received, but it can also be trans- formed before it is stored as it is done in some of the described experiments. When two layers are fed to a single layer they can be combined by weighting the two parts. Some other functions can also be useful, as for instance, calculating the error at the output as the difference between the output and the target. The performance of neural networks in general is de- pendent on the network architecture, and also highly dependent on how the input is pre-processed. For in- stance, the performance can often be improved by ex- plicitly giving the difference between two values. It can further be improved by employing appropriate tech- niques for handling temporal aspects as, for instance, the formation of memories. The objective of the ex- periments presented in the following section is to find a way of optimally combining and exploiting such tech- niques in order to lower the error at the output. The Application The Data Set The given data set contains a time series of the num- ber of vehicles passing a highway check point per hour. grade between being very flexible and very rigid. Since various combinations might be useful, memories with different degrees of flexibility can be part of a single neural network. This way short-term memories of dif- ferent length are brought into neural networks having only long-term memories - the weights. Self-recurrent connections with low weights lead to flexible memories quickly losing information. When raising these weights the memories become more and more rigid. Since they can keep information over longer time periods, they might be useful for avoiding invariance problems arising in many neural networks. Units in such layers have similar activity no matter whether a certain event occurred a few time steps later or earlier. Combining both flexible and rigid memories would allow the networks to handle both variant and invariant properties of time series. 884 Neural Networks Figure 2: Architecture of a recurrent network with multiple hidden layer feedback used to code such information as, for instance, the fact that school holidays were going to start 2 days later. Furthermore, there was a time window over the 3 last hours starting with the number of vehicles counted be- tween 2 and 3 a.m. The last and current value of the time window was the traffic during the fifth hour of the day. Another unit coded the number of cars dur- ing the fifth hour a week before the current time. Since it seemed to be interesting to compare this value with that one week before, the difference between these two values was also supplied. It was coded by two units, one for positive and one for negative values, because they represent two different trends: an increase and a decrease in traffic respectively. Finally, the number of cars that had passed the check-point during the eighth hour a week before was also given because this corre- sponds to the value to be predicted. Hidden Layer Feedback Since not only the last hours, but also the last days are important for forecasting, in the next experiment (Net- work 2) the history of days was also taken into account. Therefore feedback was introduced. The contents of the hidden layer (10 units) were fed back after each up- dating phase (like in the network presented in (Elman 1990)). In the next updating cycle the stored values were fed forward to the hidden layer together with the input layer. In another test, the hidden layer was fed back three more times, but - like in the network pre- sented in (Jordan 1986) - into context layers in which each unit had a recurrent feedback loop to itself. The feedback from the hidden layer and the feedback from the unit itself have to be combined in some way. When they are both given equal weights, 50% of feedback from the hidden layer is added to 50% of self-recurrent feedback. In order to create memories of different flex- ibility the feedback links to the memory layers were given different weights. A weight of 75% produced a rigid memory layer slowly adapting its activations over time and thus keeping information over longer time pe- 886 Neural Networks riods whereas a memory with a self-recurrent feedback link with a weight of 25% can be regarded as a more flexible short-term memory. A network containing 4 such memory layers (Net- work 3) is depicted in Fig. 2. In a first step, the next sequence element is copied to the input layer. Then, the hidden layer is updated. It receives input from the input layer and from all context layers. The activations are then propagated to the output layer and further analyzed. Finally, in a fifth step all context layers are updated and prepared for the next time step. In many neural networks the error at the output is used to adjust the weights which form the long-term memory of the network. When feeding back network layers, this influences unit activations which can be regarded as short-term memory. Four different de- grees of self-recurrence allow the formation of short- term memories with different flexibility. This allows the network to capture short-term events in addition to the acquired long-term knowledge. Output Feedback In another experiment output, target output, and the difference between the two were also fed back (Net- work 4). They were fed back like the output in the network described in (Jordan 1986), but at first without any feedback loop from the memory units to themselves. Like for the hidden layer feedback, the next time this feedback was duplicated three times, each time with different feedback weights (Network 5). Feeding back the output and the actually observed value is only possible when they are available at the point in time when the next forecast is to be performed. When using longer lead times recent information can- not be taken into account. Here, it is possible because the lead time is 3 hours, and because the actual num- ber of vehicles having passed the check point the day before is available. Since both hidden layer feedback and output feed- back improved the performance, they were both part of tA I - In- and Output _~mmm=----=-II~___ -I -c ** - Forward Propagation ** ‘\A ---+ Layer Copy % ’ er 5 Figure 3: Architecture of the Multi-recurrent Network the next tested network (Network 6). It had 4 feedback loops for the hidden layer activations and 4 feedback loops for output information. Input Memory In another experiment, the input window covering the 3 last hours was memorized analogously to the con- tents of the hidden layer and of the output layer (Net- work 7). This network contains two different kinds of windows: one over several hours and one over two days. Then, three more input memory layers with dif- ferent degrees of self-recurrence (again 25%, SO%, and 75%) were added (Network 8). This way the input se- quence can be stored in a compressed form. A longer input history can be kept without requiring much more space. Finally, all introduced feedback links were combined. This network (Network 9) which is depicted in Fig. 3 had 4 context layers for feeding back the contents of the hidden layer, 4 context layers for feeding back out- put information (consisting of the forecast value, the actually observed value, and the difference between the two), and 4 context layers for storing the sequence of input windows. Results An overview of the results of the experiments with the 9 networks described above is given in Table 1. The RMSE on the test set is given for 3 repeated experi- ments. In the last column, their mean is listed. For better comparison, the mean is also depicted in the bar chart in Fig. 4. The value these results have to be compared with is the RMSE of 210.6 which is the best result obtained with a conventional statistical method. It is outper- formed by all tested neural networks. In most experiments, the introduction of feedback improved the results. This is remarkable because it means that the positive effect of adding feedback is much larger than the negative effect of the much larger ii! = 100.0 2 Figure 4: I -L 6 Nelwoks - 7 1 Results obtained with neural networks having di$erent types of memories input dimension. The influence of different types of memories is assumed to be dependent on the given ap- plication. In this case, the most effective technique for reducing the error turned out to be multiple output feedback which is part of Networks 5, 6, and 9. But hidden layer feedback and input processing also en- hance the result, so that the best performance is that of Network 9 which combines all presented memory techniques. This shows that it is reasonable to supply a large number of feedback links in neural networks. How- ever, this results in the problem that each additional context layer unit leads to an increase of the input dimension. Proper handling of high-dimensional in- put and dimension reduction, for instance, by pruning techniques, could be part of further research. More- over, methods for improving the quality of the memo- ries could be investigated. Neural Networks 887 Net Nr. 1 2 3 4 5 6 7 8 9 1 Feedback Hidden - 1 4 - - 4 - - 4 I RMSE output Input Test 1 Test 2 Test 3 - - 152.87 147.18 146.31 - - 133.32 141.71 139.54 - - 130.75 130.60 138.37 1 - 138.90 145.26 121.87 4 - 111.83 114.47 114.39 4 - 115.50 111.11 108.86 - 1 141.31 149.10 146.29 - 4 142.29 145.14 131.16 4 4 109.15 112.20 107.72 Table 1: Overview of the experiments Mean 148.79 138.19 133.24 135.34 113.56 111.82 145.57 139.53 109.69 Concluding Remarks The goal of the experiments was to check whether neu- ral networks can solve the task of short-term traffic forecasting. This task was solved and better results were obtained than with conventional statistical meth- ods. The novel type of network architecture developed specifically for this application will be used as a ba- sis for an actual tool at a highway check point. Var- ious types of feedback are part of the Multi-recurrent Network. Not only activations of the hidden layer are stored in memory layers, but also output information and the input window. The introduction of multiple self-recurrent feedback loops allows the formation of short-term memories with different properties. This is an important extension to neural networks which often have only long-term memories. Such short-term mem- ories are not only of use for this task, but important for a large number of other real world applications. References Canu, S.; Sobral, R.; and Lengellk, R. 1990. Formal Neural Network as an Adaptive Model for Water De- mand. In International Neural Network Conference, Paris, France, July 9-13, 1990, 131-136. Kluwer, Do- drecht . Elman, J. 1990. Finding Structure in Time. Cognitive Science 14:179-211. Hertz, J.; Krogh, A.; and Palmer, R. 1991. Introduc- tion to the Theory of Neural Computation. Addison- Wesley Publishing Company. Jordan, M. 1986. Attractor Dynamics and Parallelism in a Connectionist Sequential Machine. In Proceed- ings of the Eight Annual Conference of the Cognitive Science Society, 531-546. Erlbaum, Hillsdale, NJ. Lengelle, R.; Sys, V.; and Ding, X. 1993. Traf- fic forecasting application. Technical Report NEU- FODI/TR/SO 1/3/LYO2/1, Lyonnaise des Eaux - Dumez, France. McClelland, J., and Elman, J. 1986. Interactive Pro- cesses in Speech Processing: The TRACE model. In 888 Neural Networks Rumelhart, D., and McClelland, J., eds., Parallel Dis- tributed Processing, volume I. MIT Press. Smith, A., and Zipser, D. 1989. Encoding Sequen- tial Structure: Experience with the Real-Time Recur- rent Learning Algorithm. In International Conference On Neural Networks, volume I, 645-648. Washington D.C., IEEE. Tom, M., and Tenorio, M. 1989. A Spatio-Temporal Pattern Recognition Approach to Word Recognition. In IEEE International Conference On Neural Net- works, volume I, 351-355. Ulbricht, C.; Dorffner, G.; Canu, S.; Guillemyn, D.; Marijuan, G.; Olarte, J.; Rodriguez, C.; and Martin, I. 1992. Mechanisms for handling sequences with neu- ral networks. In Dagli, C., et al., eds., Intelligent En- gineering Systems through Artificial Neural Networks, ANNIE’92, volume 2, 273-278. ASME Press, New York. Varfis, A., and Versino, C. 1990. Univariate Economic Time Series Forecasting by Connectionist Methods. In International Neural Network Conference, Paris, France, July 9-13, 1990, 342-345. Kluwer, Dordrecht. Waibel, A. 1988. Connectionist Glue: Modular De- sign of Neural Speech Systems. In D., T., ed., Con- nectionist Models Summer School, 417-425. Wan, E. 1990. Temporal Backpropagation for FIR Neural Networks. In International Joint Conference on Neural Networks, volume I, 575-580. | 1994 | 31 |
1,657 | Knowledge Matrix ---- An Ex efinement Facility for eural Network Daniel S. Yeung Department of Computing, Hong Kong Polytechnic, Hong Kong. Fax : (852) 7642528 Email : csdaniel@hkpcc.hkp.hk Abstract One of the major shortcomings of neural network as a problem solving tool lies in its opaque nature of knowledge representation and manipulation. For instance, the way that a learning algorithm modifies the connection weights of a network cannot be easily understood in the context of the application domain knowledge. Thus, the applications of neural networks is limited in areas where user’s understanding of the situation is critical. This paper introduces a facility called knowledge matrix for a rule induced Neocognitron network. It represents the correlation between the knowledge stored internally in the network and the symbolic knowledge used in the application domain. Another facility called response matrix is developed to represent the network’s response to an input. These two facilities are then employed cooperatively to generate symbolic interpretations of the network’s response. Based on the interpretations, queries can be made against the networks responses and explanations can be provided by the system. Two detailed examples are discussed. It can be shown that the network knowledge can be refined evolutionarily without degrading its comprehensibility. An algorithm has also been formulated to adapt the system with respect to one type of recognition error. Introduction Although neural networks possess learning and generalizing capabilities, much of their internal knowledge representation and manipulation is incomprehensible. It is also difficult to make use of the ways they leam to refine the problem domain knowledge. These two shortcomings seriously hinder the use of neural networks in situations where a high degree of human interaction is required. To overcome these difficulties, one possible means is to build a neural network system with embedded high-level, symbolic domain knowledge. Several hybrid systems which attempt to integrate neural networks and symbolic knowledge manipulations have been proposed (Fu & Fu 1990, Gallant 1988, Hayashi, Krishnamraju & Reilly 1991, Towell, Shavlik & Noordewier 1990, Towel1 & Shavlik 1992). Although some of them (Fu & Fu 1990, Towell, Shavlik & Noordewier 1990, Towel1 & Shavlik 1992) incorporate domain knowledge into the neural networks, they employ conventional learning algorithms to train the networks. Hak-shun, Fong Department of Computing, Hong Kong Polytechnic, Hong Kong. Fax : (852) 7642528 Email : cshsfong @comp.hkp.hk Therefore, it is still difficult to understand why certain changes on the network have taken place. On the other hand, Hayashi (Hayashi, Kiishnamraju & Reilly 1991) has proposed a hybrid architecture in which a “cooperative module” is employed to exchange knowledge between a neural network and an expert system. Unfortunately, very little information on this module is given. In this paper, a rule induced neural network for handwritten Chinese character recognition is proposed using a priori symbolic knowledge, i.e., a set of production rules. The construction of such a rule induced network is described in Section 2. A facility called knowledge matrix which provides symbolic interpretations of the network’s response to inputs is presented in Section 3. Thus, it follows that the network knowledge can be refined based on information stored in the knowledge matrix. Section 4 gives the conclusion and possible future work. ule Induced Neural Network The neural network being considered is a rule induced network (Yeung, Fong & Cheung 1992), which is so devised to represent the syntactic structure of a small set of seventeen Chinese characters. A syntax of attribute rules is formulated to describe the structural knowledge of these characters, and a mapping scheme is also established to program the network using these rules as a template. The rule induced network thus constructed is found to bi A’ Displacement from the expected location \. \ -2 -1 0 +1 +2 Figure 1 : Structure Decomnosition Tree Figure 2 : Fuzzv Repion Neural Networks 889 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. recognize some handwritten samples of the seventeen character categories. In this section, the rule syntax and the network architecture are briefly described. Rule Representation Every rule in our system specifies a character pattern in terms of its subpatterns. Each subpattern may successively be further decomposed into simpler ones (Figure 1). The decomposition process is repeated until the subpattems being used are the commonly accepted primitives. The set of primitives chosen is called the basic stroke set. Similar stroke sets, with slight variations, are widely adopted in various Chinese dictionaries, e.g., Cihai (Shangwu-Yinshuguan 1979). The collection of all rules related to the decomposition of a particular character can be viewed as its structure decomposition tree. Such a tree description closely resembles the syntactic analysis approach of Chinese characters studies (Chen 1986, stallings 1977). The form of a general rule is given as follows : If {A, Ks,O, fwJl1 ad {Bi, [(u,V), fuz-‘I} and . . . . . then E, where the consequence E indicates the character pattern whose structural knowledge is described by this rule. Each of the antecedents holds the geometric information of one subpattem. Currently, only one writing style in each character pattern serves as its template. All rules are of conjunctive types because no subpatterns are considered as optional. Since a disjunctive rule can be transformed into a number of conjunctive rules, it seems to be quite straight forward to extend our current rule forms to include disjunctive ones. Every antecedent consists of two parts, namely, a component pattern and its positional attributes. The subpattem B1 stands for the i-th variant of the stroke class B, while A 1s a subpattem which may be a radical or a subcharacter. In the positional attribute part’ two fields of information are maintained. The first field denotes the mostly expected integral coordinates of the subpattem when the character pattern represented by the consequence indeed exists. The coordinates of the subpattems in the antecedent part are calculated as follows. The character pattern denoted by the consequence is supposed to fall on a 17x17 pixel matrix. Then, for each of its subpattems, a reference location on the matrix is associated with it, which is often chosen at approximately the centre of that subpattem. The same is done for the consequence pattern too. By treating the reference location of the consequence pattern as the origin, the relative coordinates for the subpatterns are calculated accordingly. These relative coordinates are the mostly expected coordinates. The second field defines a fuzzy region enclosing the location specified by the first field. A sample fuzzy region is shown in Figure 2. Values in the region specify the plausibilities for that antecedent subpattem to exist at the corresponding locations. Table I lists the values in several 890 Neural Networks fuzzy regions. In a fuzzy region, each value is inversely proportional to the distance between the location concerned, [r’, c’], and the mostly expected location [r,, c,]. Here, “distance” is defined by the function MAX(lr’- rJ, k’-c,l). FUZZY I Distance from the expected location Region 0 I 1 I 2 I 3 I 4 I 5 FuzJ 1.0 1 0.50 1 I I I Fuz-2 11 1.0 1 0.75 ] 0.25 1 System Architecture In Figure 3, the architecture of our proposed neural network system is shown. A 65x65 square pixel matrix at the left hand side is the input pattern grid for receiving binary input images. An input, i.e., a handwritten Chinese character to be recognized, will turn on the corresponding pixels on the matrix. A stroke extractor is then employed to locate all possible instances of the basic strokes contained in the input character. At the output layer of this extractor, there are twenty-two groups of neuron-planes corresponding to the twenty-two basic stroke classes (Yeung, Fong & Cheung 1992). There are three types of transformation applied to the basic stroke in each class, namely, scaling, skewing and rotation. With three choices allowed for each transformation, up to a total of twenty-seven variants can be generated for each stroke class. Thus, there are up to twenty-seven neuron-planes in each group. Every neuron- plane at the output layer of this stroke extractor is a 17x17 matrix arrangement of neuron-modules. The locations of the detected stroke variants are “quantized” to these 17x17 matrix locations. The firing score of a neuron-module, which is bounded between 0.0 and 1.0, reflects the degree of matching with a particular stroke variant at a particular location. In the rule induced neural network, each stage holds the structural knowledge of several patterns which may be characters or radicals. A pattern in each stage can be constructed from its components as detected in the preceding stages. A neuron-plane, which is a 17x17 matrix arrangement of neuron-modules, is allocated for the detection of each pattern. All neuron-modules on a neuron-plane are mapped with the structural knowledge of the same pattern. This duplication of knowledge is to group of neuron-planes 17x17 for one stroke class neuron- plane -A I 65 6 El Input Grid Stroke-extractor L-2 L-3 -----I ------ I I I I I I I I t I I I I I I I I I I I I I I I I I I I I I t I I I I I I I I I \ L-4 --we- t I I I t I I I I I I I I I I I I I \\\\ L-N c----- Figure 3 : Svstem Architecture facilitate positional shift tolerant detection of the pattern. During the rule-mapping phase, the internal structure of a neuron-module is determined by the rule mapped onto it. There are two types of cells in each module, namely s-cell and p-cell. While there is always only one s-cell in each module, the number of p-cells in a module equals the number of antecedents in the mapped rule. Every p-cell is responsible for detecting the existence of a particular component in an acceptable region, by connection projected from the neuron-plane of that component pattern. This acceptable region is determined by both the location of the currently concerned module on the neuron- plane, and the positional attribute (section 2.1) of that component. The rule induced network performs its recognition task stage by stage. A stage is labelled as a candidate-stage if it has a neuron-plane, which is associated to a character pattern, fire with non-zero response in one of its neuron- modules. After all stages have finished the processing, the last candidate-stage is checked. The input character is identified as the character pattern associated with the neuron-plane in that stage which fires with the highest score. If no candidate-stage is found at all, the input character is then rejected. Knowledge Matrix The knowledge matrix is introduced in this paper to function in two aspects. It is to facilitate reasoning of the network’s response to an input character, and to drive modifications on the rule-base. The modified subset of rules can then be re-mapped onto the network to refine the network knowledge without degrading its comprehensibility. In the sections below, one will first see how the knowledge matrix and an auxiliary tool, namely the response matrix, are organized. Then, the ways these two matrices co-operate to perform the above functions are elaborated. Matrix Representation Rule Induced tieural Network The knowledge matrix is a representation of the internal knowledge of the rule induced neural network (Figure 4). It has symmetric labels on its rows and columns. Every label is a 3-tuple, corresponding to a neuron-module in the network. For instance, a label (P,r,c) corresponds to the neuron-module at the location [r,c] on the neuron-plane for pattern P. Those rows (columns) which are closer to the upper (left) portion of the matrix are assigned labels corresponding to modules staying in earlier stages. Furthermore, those labels corresponding to the same pattern are grouped consecutively. Additionally, a non- diagonal, non-zero entry Ki,j on row-i and column-j indicates a connection from module-j to module-i. The entry value is the maximally attainable excitation on that connection. In contrast, the diagonal entry-values indicate the highest firing scores attainable by the s-cells in the corresponding modules. Since the value-determination procedure for the entries in the knowledge matrix is quite complicated, those who are interested are suggested to refer to the authors’ other paper (Yeung & Fong 1993). According to this label-organization, the knowledge Pattern-vector A-G : non-zero blocks @ : zero block -I --HD& mre 4 : Knowledge Matrix Neural Networks 891 matrix possesses several characteristics. Since the network allows connections only from lower stage to higher stage, all the entries at the upper-triangle of the matrix are set to zeros. Moreover, the rows (columns) of the knowledge matrix can be divided into row-groups (column-groups). All the row-labels (column-labels) in a row-group (column-group) correspond to modules from the same neuron-plane, whose associated pattern is thus called the row-group pattern (column-group pattern). The row-groups divide the diagonal on the knowledge matrix into partitions. Each of the partitions is named a pattern- vector of the associated row-group. Another kind of unit on the matrix, called block, is also identifiable which is defined as the intersection region between a row-group and a column-group. Thus, a block is a submatrix associated with one row-group pattern and one column-group pattern. However, the following discussions concerning blocks should exclude those which cover the diagonal. A block is a non-zero matrix only if its row-group pattern possesses its column-group pattern as one component. Meanwhile, every row of entries in a block forms one row-vector. The entries in a row-vector express the maximum excitations on a set of connections, projected from a p-cell in the neuron-module associated to that row onto the neuron-plane of the column-group pattern. While the knowledge matrix represents the static knowledge captured by the rule induced network, a response matrix is used to represent the network’s run- time response to an input. The label-organization, definitions of row/column-group, pattern-vector, block and row-vector on the response matrix are identical to those in the knowledge matrix. The diagonal entries carry actual fling scores of each neuron-modules, and the non- diagonal ones carry actual excitations on the corresponding connections. The example of a response matrix is shown in Figure 5. Explanation of the Network Response With the help of the knowledge matrix (and also the response matrix), it is possible to query the network’s response to an input in two ways : (0 Why is pattern-A detected {at location [r,cJ} ? (ii) Why is pattern-A NOT detected ? Note The location portion {.} in query (i) is optional. Two different algorithms are devised to handle these two types of queries. Q&i.) Why is pattern-A detected {at location [r,c]} ? Algorithm A : Steps 1) Check if pattern-A is really detected. If location is specified in the query, one can directly check if the diagonal entry on the corresponding row is non-zero. Otherwise, this can be done by tracing the row-group of pattern-A, on the response matrix, to see if it possesses a non-zero pattern-vector. 2) If the non-zero entry (or the non-zero pattem- 892 Neural Networks vector) cannot be found in step l), tell the user that pattern-A is NOT detected, or the query is invalid; then STOP. 3) If location is specified in the query, e.g., [r,c], then choose the target row Rr with row-label (A,r,c). Otherwise, in the row-group of pattern-A on the response matrix, locate the target row Rr with the highest diagonal entry-value. If more than one row possesses the highest value, choose one of them arbitrarily. 4) Extract the corresponding row, Kr, on the knowledge matrix. 5) For each of the non-zero row-vectors along Kr, find the corresponding row-vectors VRr, on the response matrix. 6) On every row-vector VRri, do the steps below. > Identify the highest excitation value. If more than one is found, choose one of them arbitrarily. > Suppose the entry identified above is M,,. Extract row-b on the response matrix. ’ 7) Suppose every row-b, extracted in step 5) has a 3- tuple label (Pi, ri, Ci), and the diagonal entry value on it equals Vi. Construct an explanation in the following format : “Pattern-A is detected because subpattern P, is detected at location [rl, ct] with score V,, and . . . . . subpattern Pi is detected at location [ri, Ci] with ,, score Vi, and 8) STOP. The user may continue the query on any particular pattern P, above. However, if Pk is a stroke variant, stroke extraction stage is reached and the user should be notified that no more detail is available. Case (ii) Why is pattern-A NOT detected ? Algorithm B : steps 1) Check if the pattern-vector on the row-group of pattern-A on the response matrix is a zero vector. If not so, tell the user that pattern-A has been detected, or the query is invalid; then STOP. 2) In the row-group of pattern-A on the knowledge matrix, identify all the non-zero blocks. Then, locate the corresponding blocks Rmj on the response matrix. 3) (9 If some Rmj are zero matrixes, do as follows. Suppose each zero block Rmi corresponds to COlUUlU-grOUp pattern Pi. (ii) Construct an explanation in the following format “Pattern-A is NOT detected because subpattern P, is NOT detected, and . . . . . subpattern Pi is NOT detected, and 9, . . . . . (iii) STOP algorithm B. 4) Trace the row-group of pattern-A on the response matrix until a row is encountered along which all row- vectors in all Rm. are non-zero vectors. If such a row ex& give an explanation : “Pattern-A is NOT detected because the degree of match is too low.” Otherwise, give the following explanation : “Pattern-A is NOT detected because the positional information does not fit the input.” 5) STOP. The two types of queries can provide much information on the network’s response. However, there are other types of queries which may be useful. In addition, details added onto the last explanation offered in step 4) of algorithm B will make it more informative. The situation can be understood better if one is informed that “the tolerance region of a subpattern X is too small”, “the expected location of a subpattern X is too close”, etc. Nevertheless, the algorithms presented above improve the transparency of the operation of a neural network. More work is to be done along this direction. In this section, the knowledge matrix and the response matrix are adopted to address the problem of knowledge refinement. Most neural network based systems employ learning algorithms which bear no explicit relationship with the problem domain. In contrast, the proposed approach attempts to adjust the knowledge represented in the rule-base, according to the network’s response to an input. The refined rules can then be used to update the network connections through mapping. In refining our system, two major error types are handled, namely wrong-rejections and wrong- recognitions. A wrong-rejection error occurs when none of the neuron-planes responds to the input character which is expected to be recognizable. This type of error requires raising the tolerance (or fuzziness) of the related rules. An algorithm for this purpose has already been devised in another paper of the authors (Yeung & Fong 1993). Thus, we will focus on the second error type here, i.e., wrong- recognition. There are two different cases for this type of error. One is that the relevant neuron-plane doesn’t respond at all, while some other irrelevant ones do. Another case is that the response of the relevant neuron-plane is suppressed by the response from neuron-planes at this or higher stages of the network. For the fast case, action adopted in handling the wrong-rejection error is taken to activate the relevant plane. Thus, the first case is transformed into the second case. At least two situations are identified as the possible causes of the second case of wrong-recognition error. The noise generated by the stroke-extractor in the system, i.e., false stroke detections, may cause irrelevant patterns to be found. Since this is the problem of the stroke-extractor, it is not considered here. Another cause is that some rules (mapped onto the irrelevant neuron-planes) may be too sensitive to give “false” response to the input. A tuning algorithm is given below to tune these rules, so as to suppress responses from irrelevant neuron-planes. Before the algorithm is presented, several definitions employed in the algorithm are described beforehand. Definitions (1) Poorly-Done pattern, PD The entry-values on a row-vector are calculated from the pattern-vector on the same column-group. If the maximum entry on a row-vector corresponds to an element in the pattern-vector which is smaller than a preset threshold (e.g., O.l), the column-group is said to be PD. Adjustment on the structure knowledge of this column-group pattern will not be attempted. (2) Low-Positional Fuzziness, LPF An antecedent is said to possess LPF if the fuzzy region (associated with an antecedent in a rule) has been reduced to a preset lower bound (e.g., 1). Its fuzzy region in that rule should not be shrunk any more. (3) Sit-Well row-vector Each row-vector on the knowledge matrix corresponds to an antecedent of the rule associated to that row. If the maximum entry of a row-vector is found to be located at the centre of the fuzzy region of the corresponding antecedent, the row-vector is said to be Sit-Well. (4) Innocent row-vector When a row-vector possesses LPF or is Sit-Well, and its column-group pattern is PD, the row-vector will not be considered as a possible item whose changes may lead to any improvement of the situation. Tuning Algorithm Suppose the input belongs to the character category A whose structure knowledge has been mapped onto a plane at stage-N. Then, the row-groups on the response matrix are traced one by one, from the highest stage to stage-N. For any row-group G other than that for pattern A, if the pattern-vector is a non-zero vector, perform the routine Neural Networks 893 <Correct> below. One should note that, in the algorithm below, any adjustment on a rule is analogous to some alterations on the network. Thus, after every rule- adjustment, both the knowledge matrix and the response matrix must be updated before the tuning process proceeds. <Correct> (1) Select the row r on G corresponding to the maximum entry in the pattern-vector. (2) Repeat ii;; Record all innocent row-vectors on r. . Among the non-innocent row-vectors on r, choose one rt which possesses the maximum entry. (2.3) Check if ri is marked. If yes, perform 2.3a; else, follow 2.3b. (2.3a) Identify the maximum entry in rt, say, R”a b’ and unmark rt. Then <Component-correct> is performed for the row b. (2.3b) Unmark all other marked row-vectors on r and mark rt. Reduce the fuzzy region radius by one of the antecedent associated to ri if this row-vector does not possess LPF. Until {G possesses a zero pattern-vector, or all the antecedents of the associated rule possess LPF} (3) Unmark all row-vectors on the response matrix. (4) STOP. <Component-correct> Suppose the row concerned is r’, which is corresponding to a rule Ri. $5 Record all innocent row-vectors on r’. Among the non-innocent row-vectors, choose one, e.g., rl’, which possesses the maximum entry value. (3) (6). If rl’ is marked but is PD, unmark it. Go to step (4) If rt’ is marked, identify the maximum entry in q’, w, m,,t. Perform <Component-correct> for the row t. (3 If rt’ is not marked, unmark all other marked row-vectors on r’ and mark rt’. Then, expand the fuzzy region of the antecedent in Ri associated to rt’. (6) STOP. It is possible that the pattern-vector of the row-group G cannot be suppressed completely after tuning. In this case, the algorithm is unable to resolve the ambiguity arisen between the input character and the structure rule associated to G. Conclusion In this paper, two shortcomings which hinder wider applications of neural networks are tackled. The neural network considered is induced by the structure rules of a 894 Neural Networks set of Chinese characters. By introducing a facility called knowledge matrix, the network’s responses can be explained to users. This type of explanation is seldom available in other neural network based systems. Additionally, the knowledge matrix is also employed to drive refinements on the rule-base. Re-mapping of the modified rules onto the network completes the adaptation cycle. This approach of rule refinement keeps the network comprehensible to users, which is another characteristic that cannot be easily achieved in learning algorithms adopted by most neural networks. At present, only a few types of explanations with respect to the network’s responses are offered. Explanations with more details are surely advantageous. Moreover, the performance of the rule refinement algorithms proposed needs to be studied. All these will require a more in depth investigation on the knowledge IlKltriX. References Chen, K.J. 1986. Computational Approaches in Topological and Geometrical Descriptions for Chinese Characters. Computer Processing of Chinese & Oriental Languages 2(4): 234-242. Shangwu-Yinshuguan 1979. Cihai. Beijing, Shanghai: Shangwu Yinshuguan (The Commercial Press). Fu, L.M.; Fu, L.C. 1990. Mapping rule-based systems into neural architecture. Knowledge-Based Systems (3) 1: 48-56. Gallant, I. 1988. Connectionist Expert Systems. Communications of the ACM 31(2): 152-169. Hayashi, Y.; Krishnamraju, V.; Reilly, D. 1991. An Architecture for Hybrid Expert Systems. In Proceedings of the IEEE International Joint Conference on Neural Networks, ‘9 1, Singapore, 2773-2778. Stallings, W. 1977. Chinese Character Recognition. In Fu, K.S. eds. 1977. Syntactic Pattern Recognition, Applications, 95-123. New York : Springer-Verlay. Towell, G.G.; Shavlik, J.W.; Noordewier, M.O. 1990. Refinement of Approximate Domain Theories by Knowledge-Based Neural Networks. In Proceedings of the 8th National Conference on Artificial Intelligence ‘90, 2: 861-866. Towell, G.G.; Shavlik, J.W. 1992. Interpretation of Artificial Neural Networks. In Moody, J.E. eds. 1992. Advances in Neural Information Processing Systems Vo1.4, 977-984. Morgan Kaufmann Pub.. Yeung, S.; Fong, H.S.; Cheung, K.F. 1992. A Neocognitron-based Chinese Character Recognition System. In Proceedings of the International Joint Conference on Neural Networks ‘92, Beijing, 3: 617-622. Yeung, S.; Fong, H.S. 1993. A Knowledge Matrix Representation for a Rule-Mapped Neural Network. (To appear in) Neurocomputing. | 1994 | 32 |
1,658 | Epsilon-Transformat ion: Exploiting Phase Transitions to Solve Combinatorial Optimization Problems - Initial Results* Weixiong Zhang and Joseph C. Computer Science Department University of California, Los Angeles Los Angeles, CA 90024 Email: {zhang, pemberto}@cs.ucla.edu Abstract It has been shown that there exists a transition in the average-case complexity of searching a random tree, from exponential to polynomial in the search depth. We develop a state-space transformation method, called e-transformation, that makes use of this com- plexity transition to find a suboptimal solution. The expected number of random tree nodes expanded by branch-and-bound (BnB) using e-transformation is cubic in the search depth, and the relative error of the solution cost compared to the optimal solution cost is bounded by a small constant. We also present an iter- ative version of e-transformation that can be used to find both optimal and suboptimal solutions. Depth- first BnB (DFBnB) using iterative e-transformation significantly improves upon truncated DFBnB on ran- dom trees with large branching factors and deep goal nodes, finding better solutions sooner on average. On the asymmetric traveling salesman problem, DFBnB using e-transformation outperforms a well-known lo- cal search method, and DFBnB using iterative e- transformation is superior to truncated DFBnB. Introduction It has been observed that phase transitions exist in many intelligent systems (Huberman & Hogg 1987) and combinatorial problems (Cheeseman, Kanefsky, & Taylor 1991; Karp & Pearl 1983; McDiarmid 1990; Mc- Diarmid & Provan 1991; Mitchell, Selman, & Levesque 1992; Zhang & Korf 1992; 1993; 1994). A phase transi- tion is a dramatic change to some problem property as some order parameter changes across a critical point. For example, water changes from a liquid to a solid when the temperature drops below the freezing point. The earliest evidence of computational phase transi- tions was the phase transition of a tree-search problem (Karp & Pearl 1983), which has recently been studied in detail (McDiarmid 1990; McDiarmid & Provan 1991; Zhang & Korf 1992; 1993; 1994). The problem is to find an optimal goal node of the following random tree. *This research was supported by NSF Grant No. IRI- 9119825, a grant from Rockwell International, a GTE grad- uate fellowship (1992-93), and a UCLA Chancellor’s Dis- sertation Year Fellowship (1993-94). Definition 1 (McDiarmid & Provan 1991) A random tree T(b,d) is a tree with depth d, and independent and identically distributed (i.i.d) random branching factors with mean b. Nonnegative edge costs are bounded i.i.d. random variables. The cost of a node is the sum of the edge costs on the path from the root to that node. An optimal goal node is a minimum-cost node at depth d. Best-first search (BFS) and depth-first branch-and- bound (DFBnB) can be used to search these random trees. Both are special cases of the general branch-and- bound (BnB) technique. See (Pearl 1984; Korf 1989; Kumar 1992) for the details of these algorithms. It turns out that the cost of an optimal goal node of T(b, d), and the expected complexity of BFS and DFBnB on T(b, d) experience phase transitions. The order parameter that determines these transitions is the expected number of children of a node whose cost is the same as that of their parent, which are called same-cost children. This is the same as the expected number of zero-cost edges emanating from a node. If ~0 is the probability that an edge has cost zero, then bpo is the expected number of same-cost children of a node. When bpo increases from less than one to greater than one, the expected cost of the optimal goal node of T(b, d) changes from a linear function of d to a con- stant, and the expected time complexity of BFS and DFBnB decreases from exponential in d to at most cu- bic in d. These phase transitions are summarized by the following lemma, and illustrated by Figure 1. Lemma 1 (McDiarmid 1990; McDiarmid & Provan 1991; Zhang & Korf 1993; 1994) Let C* be the op- timal goal cost of T(b, d) with b > 1, and NB and ND be the expected numbers of nodes expanded by BFS and DFBnB on T(b, d) respectively. As d -+ 00, (1) when bpo < 1, C*/d + cu almost surely’, where CY is a constant, and NB = ND = Q(pd), for a constant /? > 1; (2) when bp, = 1, C*/(log logd) -+ 1 almost surely, NB = 0(d2), and ND = O(d3); and (3) when bpo > 1, C* is almost surely bounded, NB = B(d), and ‘A sequence of random variables X, is said to con- verge almost suP-ely (with probability one) to X if P&m,,, X, = X) = 1 (RCnyi 1970). Neural Networks 895 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. I I I bw 1 optimal goal cost is bounded by a constant complexity is polynomial in d transition boundary optimal goal cost is linear in d complexity is exponential in d Figure 1: Phase transitions of tree search problems. ND = O(d2). •I Many practical search problems, such as planning and scheduling, require computation exponential in the search depth, even in the average case. However, we usually do not need optimal solutions, but rather ones that have a satisfactory quality and can be found quickly. In this paper, we develop a state-space transforma- tion method, called &-transformation, that can be used by a search algorithm, such as BnB, to find suboptimal solutions quickly. This method makes use of the phase transition in Figure 1. We analyze its average-case performance. We also present an iterative version of &-transformation for finding both suboptimal and op- timal solutions. Finally, we evaluate the performance of both methods on random trees and the asymmetric traveling salesman problem. Epsilon-Transformation &-transformation is based on the following very simple observation of Figure 1. For a random tree T(b, d), if we can increase the expected number of same-cost children of a node so that bpo 2 1, then the expected complexity of finding an optimal goal node becomes polynomial in d. This can be accomplished by raising the probability po of zero-cost edges, since the branch- ing factor b is usually fixed by the structure of the state space. However, increasing po means obtaining a better node-cost function (Zhang & Korf 1994), which requires more information about the problem, and is generally impractical. By sacrificing solution quality, however, we are able to transform the problem of find- ing an optimal solution with exponential average com- putation, to the problem of finding a suboptimal so- lution with polynomial average computation by artifi- cially increasing PO. This is illustrated by Figure 2. We increase po by setting some non-zero edge costs to zero. To reduce the amount of information lost, and to improve the expected solution quality, we only set to zero those edge costs that are below a particular value 1.0 I I I 0.8 - polynomial region branching factor b 15 20 Figure 2: Transform a difficult problem to an easy one. E. This is why we call our method E-transformation. E is set to the smallest value such that a suboptimal goal node can be found in polynomial average time. Definition 2 For a constant E, an E-tree T,(b, d) of a random tree T(b, d) is the same as T(b, d), except that those edge costs in T(b, d) that are less than or equal to E are set to zero in TE(b,d), and the node costs are updated accordingly. The edge and node costs of T(b, d) are referred to as actual values, and the edge and node costs of T,(b, d) are called face values. &-transformation converts one random tree to an- other one with an adjusted edge-cost distribution, i.e., with an increased probability of a zero-cost edge. Let f(x) be the density function and F(z) be the dis- tribution of edge costs. Then the probability that an edge has cost less than or equal to E is F(E) = Jl f(t)dt, which is also the probability pE that an edge of T, (b, d) has cost zero. Figure 3(a) illustrates how &-transformation adjusts an edge-cost density func- tion. Figure 3(b) h s ows a T(2,2) and its corresponding T,(2,2) with E = 0.25, where the numbers in the nodes and on the edges are node costs and edge costs, respec- tively. The optimal goal node of an g-tree is not nec- essarily the optimal goal node of its original tree, thus &-transformation is not guaranteed to find an optimal goal node. After the transformation, BFS or DFBnB can be used to find an optimal goal node of TE (b, d), and return the actual value of this goal node. For simplicity, we call BnB, BFS, or DFBnB using E-transformation E- BnB, E-BFS, or E-DFBnB, respectively. In order for E-BnB to run in polynomial average time, the value of E is chosen such that bp, s 1. To maximize the solution quality, we select the mmimum E that satisfies bpE > 1. That is, we choose &* = min{@p, 2 l}, where pE = F(E). (1) When E = E*, we use the term E*-transformation. The performance of E*-transformation is summarized by the following theorem. 896 Neural Networks initial edge-cost density original random tree n adjusted edge-cost density optimh goal node (b) transform a random tree (a) adjust an edge-cost density Figure 3: An example of e-transformation. Theorem 1 On a random tree T(b, d) with bpo < 1, as d -+ 00, E*-BnB runs in expected time that is at most cubic in d, and finds a goal node whose relative solution cost error ((C - C*)/C*, where C is the so- lution cost and C* is the optimal solution cost) is al- most surely a constant less than or equal to (S/a - l), where a is a constant as defined in Lemma 1, and S = E[edge cost x 1 x 5 E*]. Proof See (Zhang & Pemberton 1994). •I A useful feature of E-transformation is that a trade- off can be made between the average search effi- ciency and the average solution quality. Solutions with higher (lower) average costs can be produced with less (greater) average computation by using a larger (smaller) value of E . Learning E and Actual-Value Pruning The value of E is a function of the branching factor b and the edge-cost distribution F. For practical prob- lems, b and F are generally not available. Neverthe- less, the value of & can be learned on-line during search. Consider DFBnB as an example. If DFBnB examines the children of the current node in increasing order of their face vales (node ordering), and breaks ties in favor of a node with a lower actual node cost, then the first leaf node reached is the same whether &-transformation is used or not. DFBnB can sample the branching fac- tors and edge costs of all nodes along the path to the first leaf node, and use them to estimate b and F. As the search proceeds, the estimates of b and F can be refined and used to update the value of E. &-BnB can also use actual-value pruning, which pre- vents BnB from exploring an interior node if its actual value exceeds the actual value uaV of the best goal node found up to that point. This pruned interior node can- not lead to a goal node with an actual value less than uaV. Intuitively, one might expect actual-value prun- ing to improve the efficiency of BnB, and not to af- fect the solution quality. However, actual-value prun- ing reduces the opportunity to update the face-value upper bound, consequently causing some nodes with higher face value to be expanded, which are not vis- ited by &-BnB without actual-value pruning. Overall, &-BnB with and without actual-value pruning explore different parts of the search tree. Their relative effect on runtime and solution quality depends on their rela- tive pruning power and the specific problem instance. Our results on random trees show that E*-DFBnB with actual-value pruning runs longer but finds better solu- tions than &*-DFBnB without actual-value pruning. Iterative dhansformation If we need a better solution than can be guaranteed by E-transformation, then we can use an E that is less than E*. In order to determine the largest value of E that satisfies a given error bound, we need to know the optimal solution cost, which in general is not available. We suggest an algorithmic approach to address this issue, which is called iterative E-BnB. Iterative &-BnB performs a sequence of BnB searches with a series of E-transformations, where the value of E is reduced over successive iterations. The first iteration performs E*- BnB. Within each iteration, BnB keeps track of the largest actual edge cost encountered that is strictly less than E‘, among all those that are set to zero. Call this value fvmaa:. At the end of an iteration, if the cost of the solution found is less than the required solu- tion cost by comparing it to some lower bound, then the algorithm stops. Otherwise, a new value of E is calculated. The algorithm is then repeated until a sat- isfactory solution is found. The most conservative way to update E is to set 5 = fvrna,. It can be easily shown that if edge costs are integers bounded by a constant, then iterative E- BnB that uses E = fv,,, in the next iteration expands asymptotically the same number of nodes as &-BnB that uses the exact value of E for finding a solution of required quality. In general, however, a small reduc- tion in the value of E may only cause a few new nodes to be explored in the subsequent iteration, which in turn may lead to a large number of iterations, and consequently a large node-regeneration overhead. Al- ternatively, we may decrease the value of E by a larger amount, such as E = fvmac/2. Experimental Study In this section, we identify the conditions under which &-transformation and iterative &-transformation are ef- fective. To this end, we compare &-DFBnB and itera- tive E-DFBnB with other approximation algorithms. Iterative E-DFBnB can be used in the same way as truncated DFBnB (Ibaraki et al. 1983; Zhang 1993) to find approximate and optimal solutions. Truncated DFBnB is a DFBnB that terminates prematurely when the total available computation has been exhausted. Neural Networks 897 ncated DFBnB &-DFBnB with actual value pruning lo2 node expansions (a) b=2, d= 10 90 -$ 80 ‘5 io 9 60 edge costs from (0,1,2, . . . . 2’6-1) truncated DFBnB E-DFBnB with 102 103 104 105 node expansions (b) b= 10, d=20 Figure 4: Iterative E-DFBnB vs. truncated DFBnB. The best solution found up to that point can then be taken as an approximation. The main difference be- tween these two algorithms is that the territory ex- plored by iterative E-DFBnB is generally smaller than the territory explored by truncated DFBnB, although iterative e-DFBnB may re-expand a node many times. Local search (Johnson 1990; Kanellakis & Papadim- itriou 1980; Lin & Kernighan 1973) is a well-known approximation method for many difficult combinato- rial problems. Starting at an initial solution, such as one generated by a polynomial-time approximation al- gorithm, local search continuously improves the cur- rent solution by local perturbations, until no further improvement can be made. This process may be in- voked many times with different initial solutions. A serious drawback of local search is that it cannot de- termine if the best solution found so far is optimal, unless the optimal solution cost is already known. Random Trees We ran both iterative E-DFBnB and truncated DFBnB on the same set of random trees, and recorded the total number of node expansions when either algorithm up- dated its current best solution. We then measure their performance as the average solution cost for a given number of node expansions, since expanding a node is the primary operation. In our experiments, the value of E was updated to fvmac/2 after each iteration. Figure 4 shows our results on uniform random trees T(b = 2,d = 10) and T(b = 10, d = 20). The edge costs are uniformly chosen from (0, 1,2,. . +, 216 - 1). The results are averaged over 1000 trials. The hor- izontal axes, on a logarithmic scale, are the average number of node expansions, and the vertical axes are the average relative goal cost error. Figure 4 indicates that iterative &-DFBnB without actual-value pruning is slightly better than with actual-value pruning. Com- pared to truncated DFBnB, iterative E-DFBnB finds a better solution with the same average number of node expansions. For instance, at 1000 node expansions in Figure 4(b), the relative error for iterative E-DFBnB is 10.4010, while the relative error for truncated DFBnB is 40.4%. The results also show that when the branch- ing factor and tree depth are increased (from Figure 4(a) to 4(b)), t t i era ive &-DFBnB further outperforms truncated DFBnB. The relative advantage of iterative E-transformation also depends on the edge-cost distribution. Specifi- cally, the relative improvement in average solution cost of &-DFBnB over truncated DFBnB decreases when the probability of a zero-cost edge is increased. Asymmetric Traveling Salesman ProbIem The asymmetric traveling salesman problem (ATSP) is an NP-hard combinatorial problem (Garey & John- son 1979). Given n cities and an asymmetric matrix (c;,j) that defines a cost between each pair of cities, the ATSP is to find a minimum-cost tour that visits each city exactly once and returns to the starting city. The ATSP can be optimally solved by BnB, using the solu- tion cost of the related assignment problem (AP) (Pa- padimitriou & Steiglitz 1982) as a monotonic heuristic function. The state space of the ATSP under BnB is a tree without duplicate nodes. See (Balas & Toth 1985) for a description of the method. In our implementation of E-DFBnB and iterative EDFBnB, we used the sampling method described above to learn the value of E* for the first iteration. In each subsequent iteration, the value of E was set to fvmaz/2. F rom our experiments, &-DFBnB without actual-value pruning performs worse than &-DFBnB with actual-value pruning, and thus we present the re- sults of &-DFBnB with actual-value pruning. We used many different cost matrices in our exper- iments. Our data shows that iterative E-DFBnB finds better solutions sooner than truncated DFBnB on av- erage, and local search performs much worse than E- DFBnB and truncated DFBnB. Figure 5(a) compares &-DFBnB with truncated DFBnB on 500-city random ATSP’s, where costs ci,j are uniformly chosen from (0, 1,2, * * *, 216 - 1). The results are averaged over 100 trials. The horizontal axis is the CPU time on a 898 Neural Networks ; 0.190- ‘2 0.185- x 0.180- g 0.175- ; 0.170- 0.165t 500&y ATSP c(Q) uniformly chosen from I I I I 0 200 400 600 time (sec.) z 6.0 8 2 5.0 random matrix c(Q) = {0,1,2, . . . ,2*6-l} I g 1.0 & 0.0 200 400 600 800 1000 number of cities (a) iterative E -DFBnB vs. truncated DFBnB (b) &*-DFBnB vs. local search Figure 5: Iterative &-DFBnB vs. truncated DFBnB and local search on the asymmetric TSP. Sun4/sparc460 workstation, and the vertical axis is the average relative solution cost error with respect to the AP lower bound. We also compared &*-DFBnB with a local search method (Papadimitriou & Kanellakis 1980) which was applied five times for each problem instance in our ex- periments. The five different initial tours were gen- erated by the nearest-neighbor, nearest insertion, far- thest insertion, greedy algorithms, and the patching algorithm (Johnson 1990; Karp 1979). We used ran- dom cost matrices and matrices converted from no- wait flowshop scheduling for four machines, which is NP-hard (Kanellakis & Papadimitriou 1980). No-wait flowshop scheduling involves determining a sequence for processing a set of jobs where each job must be handled by a set of machines in the same preset order. The objective is a sequence that minimizes a cost func- tion, such as total completion time, which was used in our experiments. The no-wait constraint additionally requires the next machine to be available when a job is ready for it. The scheduling problem instances were generated by uniformly choosing the processing time of a job on a machine from (0, 1,2,. . ., 216 - 1). We then converted them into ATSP’s using the method in (Reddi & Ramamoorthy 1972). Local search runs much longer than e*-DFBnB on average for the problem instances we considered, be- cause we used five initial tours for local search. Figure 5(b) shows the solution quality, expressed as the av- erage tour cost error relative to the AP lower bound, versus the number of cities. Each data point is aver- aged over 100 trials. The results show that &*-DFBnB outperforms local search: it finds better solutions than local search on average even though local search was allowed to use more computation. Related Work Phase transitions of heuristic search were originally re- vealed by Karp and Pearl (Karp & Pearl 1983). Their results have been extended by McDiarmid and Provan (McDiarmid 1990; McDiarmid & Provan 1991), and Zhang and Korf (Zhang & Korf 1993; 1994) to random trees with arbitrary branching factors and real-valued edge costs. Huberman and Hogg (Huberman & Hogg 1987) argued that phase transitions are universal in large intelligent systems. Cheeseman et al. (Cheese- man, Kanefsky, & Taylor 1991) empirically showed that phase transitions exist in many NP-hard combi- natorial optimization problems. In their seminal paper, Karp and Pearl (Karp & Pearl 1983) also proposed an algorithm that finds a suboptimal goal node of a tree most of the time, but may fail sometimes, and runs in expected time linear in the tree depth. McDiarmid and Provan (McDiarmid 1990; McDiarmid & Provan 1991) extended Karp and Pearl’s approximation algorithm to a general random tree. One problem with Karp and Pearl’s algorithm is that it is incomplete, meaning that it is not guaran- teed to find a goal node. Furthermore, the algorithm uses parameters that depend on the optimal goal cost, which is generally unknown, and hence their algorithm is difficult to apply in practice. It is well known in the operations research commu- nity that approximate solutions can be obtained by prematurely terminating DFBnB, taking the best so- lution found so far as an approximation. This method is also referred to as truncated DFBnB (Zhang 1993), which we adopted in this paper. The earliest study of this method that we found was made by Ashour (Ashour 1970). Ibaraki et al. (Ibaraki et al. 1983) sys- tematically studied approximation methods based on BnB, which they called suboptimal BnB algorithms. Conclusions We have presented a new method, called E-transfor- mation, that can be used by branch-and-bound (BnB) to find approximate solutions to combinatorial prob- lems. This method is a state-space transformation, which exploits the computational phase transitions of tree search problems. On a random tree, E-BnB runs Neural Networks 899 in expected time that is cubic in the search depth, and finds a suboptimal goal node whose expected relative solution cost error is bounded by a small constant. We also developed an iterative version of s-transformation to find both approximate and optimal solutions. On random trees with large numbers of distinct edge costs, large branching factors, and deep goal nodes, it- erative e-DFBnB outperforms truncated DFBnB, find- ing better solutions sooner on average. On the asym- metric traveling salesman problem, &-DFBnB outper- forms a local search method, and iterative E-DFBnB is superior to truncated DFBnB. Overall, we recommend that &-transformation be used for problems whose search trees have a small prob- ability of a zero-cost edge and large branching factors. To our knowledge, E-transformation is the first at- tempt to exploit phase transitions in order to solve combinatorial problems. Since phase transitions exist in many intelligent systems and combinatorial prob- lems, we hope that the idea of E-transformation can be carried over to other problems and search methods. Acknowledgment The authors are grateful to Colin McDiarmid and Judea Pearl for helpful discussions, and to the anony- mous reviewers for comments. Special thanks Korf for support, discussions and comments. to Rich References Ashour, S. 1970. An experimental investigation and comparative evaluation of flow-shop scheduling tech- niques. Operations Research 18:541-545. Balas, E., and Toth, P. 1985. Branch and bound methods. In Traveling Salesman Problem. Essex: John Wiley and Sons, Essex. 361-401. Cheeseman, P.; Kanefsky, B.; and Taylor, W. M. 1991. Where the really hard problems are. In Proc. 12th IJCAI 331-337 . Garey, M. k., and Johnson, D. S. 1979. Computers and Intractability. New York, NY: Freeman. Huberman, B. A., and Hogg, T. 1987. Phase tran- sitions in artificial intelligence systems. Artificial In- telligence 33:155-171. Ibaraki, T.; Muro, S.; Murakami, T.; and Hasegawa, T. 1983. Using branch-and-bound algorithms to ob- tain suboptimal solutions. Zeitchrift fir Operations Research 27~177-202. Johnson, D. S. 1990. Local optimization and the trav- eling salesman problem. In Proc. 17th Intern. Collo- quium on Automata, Languages and Programming. Kanellakis, P. C., and Papadimitriou, C. H. 1980. Local search for the asymmetric traveling salesman problem. Operations Research 28:1086-1099. Karp, R. M., and Pearl, J. 1983. Searching for an optimal path in a tree with random costs. Artificial Intelligence 21:99-117. Karp, R. M. 1979. A patching algorithm for the nonsymmetric traveling-salesman problem. SIAM J. Comput. 81561-573. Korf, R. E. 1989. Search: A survey of recent re- sults. In Exploring Artificial Intelligence. Morgan Kaufmann. 197-237. Kumar, V. 1992. Search branch-and-bound. In Ency- clopedia of Artificial Intelligence. New York: Wiley- Interscience, 2nd edition. 1468-1472. Lin, S., and Kernighan, B. W. 1973. An effective heuristic algorithm for the traveling salesman prob- lem. Operations Research 21:498-516. McDiarmid, C. J. H., and Provan, G. M. A. 1991. An expected-cost analysis of backtracking and non- backtracking algorithms. In Proc. 12th IJCAI, 172- 177. McDiarmid, C. J. H. 1990. Probabilistic analysis of tree search. In Disorder in Physical Systems. Oxford Science. 249-260. Mitchell, D.; Selman, B.; and Levesque, H. 1992. Hard and easy distributions of SAT problems. In Proc . 10th AAAI 459-465 . Papadimitriou, Cl H., and Kanellakis, P. 1980. Flow- shop scheduling with limited temporary storage. J. of ACM 27:533-549. Papadimitriou, C. H., and Steiglitz, K. 1982. Com- binatorial Optimization: Algorithms and Complexity. Englewood Cliffs, NJ: Prentice-Hall. Pearl, J. 1984. Heuristics. Reading, MA: Addison- Wesley. Reddi, S., and Ramamoorthy, C. 1972. On the flow- shop sequencing problem with no wait in process. Op- erational Research Quarterly 23:323-331. Renyi, A. 1970. Probability Theory. Amsterdam: North-Holland. Zhang, W., and Korf, R. E. 1992. An average- case analysis of branch-and-bound with applications: Summary of results. In Proc. 10th AAAI, 545-550. Zhang, W., and Korf, R. E. 1993. Depth-first vs. best-first search: New results. In Proc. llth AAAI, 769-775. Zhang, W., and Korf, R. E. 1994. Performance of linear-space search algorithms. Artijkiul Intelligence to appear. Zhang, W., and Pemberton, J. C. 1994. Epsilon- transformation: Exploiting phase transitions to solve combinatorial optimization problems. Technical Re- port UCLA-CSD-940003, Computer Science Depart- ment, University of California, Los Angeles, CA. Zhang, W. 1993. Truncated branch-and-bound: A case study on the asymmetric TSP. In Working Notes of AAAI-93 Spring Symp.: AI and NP-Hard Prob- lems, 160-166. 900 Neural Networks | 1994 | 33 |
1,659 | Unclear Distinctions lead to Unnecessary Shortcomings: Examining the rule vs fact, role vs filler, and type vs predicate distinctions from a connect ionist representation and reasoning perspective Venkat Ajjanagadde Wilhelm-Schickard Institute, Universitaet Tuebingen Sand 13, D-72076 Tuebingen, Germany venkat@occam.informatik.uni-tuebingen.de Abstract This paper deals with three distinctions pertai- ning to knowledge representation, namely, the rules vs facts distinction, roles vs fillers distinc- tion, and predicates vs types distinction. Though these distinctions may indeed have some intuitive appeal, the exact natures of these distinctions are not entirely clear. This paper discusses some of the problems that arise when one accords these distinctions a prominent status in a connectionist system by choosing the representational structu- res so as to reflect these distinctions. The exam- ple we will look at in this paper is the connec- tionist reasoning system developed by Ajjana- gadde & Shastri(Ajjanagadde & Shastri 1991; Shastri & Ajjanagadde 1993). Their1 system per- forms an interesting class of inferences using acti- vation synchrony to represent dynamic bindings. The rule/fact, role/filler, type/predicate distinc- tions figure predominantly in the way knowledge is encoded in their system. We will discuss some significant shortcomings this leads to. Then, we will propose a much more uniform scheme for representing knowledge. The resulting system enjoys some significant advantages over Ajjana- gadde & Shastri’s system, while retaining the idea of using synchrony to represent bindings. Introduction Given a particular piece of knowledge, can one unambi- guously decide whether it is a rule or a fact? Are there entities which always act as roles and never as fillers? Are there entities which always act a.s f2Zers and ne- ver as roles? What is a type and what is a general predicate? In spite of the fact that the rule/fact, role/filler, type/predicate distinctions get mentioned not too in- frequently in general AI parlance, a.n attempt to clearly state the distinctions faces difficulties (Some of the dif- ficulties will be listed in the following section). This paper illustrates that taking these rather unc1ea.r di- stinctions and according them prominent representa- ‘This paper was written in third person for double-blind reviewing. tional status in a connectionist network may not be a desirable thing to do. Specifically, the example we con- sider here is the connectionist reasoning system(Ajja- nagadde & Shastri 1991; Shastri 8~ Ajjanagadde 1993) developed by Ajjanagadde & Shastri (Henceforth A & S). Their system performs an interesting class of infe- rences extremely fast. A major idea underlying their approach is the use of activation synchrony to represent dynamic bindings. We consider the idea of using syn- chrony to represent bindings to be indeed efficient, ele- gant, and as discussed in (Ajjanagadde & Shastri 1991; Shastri & Ajjana.gadde 1993), neurologica.lly pla.usible. However, the system of A & S has some shortcomings. These shortcomings are due to the representational methodologies A & S have chosen and are not due to the use of synchrony i&elf. The major reason for t,he shortcomings of their representationa. schemes can be diagnosed to be the prominence A Ri S have accorded to the distinctions of rules & facts, roles & fillers, ty- pes Pt predicates. The representational structures in their system directly reflect these distinctions. For ex- ample, Fig. 1 shows how A SC S encode the following knowledge base: give(x,y,z) + own(y,z) ; buy(x,y) 3 ow~z(x,y); own(x? y) + can-selZ(x. y) ; give(‘ohn, mary, bookl); bu y(mike, house3) Fig. 1 An example network of A & S. Fig.2 illustrates how A & S encode the following knowledge by interfacing the rule-based reasoner with a type hierarchy: prey-on(x, y) + scared-of(y,x) ; prey-on(cat, bird); isa(catl,cat); isa(cat2, cat); isa(bird1, bird): isa(bird2, bird); isa(cat, animal); isa(bird, animal). 846 Neural Networks From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Rule-based Reasoner Type H&m&y scared-of Fig. 2 Encoding the type hierarchy in A & S’ system. Now, note how the representational structures in A & S’s system directly reflect the rule/fact, role/filler, and type/predicate distinctions. For example, note that “facts” a.re encoded in a way very different from the rules (e.g., look at the encoding of the fact give(john, mary, bookl) (shown enclosed by the box Fl in Fig. 1) with the encoding of t,he rule gizre(x, y,x) 3 own(y,z)). Similarly, A & S treat role nodes (e.g., in Fig. 1, giver, recipient, give-obj, owner, own-obj ,...) in a fashion different from filler nodes (e.g., in Fig. 1, john, mary, bookl, house3,. . .). The type/predicate di- stinction manifests in A & S’s syst,em as two different modules (shown separated by a curved line in Fig. 2). Having recalled that the representational structu- res in A & S’s system directly mirror the rule/fact, role/filler and type/predicate distinctions, let us dis- cuss the appropriateness of according these distinctions such a. prominent status. A Closer Look at the Distinctions Rules and Facts What is a rule and what is a fact? Given a piece of in- formation, can we clearly decide whether it is a. fact, or a rule? An intuitive response might be t’o say that rules correspond to general knowledge and facts correspond to specific knowledge ((Shastri & Ajjana.gadde 1993), p. 418). Now, let us try to make that intuition a little more precise. A measure of t,he generality/specificity might be the number of individuals to which a piece of knowledge pertains to. So, if a piece of knowledge applies to a large number of individua.ls we may call it a rule and if <he knowledge is about indi viduals, we may call it a fact. only particular Now, let us imagine ourselves as having been gi- ven the task of representing a knowledge base as a connectionist network. For each piece of knowledge in the knowledge base, we have to decide whether it is a fact or a rule and choose the corresponding enco- ding scheme in A & S’s system. Where do we draw the boundary between rules and facts? How general (specific) a piece of informa.tion has to be in order to be classified as a rule (fact)? We think that there is no such clear boundary and various pieces of know- ledge fall in a continuous spectrum of generality rather than in two distinct bins. On the one ha.nd, note that there are very few statements that apply to all indi- Reasoning Power: Note that in the network of vidua.ls. So, for example, though A & S would consi- Fig. 1, there is an asymmetry in the flow of bindings der the information that “When someone hits another, between rules and facts. Binding information can Aow the ‘hittee’ gets hurt” to be a rule(Ajjanagadde & Sha- from the rules into facts, but not vice versa. Specifi- stri 1989), this statement does not really apply to all cally, note that there are no distinct connections from objects. For example, the ‘hittee’ has to be a senti- ent being to get hurt. On the other hand, though the knowledge “John loves Mary” may appear qualified to be called a fact (because it is about two particular hu- man beings), that knowledge does hold about many particular instances of John and Mary: “John while wearing red shirt”, “John while sitting in the pub”, “John while having dinner” etc. still loves “Mary in blue skirt”, “Mary while sitting in the pub”. Hence what we refer to as “John” and “Mary” in the know- ledge “John loves Mary” correspond to sets of speci- fic instances of John and Mary. Thus classifying an available piece of information as a rule or as a fact is not a clear-cut task. The unclear distinction bet- ween rules and facts gets blurred further in A k: S’s system with the interfacing of a type hierarchy with the rule-based reasoner(Shastri & Ajjanagadde 1993; Mani SC Shastri 1991). They represent the knowledge “Cats prey on birds” as the fact prey-on(cats, birds,), which is a piece of knowledge about, whole classes of cats and birds. In summary, a representational scheme that forces us to divide the rather continuous spectrum of generality into two discrete bins does not seem appropriate. Our proposal is to represent all the knowledge in the form of rules of the kind: Pl(...) A lq...)... A P,J...) * &(...) Now, representing more (less) specific knowledge is just, a matter of having more (less) conjun& on t,he ante- cedent of t#he rule. With this choice of representation the knowledge that “John loves Mary” will be represented as the rule: john(x) A mary(y) a Zove(x,y). In addition to the problem of conceptual clarity, the rule/fact distinction made in A & S’s system leads t#o two other main short’comings. The first one pertains to the ease of learning and the second pertains to rea- soning power. Learning: Learning involves generalizing from our specific experiences. One has to be a.ble to learn “ru- les” from “facts” . When significantly different kinds of network representations are used t.o represent spe- cific experiences and more general knowledge, learning gets harder. Starting from one kind of representation and arriving at a significantly different kind of repre- sentation is a difficult thing to achieve with only lo- cal readjustments that are normally made use of in connectionist learning. When we use a uniform re- presentation, generalizing (specializing) corresponds to dropping (adding) some conjuncts in the rule a.nd can be achieved by simply weakening (strengthening) the relevant links. Neural Netwoi-ks 847 the filler nodes involved in a fact to the correspon- ding role nodes. For example, consider the encoding of the fact give(john, mary, booki). There are no (distinct) connections from the filler nodes john, mary, book1 to the role nodes giver, recipient, give-obj. That means that facts cannot induce bindings in the argument no- des. Note that, in general, when we are unifying two expressions, we would want bindings to flow in a bi- directional fashion. So, for example, when unifying W,x) and P(y,b), we want x to be bound to b and y to be bound to a. But, this does not happen in A & S’s system. A specific example where such bidirectio- nal transfers of bindings are necessary corresponds to “answer extraction”. Suppose we ask the query ?!kr can-seZZ(mary,x) with respect to the network of Fig. 1. We would expect a: to get bound to book1 (That way, we know not only that “Mary can sell something” but also what can Mary sell.), This binding has to come from the fact give(john,mary, bookl). But, since in the network of Fig. 1, facts cannot induce bindings, one can only prove that 3x can-seZZ(m,ary,x) is true, but, cannot get the answer can-seZZ(m.ary,booki). This is the reason why A & S add extra circuitry (not shown in Fig. 1) and a two sta.ge process to get, back such ans- wers (see section 4.7 in (Shastri & Ajjanagadde 1993)). When we adopt a uniform scheme for representing ru- les and facts, the asymmetry between rules & fa.cts goes away, and bidirectional transfer of bindings is na- turally obtained. “Answer extraction” happens to be a special case benefit (without having to use additional circuitry for that purpose) of such bidirectional trans- fer of bindings. Rule-based reasoner and type hierarchy Let us consider representing the information “Cats prey on birds”. One can represent this knowledge as the rule “VxVy cat(x) A bird(y) + prey-on(x,y). But, A & S choose not to do this ((Shastri St Ajjanagadde 1993), p. 435). Instead, they introduce filler nodes cor- responding to “cats” and “birds”. These nodes behave similar to the nodes corresponding to individuals such as john, mary etc. Hence, simi1a.r t(o the way one re- presents facts about individuals (e.g, love(john, mary)), one can represent the knowledge “Cats prey on birds” as the fact prey-on(cat,bird) (Fig. 2). Why do A & S go for the extra trouble of interfacing the rule-based reasoner with a type hierarchy, when they could repre- sent the same information as just another rule? The reason they give is “. . . The rule-based reasoner . . . can- not answer queries such as prey-on( cat ,bird)” (( Shastri & Ajjanagadde 1993), p. 435). That is, one could not ask their rule-based reasoner queries a.bout classes of individuals. But, as we will discuss in the next sec- tion, with the representation and reasoning scheme we are proposing, the rule-based reasoner itself can answer queries such as “Do cats prey on birds?“, “Are birds scared of cats?“. In fact, queries of this kind ha.ppen to be just special cases of the queries tha,t can be handled by the system we are proposing. Having said that one does not need to go for a type- hierarchy interface to be able to ask the kind of queries A & S mention, we would like to go one step further and note that the idea of type-hierarchy interface is not, just redundant, but, a handicap too. There are four re- asons why this is so. Firstly, as mentioned a.bove, with the scheme we are proposing one can have more gene- ral queries than the ones A Sr. S consider. With A Sr. S’s approach, these general queries cannot be handled. Secondly, with the idea of type hierarchy interface, only isa knowledge can be used to make inferences about types. But, we do need an ability to infer ty- pes based on relational knowledge. For example, when we see particular spatial relationships between three blocks, we would like to be able to infer that the the a.r- rangement formed by the three blocks is of type ‘arch’. Due to the way relations (predicates) and types are separated into two different modules in A & S’s sy- stem, the knowledge of relations is not used to make inferences about types. Thirdly, there are conceptual problems with the idea of type-hierarchy interface. What is the distinction between types and predicates? If they are not comple- tely distinct and there is a semantic overlap, how do we represent that overlap? Fourthly, the comment made in the previous subsec- tion about the advantage of having uniform represen- tations from the point of view of learning, a,pply here as well. Roles and Fillers The role vs filler distinction in A & S’s system cor- responds to the term vs predicate distinction in first- order logic. First-order logic represents the world as a set of objects a.nd allows one to make assertions about, those objects. The terms of first-order logic correspond to the objects and predicates are used to make asser- tions about those objects. In A & S’s rule-based re- asoner (without the type hierarchy interface), “filler nodes” correspond to objects in the world a.nd “role nodes” are used to make assertions about those ob- jects. Thus, the roles vs fillers distinction in A SL S’s system is indeed c1ea.r and well motivated to the extent, the predicate vs term distinction in first-order logic is. Having sa.id that the distinction between role nodes and filler nodes is indeed clear in that way , we would like to make two observations. Firstly, it is relevant to note that sometimes, one wants to make assertions about not just objects in the world but also about concepts. It is not so straight, forward in first-order logic to do the latter. Two of the classic exa.mples illustrating this problem are the “te- lephone number problem” and the “morning star pro- blem”(McCarthy 1979). Following A & S’s approach, in order to represent assertions such as “John knows Mike’s telephone number”, one will have to have a. fil- ler node for the intent’ion of “Mike’s telephone nuni- 848 Neural Networks be?. When one does that (i.e., relaxes the condition that filler nodes correspond to objects in the world), the distinction between role nodes and filler nodes gets blurred2. Our second observation concerns plausibility under resource constraints. As mentioned above, in A & S’s system, filler nodes denote individuals in the world. But, it is obvious that there cannot be a distinct node corresponding to every object we ever reason about. The number of such individual objects is extremely large (virtually infinite). It is infeasible to say that there is a distinct node in the network corresponding to every such individual. A & S indeed take this fact into consideration. Avoiding the need to allocate a unique node corresponding to every object is precisely the reason they use activation synchrony to represent dynamic bindings. In A & S’s system, a phase corre- sponds to an object participating in a particular rea- soning episode. All the nodes active in that phase to- gether represent that individual. Synchrony is a means of representing the grouping of the nodes representing the features of an object. Thus, the idea of represen- ting an object by a group of nodes instead of a single node is indeed present in A & S’s system though they do not exactly describe it in this way. However, while A & S do not assume the existence of a distinct node corresponding to every object, they do assume the exi- stence of a distinct node corresponding to every object that is involved in a long-term fact. Thus, in Fig.1, for representing the long-term facts give(john, mary, bookl) and buy(mike,house3), A & S assume the existence of distinct nodes corresponding to the objects in these facts, namely, john, mary, bookl, mike, house3. A logical extension would be to abandon altogether the idea of having distinct nodes corresponding to indivi- dual objects (i.e., irrespective of whether or not there is a long-term fact about that individual). With this suggestion, the very notion of filler nodes (i.e., nodes corresponding individual objects) looses its utility. An Alternative Scheme of Representation In the scheme we are proposing, there are no assorted types of nodes such as role nodes, filler nodes, collec- tors, enablers etc. that A & S make use of. Instead, the nodes in the network are all feature nodes. Each node corresponds to a basis feature. An object is repre- sented by a group of basis features. “Basis features” are unary features and are akin to what are usually referred to in connectionist literature as microfeatures. We are using a different terminology just because we suspect that some of what we mean by a “basis fea- ture” may be in disagreement with what some people 2For a discus sion of some related issues, see (Wilensky 1986), where Wilensky examines some of the distinctions often made in frame-based systems and then, argues for a more uniform representational scheme. may mean by a “microfeature”. For example, it is not necessary that there should not be a sub&mption relation between one basis feature and another.- For instance, human and animal could both be basis fea- tures. Even though it might be possible to represent some feature (say, human), by a combination of the already existing basis feat&es (say, animal, biped,...), an agent may &ill have a node ‘corresponding to that, feature. The nodes in A & S’s network happen to be a rather extreme special case wherein john, mary, etc. themselves happened to be basis features. It is perhaps worth mentioning that this paper is not concerned with what the basis features are; in- stead, the focus is on how to represent knowledge as an interconnection of the nodes corresponding to ba- sis features and how does reasoning take place in that network. Generally, in our examples, we will be ta- king the nodes in A & S’s networks themselves to be basis features. This will help one to contrast and see how our representational scheme differs from that of A & S even if we hadn’t brought in the idea of not’ having to have distinct nodes corresponding to indivi- book1 dual objects own-object, basis features. Thus, in Fig.3, giver, recipient, owner, etc. themselves have been chosen as cs-agt Fig. 3 Network as per the proposed scheme tl1a.t corresponds to A & S’ network of Fig. 1. Having said what individual nodes in the network represent (i.e, ba.sis features), let us now discuss the encoding of rules. Corresponding to every rule, there are a group of links, which we will refer to as a link bundle. In the figures, we denote link bundles by dra- wing a thin bar over the links forming the bundle. For example, the links between the nodes buyer, buy-obj and the nodes owner, own-obj form a link bundle re- presenting the rule buy(x, y) 3 own(x, y,J. The actual interconnection details corresponding to this rule are shown in Fig. 4(a). To avoid clutter, we will normally depict link bundles as shown in Fig. 4(b). Cd 6) Fig. 4 Encoding buy(x, y) =+ own(x, y) In fact, that is all we need to say to describe t,he details of encoding in our network. Unlike in the sy- stem of A & S, we do not need to separately explain how rules are encoded, how facts are encoded, how the type hierarchy is encoded etc. All that is there Neural Networks in our network is just these: There are nodes corre- sponding to basis features and then there are rules (which are represented by link bundles). Fa& and type hierarchy knowledge are not encoded in a dif- ferent way; they get encoded as rules. For example the network of Fig. 3 includes the encoding of the fact give(john, mcary, bookl). This fact is encoded as the rule: john(x) A mary(y) A bookl(.) 3 give(x, y,z) This encoding assumes that john, mary, and book1 are ba- sis features. But, that need not be the case; these indi- viduals can be represented in terms of some other basis features. Suppose, for example, that they are described using the following features: john: black-hair, round- face ; r-nary: blond,long-face; book 1: book, thick, red. With that representation of objects, the encoding of the fact give(john, mary, bookl) is shown in Fig. 5. Fig. 5 Encoding give(john, mary, bookl). The information represented in A & S’s network of Fig. 2 is represented in our network as shown in Fia. 6. This network encodes the following rules: prey-onrx, y) a scared-of(y,x) ; cat(x) A bird(y) 3 prey-on(x, y); c&l(x) 3 cat(x); c&‘(x) + cat(x); birdl(x) 3 bird(x); bird,Z?(x) 3 bird(x); cat(x) + animal(x): bird(x) + cmi- mal(x) Fig. 6 Network as per the proposed scheme corresponding to the network of Fig. 2 Reasoning Having discussed the encodings in the network, let us look at how reasoning takes place. The general form of querying in our system is the fol- lowing: One asks the network “If I now assert that PI, p2 ,“‘, Pr, are true about a set of objects, then can you prove Q using Pis and the knowledge already encoded in the network?“. We will refer to P;s as (dynamic) assertions and Q to be the target proposition. Note that one has to somehow distinguish Pis from Q. This is because Pis are being asserted to be true while Qs truth value is what we want to find out. We represent this distinction by using high a*ctiva.tion level for repre- senting Pis and a low activa.tion level for Q. If Q can indeed be proved to be true, then, its representation attains high activation level in time dependent on the length of the proof. Now, let us consider a simple single step inference. Suppose we want to query the network of Fig. 3 to find out whether “buy(mike,house3)” is true. We pose this query as follows: Suppose we assert thcrt mike(objl) and house3(objz) are true, can you prove that buy(objl, obj2) is true. @ That is, the assertions in this case are: mike(objl) and house3(obj2). The target proposition is ?bzry(objl, objz). To pose this query, we clamp the activity patterns representing t,he assertions at, a high level of activitCy and clamp the activity pattern corresponding to the target proposition at a low level of activity. Suppose we associate the first and second phases with objl and obj, respectively. In that case, cla.mping the assertions and target propositions involves doing the following: We make the nodes corresponding to mike and house3 to become active in t#he first and se- cond phases of every cycle (respectively) at a high level of activity. We make the nodes corresponding to buyer and buy-obj to become active in the first and second phase of every cycle respectively, but a.t a low level of activity. If the target proposition (i.e., buy(objl, objz)) can indeed be proved to be true (which is the case in our example) we would expect the activity levels of buyer and buy-obj t#o become active aft,er a while. Let us examine how this indeed happens. Since the node mike is firing a.t a high level of act,iva- tion (in pha.se l), unless the flow of act,ivit,y along the link A (Fig. 7 ) from mike to buyer is inhibited, mike will raise t(he activity level of buyer. But, there indeed are two inhibit*ory connections ontCo this link: link C’ from buyer and link D from buy-obj. In phase 1, the node buyer is active hence could potentially inhibit the flow along link A. But, note t’hat’ in phase 1, ~nike is active as well a.nd hence the activation flow along link E inhibits the flow along link C. As a net result, there will be no inhibition on link A in phase 1. Reasoning along similar lines, one can find that though buy-obj becomes active in second pha.se, it, does not succeed in inhibiting link A. That means tl1a.t there will not, be inhibition on link A during any phase of the cycle 4. Hence, the flow of activity from mike along link A takes place thereby raising the act)ivity level of buyer. Analogously, one can see that the flow of activity from house3 raises the activation level of bvy-ol)j. As a result, the target proposition buy(objl, objz) indeed getas proved to be true. 3We use obj $s to denot.e arbitrary objects. The situation is similar to starting a mathematical proof by a st,at.ement such as “Let x be an arbitrary integer”. To make it sound even more analogous to our situation, consider a paraphrase of that st,at,ement, namely, “Let x be an arbitrary number having the feature of being an integer”. Quite analogousl.v, the assertion mile(objl) for example corresponds to asser- ting “Let objl be an arbitrary object halving the feature of being mike”. 41t is important to not,e that, we assume t,hat for activit,y flow to take place along a link, there should not be inhihi- tion on that link during any phase of a cycle; we assume that an inhibitory effect lasts for the duration of a cycle. 850 Neural Networks Fig. 7 Encoding of mike(x) A house3(y) a buy(x, y). The essential thing to note about the inhibitory connections in a link bundle (see e.g., Fig. 7) is that they are designed to check the binding consistency bet- ween the antecedent and the consequent of the rule. When there is a binding mismatch, all the links from the feature nodes corresponding to the antecedent of the rule to the fea.ture nodes corresponding to the con- sequent of the rule get inhibited. - - Having seen how a single-step inference involving a rule takes place, it is easy to see how multi-step in- ferences take place in the network. Regrettably, due to space limitation, it is not possible to take the rea- der through some more examples. But, t*he informa- tion provided so far should be sufficient for a reader to check how the system works for other examples. One particular point that is to be remembered however is that we are assuming here that only one instance of a feature needs to be represented during a reasoning episode. The issue of representing multiple dynamic instances(Shastri & Ajja.na.ga.dde 1993) is quite ortho- gonal to the subject ma.tter of this paper. Two par- ticularly interesting examples to consider pertain to the bidirectional transfer of bindings and dealing with queries such as “Are birds scared of cats?“. Consider asking the query 2% bu y(?,, ike, xl. This corresponds to the case when the assertion is mike(objl) and the target proposition is 3xbuy(objl,x)5. It may be noted that if the object house3 happens to be in focus, i.e., if the node house3 happens to be active, say, in some phase i, then, the node buy-obj will also start firing in phase i representing the desired answer that the thing Mike bought is “house3”. Now consider the query “Are birds scared of cats’?“. In this case, the assertions correspond to cat(objl) and bird(obj2). The ta.rget proposition is Zscnred- of(obj2, objlj.’ One may w&k through the network of Fig. 6 to see that, this indeed produ ces the desired - answe#. This illustrates wer queries about classes that our scheme can ans- of objects without needing a typk hierarchy interface. The reason for saying thai our scheme can deal with even more general queries than A & S’s system is the following: The queries 5As in A & S’s system we do not activate the nodes corresponding to the unbound arguments in the target proposition. 6Note that objl and obj:! are arbitrary objects and the only thing assumed to be known about them is that cat(obj~)) and bircI(objz). That is, objl and objs are arbi- trarily chosen members of the classes of cats and birds re- spectively. Hence, if we can prove that. scared-of(obja, objl), that means that birds in general are scared of cats. A & S are able to deal with the type hierarchy in- terface correspond to t,he case when assertions involve only unary predicates such as, for example, cat(objl) and bird(obj2). In addition to such assertions, in our system the assertions can also involve n-ary relations such as P(objl , objz). Conclusion As concluding remarks, let us summarize the intended contributions of this paper. Firstly, the paper provides a critique of some of the representational structures employed in the connectio- nist reasoning system of Ajjanagadde & Shastri. While this critique of the specific system by A 8i S should be of interest by itself, it is our belief that the issues rai- sed are of genera.l interest and merit consideration in connectionistO knowledge representlation effort,s in gene- ral. Secondly, the paper proposed an alternative scheme for representing knowledge and presented a. system that enjoys some significant advantages relative to the system of A & S in reasoning a.bility, concept8ual cla- rity, ease of learning, representational efficiency and neurological plausibilit)y. Acknowledgments. This work was supported 1)~ DFG grant Schr 275/7-l. I would like to thank 111~ colleague Seppo Keronen for numerous useful discussi- ons spread over many lunches and aft,ernoon t,eas. References Ajjanagadde, V. G., and Shastri, L. 1989. Efficient inference with multi-place predica.tes and variables in a connectionist system. In Proceedings of the Confc- rence of the Cognitive Science Society, 396-403. Law- rence Erlbaum. Ajjana.gadde, V. G., and Shastri, L. 1991. Rules and variables in neural nets. Xeurul Computation 3:121- 134. Mani, D. R., and Shast’ri, L. 1991. Combining a connectionist type hierarchy with a connectionist rule-based reasoner. In Proceedings of the Conferenw of the Cognitive Science Society, 418-423. McCarthy, J. 1979. First-order theories of individual concepts and proposit8ions. In Hayes, J.; Michie, D.; and Mikulich, L., eds., Machine Zntelligence 9. Hal- stead Press : New York. 129-147. Shastri, L., a,nd Ajjanagadde, V. G. 1993. From sim- ple associations to systematic reasoning: A connectio- nist representation of rules, variables, and dynamic bindings using temporal synchrony. Behavioral and Brain Sciences 16:417-494. Wilensky, R. 1986. Knowledge representation - a critique and a proposal. In Kolodner, J . , and Ries- beck, C., eds., Experience, Memory, and Reasoning. Erlbaum: Hillsdale, NJ. Neural Networks 851 | 1994 | 34 |
1,660 | ing for and vision sensing David Kortenkamp*and Terry Weymouth Artificial Intelligence Laboratory The University of Michigan Ann Arbor, MI 48109 korten@aio.jsc.nasa.gov Abstract Topological maps represent the world as a network of nodes and arcs: the nodes are distinctive places in the environment and the arcs represent paths be- tween places. A significant issue in building topologi- cal maps is defining distinctive places. Most previous work in topological mapping has concentrated on us- ing sonar sensors to define distinctive places. However, sonar sensors are limited in range and angular resolu- tion, which can make it difficult to distinguish between different distinctive places. Our approach combines a sonar-based definition of distinctive places with vi- sual information. We use the robot’s sonar sensors to determine where to capture images and use cues ex- tracted from those images to help perform place recog- nition. Information from these two sensing modalities is combined using a simple Bayesian network. Results described in this paper show that our robot is able to perform place recognition without having to move through a sequence of places, as is the case with most currently implemented systems. For these reasons, topological maps have become in- creasingly popular in mobile robotics. Introduction Topological maps represent the world as a graph of places with the arcs of the graph representing move- ments between places. Brooks (Brooks 1985) argues persuasively for the use of topological maps as a means of dealing with uncertainty in mobile robot navigation. Indeed, the idea of a map that contains no metric or ge- ometric information, but only the notions of proximity and order, is enticing because such an approach elim- inates the inevitable problems of dealing with move- ment uncertainty in mobile robots. Movement errors do not accumulate globally in topological maps as they do in maps with a global coordinate system since the robot only navigates locally, between places. Topolog- ical maps are also much more compact in their repre- sentation of space, in that they represent only certain places and not the entire world, in contrast to robots which use detailed a priori models of the world, such as (Kosaka & Kak 1992) and (Fennema & Hanson 1990). *Now at The MITRE Corporation, Houston, TX 77058. A significant issue in building a topological map is defining distinctive places in the environment; these distinctive places correspond to the nodes of the result- ing topological map. Most researchers use sonar sen- sors to define distinctive places (Basye, Dean, & Vitter 1989; Kuipers & Byun 1991; Mataric 1992). However, sonar sensors are limited in range and angular resolu- tion and therefore can only give a rough approximation of the robot’s environment. Because of this, many “dis- tinctive” places in the environment actually look very similar to sonar sensors. For example, in a long hall- wa.y with left and right doorways to rooms, using only sonar sensors it would be impossible to distinguish any particular left or right door from any other left or right door along the hallway. Most systems overcome this limitation by determining the robot’s location based on a sequence of distinctive places instead of on a sin- gle distinctive place. Such approaches, while certainly effective, require the robot to make many navigational movements in order to determine its location in the environment. It is our hypothesis that by adding visual informa- tion to the robot’s sonar information, we can dramat- ically reduce the ambiguity of places that look iden- tical to the robot’s sonar sensors. In our approach, sonar sensors are used to determine generic places in the environment called gateways. Gateways mark the transition from one space to another space. Since a gateway marks the entrance to a new space, they offer the robot a perfect opportunity to look around and ac- quire visual cues that will distinguish among gateways. Thus, at each gateway one or more images (scenes) are captured. Visual cues are extracted from the image and stored with the gateway. On subsequent visits to the same gateway, the robot can use the visual cues, in conjunction with the sonar signature of the gateway, to determine its location. Sonar information This research was sponsored by Department of Energy Most topological maps are built around distinctive grant DE-FGO2-86NE37969 places. In our topological map, rather than looking Perception 979 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. for places that are locally distinguishable from other places and then storing the distinguishing features of the place in the route map, we instead look for places that mark the transition between one space in the en- vironment and another space. We call these places gateways. In indoor environments, gateways are places such as entrances to rooms and intersections of hallways. For a mobile robot in an indoor environment, gateways are important for several reasons. First, gateways tend to be places that are visited frequently. Second, gateways are places that open up new views for a robot, views from which it can extract visual cues to distinguish be- tween similar gateways. Third, a robot typically must go through a gateway in a small number of directions. For example a robot can only pass through a door- way in two directions. This constrains the range of views that a robot can have at a gateway and simpli- fies matching of visual cues. Finally, gateways are ex- its from a space and, for safety reasons, a robot should stay aware of exits. Detecting gateways We have defined gateways, for orthogonal indoor envi- ronments, as openings to the left or right of the robot’s direction of travel that are wide enough for the robot to pass through. These openings are detected using sonar sensors. Our gateway detection algorithm has the following components: 1. 2. 3. 4. 5. 6. The robot aligns itself along a wall (or along both walls of a corridor) using its sonar sensors. The robot moves along the wall and maintains its orientation and distance with respect to the wall (or walls in a corridor) using its sonar sensors. While moving, the robot continually checks its left and right sonar readings for openings; the robot also checks for obstacles in front of it. When an opening is found, the robot continues mov- ing and looks for a closing to that opening. While looking for a closing, the robot also checks the op- posite direction for any openings as well as checking the front for any obstacles. When a closing to the opening is found (a closing can be an end to the opening, a blockage in front, or a certain distance traveled), the robot determines if the opening is large enough to pass through and, if so, signals a gateway. The robot positions itself in the middle of the gate- way. Experiments with our Labmate TRC robot in the hallways of our laboratory show that this gateway de- tection algorithm has an error of no more than 3.5 de- grees in orientation along the axis of the hallway and 70mm in position along the axis of the hallway. These errors were determined by repeatedly having the robot a I T-shape Right Room Right Corner Exit Figure 1: A few examples of different types of gate- ways. stop at the same set of orientation and location. gateways and measuring its Classifying gateways Once a gateway has been detected it can be classified as a certain type using local sensory information. For example, a T-SHAPE gateway is characterized by a si- multaneous opening on both the left and right of the robot followed by the robot being blocked in the front (see figure 1). A RIGHT ROOM gateway is characterized by a right opening followed by no closing. In rooms, gateways are typically exits, such as the RIGHT COR- NER EXIT in figure 1. We have identified a total of 25 gateway types in typical indoor environments. Clas- sifying each gateway using local sensory information helps the robot perform place recognition. Gateways extend the traditional sonar-based topo- logical place by being not just distinctive places, but important places in that they open up new views for the robot. The robot can take advantage of these views to store visual scenes that can help it distinguish be- tween gateways. In essence, gateways represent generic places in the environment (for example, doors, inter- sections) and not specific places (for example, the door to room 200). This is acceptable for some forms of navigation. For example, if the robot is told to take the third right opening, then the algorithms described in this section will be perfectly adequate. However, if the robot does not know its starting location or the environment changes (that is, the second opening on the right is closed) then simply relying on local sonar information can be dangerous. For this reason, our gateway mechanism is augmented with visual informa- tion, described in the following section. Visual information We augment our sonar information with visual infor- mation. Our visual information takes the form of vi- sual scenes captured at gateways from which we extract visual cues. Scenes, as they are presented here, differ from the traditional computer vision paradigm. In our approach, cues are not simply extracted from an image and then stored apart from the scene, but their location in the scene is of equal importance. Kaplan, Kaplan, and Lesperance (Kaplan 1970; Kaplan & Kaplan 1982; 980 Perception Lesperance 1990) d iscuss the importance of a fast and unobtrusive mechanism that gives a rough assessment of the objects surrounding an organism and their rela- tionships to each other. Extracting visual cues Programming a robot to autonomously find visual cues (or landmarks, although that term is generally used for highly complex objects as opposed to the simple features discussed in this subsection) is an area of active research and there are several proposed land- mark detection algorithms (Levitt & Lawton 1990; Tsuji & Li 1993). For our experiments we have cho- sen a simple cue-vertical edges. Vertical edges have proven very useful as indoor visual cues in other mo- bile robot systems (Kriegman, Triendl, & Binford 1989; Crowley et al. 1991) and are especially effective in our experimental space due to the sharp contrast be- tween black doorway frames and white walls. Vertical edges are extracted from a black-and-white image by a modified Sobel edge detector. A second image is an- alyzed in the same way as the first, but it is offset by l&m from the first image. This produces two lists of edges, one list for the right image and one list for the left image. The edges on the two lists are matched to each other using the direction of transition of the edge (that is, was the edge from light to dark or dark to light?), length, and location. The pixel shift in the matched edges from the first image to the second image (called the disparity) is calculated and used to deter- mine a rough distance to the edge. Each visual cue, thus, has three scene-independent features: direction, length, and distance. Storing visual scenes We store the robot’s visual cues in an abstracted scene representation (ASR), which is a 5 X 5 grid. The choice of a 5 X 5 grid size is based on the experiments in sonar gateway detection. The orientation error at a gateway is a maximum of 3.5 degrees. Using a camera with a focal length of 4.8mm, a 3.5 degree variation in orien- tation yields a 47 pixel displacement for cues 2m away (objects further away will have a smaller disparity). Doubling this to 94 pixels and dividing it into the im- age size of 480 X 480 pixels gives a 5 X 5 abstracted grid. In such a grid, a cue that falls in the middle of a cell and is further than two meters away will remain in that same cell given a 3.5 degree difference in orienta- tion. Each cell of the ASR can be connected to a rep- resentation of a visual cue that occupies that location in the scene. In the current system, the representa- tion of the visual cue contains the direction, distance, and length of the cue. However, in more sophisticated implementations the representation of the visual cue could contain detailed information about how to rec- ognize the cue, maybe even a small neural network that performs pattern recognition for the pattern located in those cells. visual cue 2 i\\ visual cue 3 visual cue 4 Figure 2: Cues are stored in abstracted representa- ASRs can be stored for anv of eight directions that the robot can be told to faceMat a g\teway. The num- ber of directions represented is dependent on the vi- sual field of view; in our robot the field of view is 60 degrees, which allowing for overlap, gives 8 directions each representing 45 degrees. Typically, the robot will only store one scene (in the forward direction) at each gateway. Figure 2 shows some sample ASRs and how several can be stored at a single gateway. ASRs are not static structures as that would render them useless in a dynamic world. An ASR sho;lld only contain those cues that remain constant over many traversals, since they will be the most reliable cues in the future. To accomplish this, the connection that links each cell of the ASR to a cue representation can be strengthened or weakened, depending on whether the cue is present or not during each traversal. Currently, it is necessary to have guided training runs in order to build up a stable set of cues. In the fu- ture, we would like our robot to explore autonomously, attempting to determine where it is as well as it can and updating appropriate maps as much as it can. Such a system would make more mistakes at first, but would not need to rely on directions to find routes to goals. Also, such a system would take much longer to learn a stable set of cues. The current implementation can be compared to someone taking you on a guided tour of a building several times before letting you loose. During training the robot is only told at which gate- way it currently is. The robot detects and stops at the gateways completely autonomously. Matching ASRs The robot must have some mechanism for matching its current scene with the ASRs that are stored with each gateway. Four different match algorithms were implemented and then compared using actual scenes acquired by the robot. The four algorithms are: 1) a feature-to-feature match using distance and direction Perception 981 1 0 e Figure 3: The experimental space for place recognition. in which an entire feature in the current scene must match an entire feature in the stored scene; 2) a cell-to- cell match using distance and direction in which each occupied cell in the current scene must match an oc- cupied cell in the stored scene; 3) a cell-to-cell match using only direction; 4) a cell-to-cell match using only occupancy. The comparison procedure consists of having the robot traverse three routes five times each and build- ing up 16 ASRs at seven different gateways. Figure 3 shows the locations of the gateways. In this figure, the black circles with arrows are the three starting points for the routes. After the robot has acquired its ASRs, it traverses each route a final time; this is the testing run. It then matches each scene along the testing run with all of the ASRs stored during the initial traver- sals. A current scene was said to match a stored ASR if the ratio of matched cues (or cells in methods 2, 3, and 4) to total stored cues (or cells) is higher than any other scene (a tie resulted in no match). Under these conditions, method 1 matched seven out of six- teen scenes, method 2 matched nine of sixteen, method 3 matched five of sixteen, and method 4 matched six of sixteen. Given these results, the second match algo- rithm was chosen for the remainder of the experiments in this paper. Our notion of storing visual scenes to aid mobile robot navigation is not unique; there has been ac- tive research in using visual scenes to provide robots with homing capabilities. These robots do not build maps, but instead the robot stores sensory data about the environment and associates movements with sen- sory events. As sensory events trigger movements, the robot navigates the environment. Examples of homing robots are (Nelson 1989) and (Hong eZ al. 1992). Our contribution is that instead of storing visual scenes at regular intervals, as is done in homing, we store visual scenes only at locations that are considered interesting by the robot’s sonar sensors. Figure 4: The Bayesian network used for place recog- nition Stored places A B C D E F G Table 1: Likelihoods for each place using only vision. Place recognition A single source of information, whether it be sonar or vision, is not enough to perform robust place recog- nition without further navigation. Thus, we use both gateway characterization and visual cues in the place recognition process and combine them using a simple Bayesian network (Pearl 1988), in which a location is determined by a scene and a gateway. The probabilis- tic network used by our robot is shown in Figure 4. The scene node of our network is the likelihood of a given location as determined by matching the visual cues stored for that location with the cues in the cur- rent visual scene. The gateway node is the likelihood of a given location determined by comparing its classi- fication with the classification of the current gateway. Both of these leaf nodes are combined to determine the robot’s location. The goal of integrated place recognition is to perform place recognition better using a combination of vision and sonar than would be possible using either alone. Better is defined in three ways: 1) A higher accuracy in place recognition; 2) A greater resilience to sensor errors; and 3) An ability to resolve ambiguous places. We have tested our topological mapping system us- ing a real robot in an unaltered environment. In our ex- perimental set-up, the robot has built up ASRs of seven places along three routes each traversed five times (see figure 3). Each ASR has one scene in the forward di- rection and has a gateway classification for each place. Then the three routes are traversed a final time and a test scene is stored at each of the seven gateways, along with a test gateway classification. The test scene is matched against all the stored ASRs and the test clas- sification is matched with all the stored classifications 982 Perception I Stored places I I I 1 ABC-DEFGl A 11 .82 1 .04 1 .04 1 .04 1 .04 1 0 0 B II .02 I .31 I .31 I .31 I .06 1 0 0 I I, I I I I I I Table 2: Likelihoods for each place using only sonar. Stored places A B C D E F G A 11 .95 I I .O BII 0 Table 3: Combined likelihoods (vision and sonar) for each place. in order to do place recognition. Table 1 gives the likelihood for each place using only the visual evidence. Across the top are the stored places and down the side are the places at which the robot is (that is, the test scenes). The numbers reflect the likelihood that the robot is at that place given the visual scene information. They were determined by normalizing the percentage of matching cues between the test scene and the stored ASRs. For example, if there are three scenes and the match percentages are: .25, .90, and .75 then the likelihoods would be .13, .47, and .40. If no cues matched then the algorithm still assigned a small match percentage (0.10) to that place, since a zero likelihood would cause the final likelihood for that place to be zero no matter how strong the sonar evidence. The table shows that four out of seven places (A,B,C, and D) would be correctly identified (that is, have the highest likelihood) using only visual information. Table 2 gives the likelihoods for each place using only sonar information (that is, gateway characterization). These likelihoods were determined by us and entered into the system: the correct gateway is given the high- est likelihood; similar gateways are given much smaller likelihoods; and dissimilar gateways are given a zero likelihood. Sonar information also gives a 57% accu- racy in place recognition. This is because three places (B, C, and D) look identical to the sonar sensors and are all characterized as RIGHT OPENING, so only four out of the seven places (57%) can be uniquely recog- nized (that is, have the highest likelihood) using sonar sensors. Finally, Table 3 shows the likelihoods for each place Figure 5: Each ASR is a small component of a larger representation. when the vision and sonar evidence is combined us- ing the Bayesian network (both sources of evidence are weighted equally). While consisting of a small number of places, this experiment demonstrates how sonar and vision combined can result in place recognition that is more accurate than would be possible using either sens- ing modality by itself; when the sonar information is ambiguous, the visual evidence distinguishes between places, and vice versa. Integrating sonar and vision can also help overcome sensor errors during place recognition. For example, let’s assume that the robot misclassified place D as a RIGHT ROOM instead of a RIGHT OPENING (in reality the robot never made this mistake, so the error had to be simulated). In this case, its sonar likelihood for place D is only .ll, while its sonar likelihood for place E (which actually is a RIGHT ROOM) is .61. When vision evidence is considered, the likelihoods are updated to .42 for place D and only .25 for place E, thus correcting the sonar error. Conclusion All previous research into topological mapping for mo- bile robots uses sonar sensing for place recognition. Many mobile robots also use vision sensing for place recognition. Both approaches have their merits and we believe that combining sonar and vision sensing in a topological representations results in a better robot navigation system. Our system can reduce or eliminate the need for additional robot movements to distinguish between places that appear identical to sonar sensors and it can also reduce the number of scenes that need to be stored by only acquiring scenes at those places that are determined as interesting by the sonar sensors. There are also some drawbacks to our approach when compared to other systems. First, our robot requires several initial, guided traversals of a route in order to acquire a stable set of locational cues to navigate au- tonomously. Second, acquiring, storing and matching Perception 983 visual scenes is very expensive, both in computation and storage. Finally, we are restricted to highly struc- tured, orthogonal environments. There is also the question of how our system will scale up, given that our experimental space consisted of only seven gateways, due to the time consuming na- ture of experimenting with real robots. Certainly, the perfect place recognition performance we achieved in our experiments will not hold up as more and more places are added. However, it is unrealistic to expect the robot to have no idea of where it has started; this is a worst case scenario used for experimental purposes only. As the robot gets more gateways we expect that knowledge of the robot’s previous location can elimi- nate all but a handful of possibilities for the current location, which can then be resolved using sensory in- formation as was demonstrated in our experiments. In the future we hope to expand our robot’s visual sensing beyond simple vertical edges. We are also in the process of implementing a better gateway detec- tion algorithm that incorporates more sophisticated obstacle avoidance (see (Kortenkamp et al. 1994) for preliminary results). On a broader scale, this work is a small part of a larger robot mapping system de- tailed in (Kortenkamp 1993). The larger system ad- dress such issues as representing the topological map, extracting routes from the topological map, travers- ing previously learned routes and building a geometric map from the topological data. The complete repre- sentation is shown in figure 5. Each ASR is a node in the topological network upon which a global map is constructed. The global map has a structure similar to an ASR but instead of storing visual cues it stores loca- tions of distant places. This representation is based on a cognitive model of human spatial mapping described in (Chown, Kaplan, & Kortenkamp 1994). References Basye, K.; Dean, T.; and Vitter, J. S. 1989. Cop- ing with uncertainty in map learning. In Proceedings of the International Joint Conferences on Artificial Intelligence. Brooks, R. A. 1985. Visual map making for a mobile robot. In Proceedings IEEE Conference on Robotics and Automation. Chown, E.; Kaplan, S.; and Kortenkamp, D. 1994. Prototypes, location and associative networks (PLAN): Towards a unified theory of cognitive map- ping. To appear in The Journal of Cognitive Science. Crowley, J. L.; Bobet, P.; Sarachik, K.; Mely, S.; and Kurek, M. 1991. Mobile robot perception using ver- tical line stereo. Robotics and Autonomous Systems 7(2-3). Fennema, C., and Hanson, A. R. 1990. Experiments in autonomous navigation. In Proceedings Image Un- derstanding Workshop. 984 Perception Hong, J.-W.; Tan, X.; Pinette, B.; Weiss, R.; and Riseman, E. M. 1992. Image-based homing. IEEE Control Systems 12( 1):38-45. Kaplan, S., and Kaplan, R. 1982. Cognition and Environment: Functioning in an Uncertain World. Ann Arbor, MI: Ulrichs. Kaplan, S. 1970. The role of location processing in the perception of the environment. In Proceedings of the Second Annual Environmental Design Research Association Conference. Kortenkamp, D.; Huber, M.; Koss, F.; Lee, J .; Wu, A.; Belding, W.; and Rogers, S. 1994. Mobile robot exploration and navigation of indoor spaces using sonar and vision. In Proceedings of the AIAA/NASA Conference on Intelligent Robots in Field, Factory, Service, and Space (CIRFFSS ‘94). Kortenkamp, D. 1993. Cognitive maps for mobile robots: A representation for mapping and navigation. Ph.D. Dissertation, The University of Michigan. Kosaka, A., and Kak, A. C. 1992. Fast vision-guided mobile robot navigation using model-based reason- ing and prediction of uncertainties. Computer Vision, Graphics, and Image Processing 56(2). Kriegman, D. J.; Triendl, E.; and Binford, T. 0. 1989. Stereo vision and navigation in buildings for mobile robots. IEEE Transactions on Robotics and Automa- tion 5(6). Kuipers, B. J., and Byun, Y.-T. 1991. A robot ex- ploration and mapping strategy based on a semantic hierarchy of spatial representations. Robotics and Au- tonomous Systems 8. Lesperance, R. 1990. The Location System: Using Approximate Location and Size Information for Scene Segmentation. Ph.D. Dissertation, The University of Michigan. Levitt, T. S., and Lawton, D. T. 1990. Qualitative navigation for mobile robots. Artificial Intelligence 44(3). Mataric, M. K. 1992. Integration of representation into goal-driven behavior-based robots. IEEE Truns- actions on Robotics and Automation 8(3). Nelson, R. C. 1989. Visual homing using an asso- ciative memory. In Proceedings of the Image Under- standing Workshop. Pearl, J. 1988. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Mateo, CA: Morgan Kaufmann. Tsuji, S., and Li, S. 1993. 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1,661 | Applying VC-dimension Analysis To 3D Object Recognition from Perspective Projections * Michael Lindenbaum and Shai Ben-David Computer Science Department, Technion Haifa 32000, ISRAEL (mic, shai) @cs.technion.ac.il Abstract We analyze the amount of information needed to carry out model-based recognition tasks, in the context of a probabilistic data collection model, and independently of the recognition method employed. We consider the very rich class of semi-algebraic 3D objects, and derive an upper bound on the number of data features that (prov- ably) suffice for localizing the object with some pre-specified precision. Our bound is based on analysing the combinatorial complexity of the hy- potheses class that one has to choose from, and quantifying it using a VC-dimension parameter. Once this parameter is found, the bounds are ob- tained by drawing relations between recognition and learning, and using well-known results from computational learning theory. It turns out that this bounds grow logarithmically in the algebraic complexity of the objects. Introduction We present here a quantitative analysis of the amount of information required for Model-based object recog- nition. Taking a statistical approach, we consider a random data collection model and analyse the number of measurements that guarantees recognition success within a certain confidence. Intuitively, more data is needed if the recognition procedure is required to dis- criminate between object instances that are visually similar, and if more alternatives are allowed by the possible instance specification. In this paper these in- tuitive observations are quantified by deriving a rigor- ous upper bound on the number of features required to succeed. Our approach is very general and applies to a very large class of objects, and to several transfor- mation classes. It is based on a combinatorial analysis, which provides the VC-dimension of concept classes as- sociated with this objects and the transformations. In this note we concentrate on localizing 3D objects from their perspective projections. The bounds are derived relying on the observation that the recognition task is related to a learning task, *This work was supported by the Technion fund for the promotion of research and by the Smoler research fund in which one tries to learn a subset of some space, by observing samples of this space. We consider the Probabh~ Approximately Correct (PAC) learning model, which assumes that the samples available are randomly drawn, and requires that the hypothesis provided is a good approximation to the true subset, within a cer- tain prespecified confidence. In this setting, the ele- gant PAC learning theory guarantees that the num- ber of samples required to learn is not higher than a certain threshold, which grows with the accuracy of the hypothesis, the required confidence, and a certain parameter, associated with the of allowed hypotheses, and known as the VC-dimension. The mathematical heart of our result is therefore an analysis of the VC- dimension of a certain concept class, related to the localization task. Interestingly, the analysis and its results are independent of the particular object con- sidered, and the derived VC-dimension parameter de- pends only on the object’s complexity and the class of transformations. The results we provide, besides quantifying the fun- damental dijgiculty of recognition tasks, should be use- ful for analyzing reported results by comparing them to the theoretical bounds, and to designing recognition procedures. Many recognition paradigms use a consis- tent data subset as a sufficient evidence to the presence of an object in the scene. Our results,together with other considerations described latter, may be used to set the sufficient size of such subsets that guarantees the reliability of such a procedure. The fundamental dificulty of recognition tasks was already considered before in several papers: Linden- baum used a different approach to set upper and lower bounds on the amount of data required to succeed in recognition and localization tasks (Lindenbaum 93). Grimson and Huttenlocher considered a complemen- tary aspect of the recognition fundamental dificulty (Grimson and Huttenlocher 91). While we basically assume that all the data features belong to an object, they examine the possibility that a subset of “noise data features” will give a false evidence for the pres- ence of an object in the scene. Some of the abstract mathematical treatment, without the interpretation we Perception 985 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. give here, was already considered in (Ben-David and Lindenbaum 93 ) and (Goldberg and Jerrum 93 ). The paper is divided into two major parts: explain- ing the relation between learning and recognition, and calculating the VC-dimension associated with the task of localizing a 3D object from its 2D perspective image. Learnability and the VC-Dimension Given a collection, Kc, of subsets of some base set, X, and a measure of difference between the members of K, a set of points (21,. . . , z~) c X is said to c-pin down K, if, for every pair of sets A, B E Ic, if A n (21,. . ., 2,) = B n (21,. . ., z,} then the difference between these members of K: is at most E. It is evident that the size of such ‘pinning down’ sets, as well as their number, depends upon the family K of sets. The theory of computational learnability formal- izes this issue within the framework of Valiant’s PAC learning model. In that model the family of sets K is usually called a ‘concept class’ and its members are ‘concepts’. The model assumes the existence of some probability distribution P over X. This probability plays a double role: First, the difference between con- cepts is specified as the P-probability of hitting their symmetric difference. Second, the ‘fraction’ of pinning- down n-tuples (among all n-tuples of points of X) is measured by the probability of picking such a tuple by i.i.d. sampling n-many times according to P. A class K is called PAC-learnable (or just ‘learn- able’) if, for every positive E, 6, there exists a finite number m (depending upon these parameters) such that for every probability distribution P over X, the pm-probability of picking an m-tuple that e-pins down K exceeds (l- 6). It turns out that a concept class is learnable iff a purely combinatorial parameter - the Vapnik-Chervonenkis dimension of this class, is finite (Blumer et al. 89). Definition 1: [Vupnik-Chervonenkis Dimension] Let X e e be some set and K a collection of its subsets. We say that K: shatters a set A & X, if, for every B C A, there exists some C E K such that C n A = B. The Vapnik-Chervonenkis Dimension (in short, VC- dim) of K is the maximum number d such that K shutters a set of size d. (If X: shutters sets of un- bounded size, we say that its VC-dim is 00). Example: Let X be the unit interval and K be the collections of all its subintervals whose length is 0.1. I.e., K = {[a,~ + 0.11 : 0 < a 2 (1 - 0.1)). It is not hard to realize that K shatters every pair of points in [O.l, 0.91 which are at most 0.1 apart. On the other hand, Ic shatters no subset A of the interval whose cardinality exceeds 2. It follows that VC-dim(K) = 2. We can now state the result of Blumer et. al. (Blumer et al. 89) showing how the VC-dim of a class determines its learnability. theorem 1 [(Blumer et ad. 89)] e A class K is PAC-learnable ifl it has a finite VC- dimension. e If VC - dim(K) = d th en, for every positive E and 4 1. if 4 2 8d 13 m>max Flogs, Flog7 > then, for every probability distribution P over X, the Pm-probability of picking an m-tuple that E- pins down II exceeds (1 - 6). 2. On the other hand, if d(l - a(~(1 - 6) + 6)) then,there exists a probability distribution P over X, such that the Pm-probability of picking un m- tupde that c-pins down I< is less than (1 - 6). Note that the upper bound of this theorem guar- antees the existing of many e-pinning-down tuples of size linear in the VC-dim of a class and in $, for every underlying probability distribution. The lower bound, on the other hand, only states the existence of a ‘diffi- cult’ distribution and does not rule out the possibility that, for some specific distribution, the task of pinning down a class may require fewer sample points. In (Ben- David and Lindenbaum 93 ) some evidence is provided to show that, for classes of algebraically-defined ob- jects in the Euclidean space, the lower bound above is indeed a close estimate of the minimal size of pinning- down sets relative to the uniform distribution. Learning and recognition This section discusses the relation between learning and recognition, and shows that in a proper setting, recognition tasks are equivalent to learning tasks in the sense that an object is recognized (or localized) if some related concept class is PAC learned with a cer- tain prediction power. We consider recognition processes that are composed of a data collection stage followed by an interpretation stage. In the first stage data features are collected in random locations, independently, and according to fixed distribution. In the second stage the data col- lected is combined with prior knowledge, and is inter- preted, to yield an hypothesis on the identity and pose of the object in the scene. These stages are described in the next two sections. The data collection stage In Vision scenarios, information is usually obtained from the observed object’s edges in an image, and is usually associated with some location error. Data ex- traction from images involves many factors including illumination, occlusion, the effect of edge detectors and 986 Perception seems very difficult to model. The simple model, sug- gested in the following lines, is not claimed to cover all - situations in computer vision. the uncertainty on the observed It addresses, however, part of the object and the inaccuracy of the measurements. We model the uncertainty in the data features avail- able by assuming that the data features are randomly drawn in the neighborhood of the object boundary. Let LJV, be the boundary of the instance of the object V, after a transformation t. In the simple case, where only boundary points associated with inaccuracy A are available, we assume that they are independently sam- pled according to a uniform distribution, inside vtA = { r 1 3s E av, s.t. IIS - rll < A), (1) to which we refer as either “extended boundary” or “observable object”. More complicated data collection models, which include arbitrary but bounded sampling distributions and data features which include bound- ary slope measurements, are considered in the full ver- sion I The interpretation stage We refrain from referring to any particular method for inferring the hypothesis. The only assumption taken is that the interpretation stage may draw any hypoth- esis that is consistent with the data. Let H be the set of possible hypotheses, which, in the model based setting, may contain instances of different objects un- der different transformations. Then, for M being the data set, the algorithm may draw any hypothesis in {hlM c h; h E H}. An error measure We treat all recognition tasks uniformly and con- sider them successful if a special error measure, defined below, between the true object and the hypothesized one, is guaranteed to be lower a threshold value. For Vt being the true object that is present in the scene and Wtj being some hypothesized instance, the error associ- ated with this hypothesis is defined as the normalized difference between observable objects. the volumes of the corresponding JqVt, Wl> = voz(v,A \ W$) Vod( v,A) (2) This error measure agrees with the intuitive meaning of recognition and localization. High localization ac- curacy, for example, implies that the boundaries of the true object and the hypothesis are very close, and leads to a small difference between the corresponding ex- tended boundaries. Low localization accuracy, on the other hand, allows larger error. The uniform recognition accuracy measure may be used to specify recognition success in the more famil- iar forms, by setting the maximal error, for which the hypotheses is still considered successful. For example, reagarding the localization tusk, one may consider any distance measure D(., e) (say, Hausdorff distance,) be- tween two object instance, and denote a localization procedure successful if, for the hypotheses drawn, the distance between the true object Vt and the hypothe- sis Vi) is do or smaller. (The value do may be adjusted arbitrarily according to the localization precision re- quired.) Requiring a recognition accuracy better than eo = t,t’cT ; !?(?&Q)>& JqVt, v,'). (3) guarantees that no instance of V which is do-far from the true instance is drawn as an hypothesis. Therefore, we are interested in the following ques- tion: How many measurements are needed to guarantee, with a certain confidence 1 - S, that ad1 hypotheses that are at least eo-far from the true object instance are rejected ? Learning and recognition Now, the equivalence between the localization task and PAC learning should be apparent: let {&It E T} be a set of instances associated with one object V and a class of instances T. To every instance from this set, associate a concept identical to the extended boundary. vt * KA (4) {&It E T} c---) &-A(V) = {vtAIt E T} (5) Every data feature extracted from the object bound- ary provides a (positive) example to the corresponding concept. Learning a concept in CTA( V) with an ac- curacy better than ee means that all concepts in the class, associated with a symmetric difference greater than ec, are not consistent with the examples. Note however, that according to our data collection model, the density is zero everywhere except inside the con- cept itself. Assuming further that the distribution is uniform within the extended boundary, implies that the recognition error (2) is also smaller than eo, and that the recognition task is successful. While the PAC learnability results usually holds for arbitrary distribution, we will assume that the data features are placed according to a uniform distributions densities. The reason is the need to establish a relation between the recognition accuracy measure E(&, Wt,) and the symmetric difference VtAAWt+, induced by the sampling density. This cannot be achieved by all dis- tributions: Consider for example a distribution that is concentrated in a single point. The learning per- formance in this case will be excellent as the density weighted symmetric difference and the associated pre- diction error will be null after one example, The knowl- edge about the location of the object will, however, be poor because completely different hypotheses can be consistent if they share one point with the true object (either inside or outside). Inserting the VC-dimension of the concept class CTa (V) = {KA It E T} into the bound in theorem (l), Perception 987 we may now calculate the number of data features suf- ficient to guarantee that every consistent hypothesis is eo-accurate with confidence 1-S. In the rest of the pa- per we bound the VC-dimension of one particular class: extended boundaries of perspective projections of 3D objects. We do not refer to particular objects, but just assume that the object belongs to the extremely large class of objects, defined in the next section. The ,class of objects considered - Semi-algebraic sets We shall focus on well behaved geometrical objects - the Semi-Algebraic subsets of IR2 and IR3. Definition 2 : A semi-algebrai (k,m) in lFLn is a set that can boolean combination of k sets of fj (2) Q 0) where the functions fj of maximal degree m, and Q is <,=,<. c open set of degree be represented as a the form {Z E lFP : are read polynomials one of the relations Polynomial objects of modest degrees (e.g. 4) suffice to describe complicated objects and thus provide high representation power (see, e.g. (Taubin and Cooper 92)). The class we consider here is even richer: be- sides polynomial objects it also contains combinations of them which include, e.g., polygonal objects (which, for k being the number of polygon sides, are semi algebraic sets of degree (k, 1)). The family of Semi- Algebraic sets is parametrized, meaning that the class of objects considered is actually not limited. Localization - The VC-dimension of transformed Semi-Algebraic sets Our general approach treats both two dimensional and three dimensional semi-algebraic objects and a wide class of transformation. Here, we focus on three di- mensional semi-algebraic objects and perspective pro- jection of them, and analyse the class of concepts which are the extended boundary of these projections. We show that the VC-dimension of this class is logarith- mic in the complexity of the object, and obeys the assymptotic upper bound ~ B;;iect(V) = 712log(km), (6) thereby providing the parameter needed to determine the number of two dimensional data features (taken from the projected image), required to localize the ob- ject with the required precision and confidence. The bound does not depend on the particular object chosen but only on its complexity, as expressed by the number of polynomials that define it, k, and by their degree, m. The VC-dimension of projected 3D semi-algebraic objects. We consider the common imaging procedure, which in- volves projectin g the object on an image plane and getting the information from the projection. We as- sume here that the imaging process is done by a pin- hole camera, which implements a perspective projec- tion and, for our purposes, is a good approximation to common realistic cameras. Furthermore, we follow Kriegman and Ponce approach (Kriegman and Ponce 90) and assume that only sharp edges in the projected image are observable. Such sharp edges in the image may come either from the outline of the object, or from discontinuities of its surface normal that are usually the result of two intersecting polynomial surfaces. The object instance class Considering the model-based localization problem, we assume that the object present in the scene is an instance Vt of a known object model V, associated with some unknown but general rigid transformation t = (R,i) & = (2 =Rs+t(sE V} (7) where both s and 2 are 3D coordinate vectors that describe points in the 3D space, t is a 3D translation vector and R is a rotation matrix. (Note the follow- ing small change in notation: Unlike the description of the general framework, Vt does not describe the object after the full transformation but denotes the object before the projection. Consequently, the ex- tended boundary will be redefined.) To parametrize this transformation, we use the parameter vector t = {h,.. . , tg), which includes the translation components and the sines and cosines of the Euler rotation angles of the inverse transformation. The class of 9-tuples which are valid parameters of the rigid transformation is constrained by some equalities between the parame- ters and is denoted T. The perspective projection process Let the optical axis of the pin-hole camera coincide with the z-axis, the image plane be on the z = 0 plane, and the focal point be at f = (0, 0, -f). One line passes between every point S = (sZ, sY , sZ) in the 3D space and the focal point, and specifies the projection of s as its intersection with the image plane. This implies the simple expression for perspective projection of S: proj(S) = F = (rz,ry,O). f TX=------s f sz+f x rY z-s s,+f Ye (8) The contour generators Clearly, not all points of the object & are projected to the visible curves in the image. Points that are projected belong either to the occluding contour or to discontinuities of the surface normal and thus must obey some constraints: e The projected point may be on the occlud- ing contour but only on one polynomial surface ~~x+.~;o~ ; = 0. In this case the viewing direc- ---f= (s2,sy,sz)-(0,0,-f) is tangent to the polynomial surface and perpendicular to the 988 Perception gradient, implying that the following degree-m poly- nomial constraint, (m = deg( fi)), [s- J] * Ofi(S) = 0. (9) In addition, the projected point S is included in the polynomial surface itself, and thus satisfies fi(S) = 0 (10) o The other source for visible contours is the intersec- tion of two polynomial boundaries which create nor- mal discontinuities and are thus visible due to shad- ing, texture, etc. The points on the intersection of the polynomial surfaces { fi (S) = 0) and { fj (ii) = 0) are simply specified by requiring them to satisfy both polynomials. Note that such visible curves may lie, in the projection, within the outline but also on it. An Algebraic expression for the extended boundary. By definition, the extended boundary contains all points that are close enough to the perspective pro- jection of some point in the contour generator. For- mally, let G(Vt) be the contour generator of the trans- formed three dimensional object, and (G(Vt)), be its perspective projection. The extended boundary of this projection, denoted [(G(&))p]A, is given by [(GW))plA = {q = (am my, 0) I 3s E G(K) s.t. Ilq - proj(s)ll < A} (11) We would like to know what is the number of random measurements needed, to guarantee with confidence 1 - S that the distance between the true instance of the object and any hypothesized instance that is con- sistent with the measurements is smaller than some value. The distance between instances is measured be- tween the corresponding observable objects, that is, as the normalized area difference between the extended boundaries [(G(T/t))p]A. To find a sufficient number of measurements, we proceed now to bounding the VC dimension of the associated concept class c ;;j”““(V) = {[(G(Vt))p]A 1 t E T}. We apply the following technique: (12) We assume that some set of points S of cardinality N is shattered by the concept class. We observe that every point in S corresponds to a partition of the parameter space into two parts: one of parameters for which the corresponding extended boundary of transformed set includes that point, and another that includes the parameters for which the corresponding extended boundary does not include that point. We observe that the N points in S partition the parameter space into connected components, such that all paprameter in the same connected compo- nent correspond to extended boundaries that contain the same subset of S. o We prove that the number of these connected com- ponents is polynomial in N implying that the num- ber of subsets A C S that may be written in the form A = KG(l/,))JA *s is also polynomial. e In order to shatter the set S, every one of its 2* subsets should be expressed as [(G(Vt))p]A f~ S for some t. Since only polynomial number of subsets can be written in this form, we conclude that this class of extended boundaries cannot shutter arbitrarily large point sets. Partitioning the parameter space. The first step in this direction is to find the structure of the parameters space: Lemma 1 For any semi algebraic set V E R3 of de- gree (k, m> (m 2 2>, t ransformed by a 30 rigid trans- formation, and projected using perspective projection on the image plane, and for every z in that image plane, the set of transformation parameters I<; = {+i E [(G(l/t))JA} is also a semi-algebraic set of degree (k, = (2k + 3)8(2. 8m)81, mp = 0.5(2.8m)8) (in the parameter space IR’). Proof: The proof is based on the theory of quanti- fier elimination from Logic theory. The parameter set KJZ may be written as the truth set of a prenex formula in the coordinates of s and the 9 parameters tl , . --, 9 t as variables. Recall that tl, . . , , tg are the parameters of the inverse transformation, which transform every point on Vt into a point on V. Ii’: = (tl3ss.t. S E G(V,) A lIZi-proj(S)ll < A} (13) Now, the second condition, ]]?:i - proj(S)II < A, does not depend on the transformation and can be easily transformed to a polynomial inequality of second de- gree in the coordinates of 5. The first condition is more complicated: a point s in the contour genera- tor G(Vt) of the transformed object Vt must be either in the transformed intersection of two polynomial sur- faces or on the occluding boundary of one transformed polynomial surface. To satisfy the first option it suffice that t will satisfy two polynomial constraints, such as fj (R’S + t') > 0 and fj,(R’S+ t') > 0, (or 2 or =), where fj and fjl are two of the polynomials that specify V. Consid- ering both the coordinates of s and the transforma- tion parameters as variables, these polynomials are of maximal degree of 4m. For the point S to be on a smooth occluding contour, the gradient of the transformed polynomial must be orthogonal to the viewing vector [S - f]. The or- thogonality is preserved if the coordinate system is changed and therefore we can write this condition as V[fj(R’S + t')] * [R’(B - f) + t’] = 0 This constraint is polynomial with maximal degree of Sm. Perception 989 Therefore, the quantifier free part of the prenex for- mula (13) depends on 2k polynomial sets with a max- imal degree of Sm. By applying well-known algorithm of Collins (Collins 75), the three coordinates of S can be eliminated leaving a quantifier free logic formula with kp = (2k + 3)8(2 . 8m)81 polynomial sets of max- imal degree mp = 0.5(2 . 8m)8. (The three quadratic constraints relating the sines and cosines of the Euler angles are also imposed.) Cl The VC-dimension of the class Cg,oject (V) is given by the following theorem. theorem 2 For every semi algebraic set V of degree (k, m) in lR3, VCdim(C!$Oj eet (V)) = O(logkm) Proof: [sketch] The proof relies on results developed in previous papers. Let S = (~1, . . . , 2~) be a sub- set of lR2 that is shattered by the class Cigjec”(V). The union of boundaries Bs = U:zr aKE of the semi algebraic parameter sets {l<[Z} divides the parameter space IRg into connected components. Milnor’s classical theorem (Milnor 64) states that any partition of IR,“, that obeys a set of Ic polynomial inequalities, has at most $(2 + d)” connected compo- nents. (d is the total degree ~~~ldeg(f~).) Recall that, by Collins decomposition, each of the parameter sets KzZ is specified by L, = (2k + 3)8(2 + 8m)“-many polynomial sets of the form {f] fj (f, xi) > 0) each of degree m?, = 0.5(2.8m)’ or lower. Note that at least one of the functions fij (9 = fj (t, zi) vanishes on each point of the boundary of Kz. Consider now the product function G(t) = fli j fij (t). Any connected component of IRg \ Bs cor- responds to a union of one or more connected compo- nents of {t : G(t) > 0) or of {t : G(t) < 0). G(t) is a (kr rnp N)-degree polynomial in 9 real variables, and, by our modification to Milnor theorem, the number of connected components of its positive set (%]G(fl > 0) (as well as of its negative set, which is the pos-set of -G) is not higher than (2 + k, mp N)‘. Therefore any cardinality N of a point set that is shattered must sat- isfy the following relation 2* < 2(2 + Icp mr N)’ (14) The theorem, as well the assymptotic lower bound (6) follows by a straightforward calculation. Cl A straightforward application of the bounds given in (Blumer et al. 89) may now give the number of data features which guarantees that the hypothesized instance is not more than ee different from the true instance. More concrete assertions, such as that the localization result is “good enough” follow by specify- ing the required localization precision, and using (3) to specify eo. Conclusion We analyzed the amount of data required to localize a 3D object from its 2D perspective projection, and obtained a rigorous upper bound on the number of data features required to draw a reliable hypothesis. The analysis was carried independently of the recognition method used, and in a certain sense, independently of the particular objects considered. The same approach was used to derive the number of data features required to localize instances of 2D ob- jects, associated with Euclidean, Similarity, Affine and Perspective transformation classes. It was also gener- alized to analyse the general model-based recognition task. Specifically, it was shown that the number of data features required for recognition grows at most logarithmically with the library size (Lindenbaum and Ben-David 94). References Blumer, A., A. Ehrenfeucht, D. Haussler and M.K. Warmuth, 1989, “Learnability and The Vapnik- Chervonenkis Dimension”, JA CM, 36(4), 929-965. S. Ben-David and M. Lindenbaum, 1993, “Localiza- tion vs. Identification of Semi-Algebraic Sets”, Pro- ceedings of the 6th ACM Conference on Computa- tional Learning Theory, pp. 327-336. Collins, G.E., 1975, “Q uantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposi- tion”, Proceedings of the 2nd GI Conf. On Automata Theory and Formal Languages, Springer Let. Notes Comp. Sci. 33, pp. 515-532. Goldberg P. and M. Jerrum, 1993, “Bounding the Vapnik-Chervonenkis Dimension of Concept Classes Parametrized by Real Numbers”, Proceedings of the 6th ACM Conference on Computational Learning Theory, pp. 361-368. Grimson, W.E.L., and D.P. Huttenlocher, 1991, “On the Verification of Hypothesized Matches in Model- Based Recognition”, IEEE Trans. on Pattern Analy- sis and Mach. Inted., PAMI-13(12), pp. 1201-1213. Kriegman, D. J . and J . Ponce, 1990, “On Recognizing and Positioning Curved 3D objects from Image Con- tours”, IEEE Trans. on Pattern Analysis and Mach. Intel., PAMI-12, pp. 1127-1137. Lindenbaum, M., 1993, “Bounds on Shape Recogni- tion Performance”, submitted. Lindenbaum, M. and S. Ben-David, 1994 “Applying VC-dimension Analysis to Object Recognition”, 3rd European conference on Comp. Vision (to appear). Milnor, J., 1964, “On the Betti Numbers of Real Va- rieties”, Proc. Amer. Math. Sot. 15, pp. 275-280. Taubin, G., and D.B. Cooper, 1992, “2D and 3D Ob- ject Recognition and Positioning with Algebraic In- variants and Covariants”, in Symbolic and Numerical Computation for ArtiJicial Intelligence, B.R. Donald, D. Kapur, and J.L. Mundy, eds. 990 Perception | 1994 | 36 |
1,662 | A New Approach to Tracking 3 bjects in 2 age Sequences Michael Chanl, Dimitri Metaxas’ and Sven IDept. of Comp uter & Information Science 2Dept. of Comp uter Science University of Pennsylvania University of Toronto Philadelphia, PA 19104-6389 Toronto, Ontario, Canada M5S lA4 mchan@grip.cis.upenn.edu, dnm@central.cis.upenn.edu, sven@vis.toronto.edu Abstract We present a new technique for tracking 3D ob- jects from 2D image sequences through the in- tegration of qualitative and quantitative tech- niques. The deformable models are initialized based on a previously developed part-based qual- itative shape segmentation system. Using a physics-based quantitative approach, objects are subsequently tracked without feature correspon- dence based on generalized forces computed from the stereo images. The automatic prediction of possible edge occlusion and disocclusion is per- formed using an extended Kalman filter. To cope with possible occlusion caused by a previously undetected object, we monitor the magnitude and direction of the computed image forces ex- erted on the models. Abrupt changes to these forces trigger scene re-segmentation and model re-initialization through the qualitative shape segmentation system. Tracking is subsequently continued using only local image forces. We demonstrate our technique in experiments involv- ing image sequences from complex motions of 3D objects. Introduction Research in 3D model-based object tracking from im- age sequences is typified by approaches which at- tempt to recover the six degrees of freedom of an ob- ject in each frame, e.g., (Thompson & Mundy 1988; Verghese, Gale, & Dyer 1990; Lowe 1991; Gennery 1992). Once correspondences between image and model features are determined, changes in the posi- tions of image features in successive frames are used to update the pose of the object. Although these tech- niques provide accurate pose of the object at each frame, they require an exact geometric specification of the object; they do not allow models to deform as they move. Recently, to cope with the challenges of nonrigidity, several researchers have adopted a physics- based approach to estimate the shapes and motions of nonrigid 3D objects from visual data to different lev- els of accuracy (Terzopoulos, Witkin, & Kass 1988; Huang 1990; Pentland & Horowitz 1991; Metaxas & 960 Perception Terzopoulos 1993). The 2D problem has received similar attention (Kass, Witkin, & Terzopoulos 1988; Duncan, Owen, & Anandan 1991; Szeliski & Terzopou- 10s 1991; Blake, Curwen, & Zisserman 1993). In this paper, we develop a new approach to tracking shapes and motions of objects in 3D from 2D image se- quences. Our method makes use of both the framework of qualitative shape segmentation (Dickinson, Pent- land, & Rosenfeld 199213; 1992a) and the physics-based framework for quantitative shape and motion estima- tion (Terzopoulos & Metaxas 1991; Metaxas & Ter- zopoulos 1993). To be able to track multiple objects, initialization of the models is performed in the first frame of the sequence based on a shape recovery pro- cess that uses recovered qualitative shapes ’ to con- strain the fitting of deformable models to the data (Metaxas & Dickinson 1993). For successive frames, the qualitative shape recovery process can be avoided in favor of a physics-based model updating process re- quiring only a gradient computation in each frame. As- suming no occlusion and small deformations between frames, local forces derived from stereo images are suf- ficient to update the positions, orientations, and shapes of the models in 3D. Kalman filtering techniques have been applied in the vision literature for the estimation of dynamic fea- tures (Deriche & Faugeras 1990) and rigid motion pa- rameters (Dickmanns & Graefe 1988; Broida, Chan- drashekhar, & Chellappa 1990) of objects from image sequences. We use a Kalman filter for the estima- tion of the object’s shape and motion, which conse- quently allows the prediction of possible edge occlu- sion and disocclusion. The occurrence of these situa- tions may be due to changes of an object’s aspect from frame to frame or due to motions of other indepen- dently moving objects (situations where most tracking approaches based on feature correspondence may not work robustly). By predicting the occurrence of these situations in our approach, we can confidently deter- mine which part of an object will be occluded and sup- press their contributions to the net forces applied to 1 We assume tha t objects are constructed from a finite set of volumetric part classes. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. the model. In fact, an advantage of our technique is that we do not need to perform costly feature corre- spondence during 3D tracking. Our approach also allows the detection of object oc- clusion due to a previously undetected object by moni- toring changes to the image forces exerted on the mod- els. In such an ambiguous situation, we invoke the qualitative shape segmentation module for scene re- segmentation and model re-initialization. Tracking can then be continued by using only local images forces. Our technique is robust and can handle scenes with complex motions and occlusion due to the triggering of the qualitative shape segmentation system when nec- essary. Dynamic Deformable Models This section reviews the formulation of the deformable model we adopted for object modeling and the physics- based framework of visual estimation (see (Metaxas & Terzopoulos 1993) for greater detail). Geometry of Deformable Models The positions of points on the model relative to an inertial frame of reference @ in space are given by a vector-valued, time varying function x(u,t) = (x(u, t), y(u, t), Z(U, t))T, where T denotes transposi- tion and u are the model’s material coordinates. We set up a noninertial, model-centered reference frame 4 and express the position function as x = c+Rp, where c(t) is the origin of 4 at the center of the model and the rotation matrix R(t) gives the orientation of 4 rel- ative to <p. Thus, p(u,t) gives the positions of points on the model relative to the model frame. We further express p = s + d, as the sum of a reference shape s(u, t) and a displacement d(u, t>* We define the reference shape as: s = T(+; UOA,...); b0,h,. . .). Here, a geometric prim- itive e, defined parametrically in u and parameterized by the variables ai( is subjected to the global de- formation T which depends on the parameters hi(t). Although generally nonlinear, e and T are assumed to be differentiable (so that we may compute the Jacobian of s) and T may be a composite sequence of primitive deformation functions T(e) = Tl(Tz(. . . T,(e))). We concatenate the global deformation parameters into the vector qs = (a~, al,. . . , bo, br, . . .)T. To illustrate our approach in this paper, we will use as a reference shape a deformable superquadric ellipsoid that can also undergo parameterized tapering deformations, as de- fined in (Metaxas & Terzopoulos 1993). Model Kinematics and Dynamics The velocity of a 3D point on the model is given by i = LQ, (1) where L is the Jacobian matrix that converts Q- dimensional vectors to 3D vectors (Metaxas & Ter- zopoulos 1993). The vector q(t) represents the general- ized coordinates of the model consisting of the transla- tion, rotation, global and local deformations. To make the model dynamic, we assume that it is made of a sim- ulated elastic material that has certain mass distribu- tion. From Lagrangian mechanics, we obtain second- order equations of motion which take the form (see (Terzopoulos & Metaxas 1991) for derivations): Mijl+Dq+Kq=g,+f,, fL= s LTfdu, (2) where fs are generalized external forces associated with the components of q, and f(u, t) is the image force distribution applied to the model. Here M is the mass matrix, ID is the damping matrix, K is the stiffness matrix and g, is the vector of the generalized coriolis and centrifugal forces. Multiple Object Tracking This section describes our new approach for track- ing multiple objects in the presence of occlusion. It is based on the intelligent use of a qualitative shape segmentation system (Metaxas & Dickinson 1993) and techniques for quantitative shape and motion estima- tion (Metaxas & Terzopoulos 1993). The deformable models are first initialized based on the qualitative seg- mentation system. Objects are subsequently tracked using a physics-based approach by applying image forces simultaneously derived from the stereo images. We can handle partial edge occlusion and disocclu- sion due to the object’s own motion or occlusion by another object by predicting their occurrences using an extended Kalman filter. We handle more complex cases of object occlusion due to a previously undetected object by monitoring changes to the image forces ex- erted on the models. These changes trigger the use of the qualitative shape segmentation system for scene re-segmentation and model re-initialization, and track- ing is subsequently continued using local image forces only. Qualitative Shape Recovery and Model Initialization We employ the methodology developed in (Metaxas & Dickinson 1993) to initialize our deformable mod- els. We start by assuming that objects are constructed from a finite set of volumetric part classes (Dickinson, Pentland, & Rosenfeld 199213; 1992a). The parts, in turn, are mapped to a set of viewer-centered aspects. During the qualitative shape recovery process, the sys- tem first segments the image into parts using an aspect mat thing paradigm. Each recovered qualitative part defines: 1) the relevant non-occluded contour data be- longing to the part, 2) a mapping between the image faces in their projected aspects and the 3D surfaces on the quantitative models, and 3) a qualitative ori- entation that is exploited during model fitting. Based on these constraints, we assign forces from monocu- lar image data points to the corresponding points on Perception 961 the 3D model. The model is then fitted dynamically to the image data under the influence of the image forces. In the following sections, we will discuss how we handle sequences of stereo images taken under non- parallel geometry without requiring the continuous use of qualitative constraints. Short Range Forces from Image Potentials For each frame in the image sequence, we create an im- age potential such that the “valleys” of this potential correspond to the locations in the image where there are sharp changes in intensity or edge features. If we denote the intensity image by 1(x, y), the image poten- tial can be computed as follows (Terzopoulos, Witkin, & Kass 1988): H(x, Y) = -4’ IV& * W, Y)I (3) where o determines the width of the Gaussian function GO, * denotes the convolution operation, and p deter- mines the “steepness” of the potential surface. The corresponding 2D force field induced by this potential is given by: f(x, Y) = -~JJI(x, Y>. (4) The model’s degrees of freedom respond to the 2D force field through a process which first projects the model’s nodes into the image. As the projected nodes are attracted to the valleys of the potential surface, the model’s degrees of freedom are updated to reflect this motion. The mapping of 2D image forces to general- ized forces acting on the model requires the derivation a Jacobian matrix. Jacobian Computation for Perspective Projection Let x = (z,y,z) T denotes the location of a point j with respect to the world coordinate frame. Then we can write x=c,+R,x,, (5) where c, and R, are respectively the translation and rotation of the camera frame with respect to the world coordinate frame, and xc = (xc, yc, z,)~ is the position of the point j with respect to the camera coordinate frame. Under perspective projection, the point x, projects into an image point xp = (z+, , xp)T based on the for- mulas: xp = Zf, Yp = Ef-9 (6) where f is the focal length of the camera. By taking the derivative of (6) with respect to time, we arrive at the following matrix equation: Based on (5) and (1) we get kc = R,% = R,lL;1. (8) 2See also (Terzopoulos, Witkin, & Kass 1988). Rewriting (7) in compact form using (8), we get By replacing the Jacobian matrix in (2) by L,, two dimensional forces f derived from image data can be appropriately converted into generalized forces f* mea- sured in the world coordinate frame. Forces from Stereo Images By computing generalized forces in the world coordi- nate frame, the 2D image forces in a pair of stereo images can be simultaneously transformed into gener- alized forces fq measured in a common world coordi- nate frame. Measurements from two different views are sufficient to determine the scale and depth parameters of the model. If we define as active nodes those model nodes on which image forces are exerted, then the gen- eralized forces are computed by summing the image forces exerted on all the active nodes of the discretized model. More precisely, if we denote the position of the jth active node on the model surface by xj, then the generalized force on the model can be computed as follows: .iEAL + x L;R(fR(P(R;; (xj - ccR >>>>, (10) jEAR where JI is the set of indices of active nodes. Here the subscripts L and R denote dependence on the left and right images respectively and P(x, y, Z) = (Ff, ff) describes the perspective projection equation. Determining Active Model Nodes When our measurements are 2D images, as opposed to 3D range data, only a subset of the nodes on the model surface are selected to respond to forces. From a given viewpoint, we can compute this active subset of model nodes based on the model’s shape and orientation. In particular, a model node is made active if at least one of the following conditions is true: 1. it lies on the occluding that viewpoint, 2 contour of the model from 2. the local surface curvature at large and the node is visible. the node is sufficiently (Note that it is possible that a model node is active with respect to one view, but not to another.). Instead of calculating analytically the positions of the active nodes on the model surface, we “loop” over all the nodes on the discretized model surface and check if one of the above two conditions is true. Condition 1 is true if: lij e nj 1 < T, where nj is the unit normal at the jth model node, ij is the unit vector from the 962 Perception focal point to that node on the model, and r is a small threshold. Condition 2 is true if 3k E Kj s.t. Ink . nj I > K & 3k E ICj s.t. nk * ik < 0, (11) where l<j is a set of indices of the nodes adjacent to the jth nodes on the model surface. /c in (11) is a threshold to determine if the angle between adjacent normal vectors is sufficiently large. Tracking and Prediction We incorporate into our dynamic deformable model formulation a Kalman filter by treating their differen- tial equations of motion (2) as system models. Based on the use of the corresponding extended Kalman filter, we perform tracking by updating the model’s general- ized coordinates q according to the following equation ; = Fti + g + PHTV-1 (z - h(G)), (12) where u = (GT, qT)T and matrices F, H,g, P,V are associated with the model dynamics, the error in the given data and the measurement noise statistics (Metaxas & Terzopoulos 1993). Since we are measur- ing local short range forces directly from the image potential we create, the term z - h(G) represents the 2D image forces. Using the above Kalman filter, we can predict at every step the expected location of the data in the next image frame, based on the magnitude of the estimated parameter derivatives 4. Self Occlusion and Disocclusion As an object rotates in space, or as the viewpoint of the observer changes substantially, certain faces of the object will become occluded or disoccluded by itself (a visual event). Hence, the corresponding line segment or edge feature in the image will appear or disappear over time. By using the Kalman filter to predict the position and orientation of the model in the next time frame, we can quantitatively predict the occurrence of a visual event. In other words, we can determine by using our active node determination approach, which subset of the model nodes will be active in the next image frame, and suppress their contributions to the net forces applied to the model. For stereo images, this prediction can be performed independently to the left and right images. In this case, two sets of active model nodes are maintained at any particular moment. Tracking Multiple Objects with Occlusion Our framework for tracking objects based on image potentials can be easily extended to deal with multiple independently moving objects and multi-part objects. The complication here is that object parts may occlude one another in different ways. By *tracking objects in 3D using stereo images, we can predict the 3D positions of the nodes on each model based on the current esti- mates of their respective model parameters and their rate of change. Active nodes on each model will be made “inactive” if they are predicted to be occluded by surfaces of other models. This visibility checking is performed for each node on a model and against every surface of the other models in the scene. In practice, much of this checking can be avoided based on approx- imate estimates of each object’s size and 3D location. We demonstrate in the experiments section that we are able to track all the objects in a scene even when some object parts become partially occluded. There are also two more cases of object occlusion in case of multiple independently moving objects. The first case occurs when another moving object that was not previously present in the scene occludes the object being tracked. The second is due to an error from the qualitative segmentation system which did not detect an object during the model initialization step. Our sys- tem can handle both situations by monitoring the local forces exerted on the model. If no force or forces of unusual magnitude and direction are exerted on some of the predicted active nodes of the currently tracked model, the event signals the possibility that we have lost track of the object. In such a situation, we apply the qualitative segmentation system to resolve the am- biguity. After proper re-initialization of our models, we continue tracking using local image forces based on our physics-based technique. Experiments We demonstrate our approach in a series of tracking experiments involving real stereo image sequences. All images are 256x256 pixels and all the examples run at interactive rates on a SGI R4000 Crimson worksta- tion, including real-time 3D graphics. In the first ex- periment, we consider a sequence of stereo images (16 frames) of two independently moving objects. The ob- jects move towards each other along 2 different paths which are approximately linear and the paths’ relative angle is about 20 degrees. The baseline of the two cameras is lOOmm, they are both at a declination an- gle of 30 degrees from the horizon, and their relative rotation is 8 degrees. Fig. l(a) shows the first pair of stereo images. The initial pose and shape of the objects are recovered using techniques mentioned before and they are subsequently tracked based on image forces only. Figs. l(b-g) h s ow snapshots of the two objects being tracked with the wire-frame models overlaid on the image potential. They demonstrate that our tech- nique is able to continue the tracking even when one of the blocks becomes partially occluded and then disoc- eluded. Note that those active model nodes which are temporarily occluded are automatically identified and made inactive. Figs. 2(a-d) show the relative positions of the recovered models at four different instants. In the second experiment, we consider a sequence of stereo images (24 frames) of a scene containing multi- ple objects, including a two-part object. Fig. 3 shows the initial stereo images of the multi-object scene. The baseline of the stereo cameras is 150 mm, the cameras Perception 963 Cd) (0 Figure 1: Tracking two independently moving blocks in a sequence of stereo images: (a) initialized models, (b) coming of a new frame, (c) beginning of the occlusion, (d) taller block partially occluded, (e) taller block becomes disoccluded, (f) no more occlusion. Note that only the active model nodes are marked, while the occluded ones are not. (a) (b) cc> Cd) Figure 2: Recovered models of the two moving blocks in 3D over time from a top view (with the stereo arrangement). Figure 3: Initial stereo images of the multi-object scene. are at a declination angle of 30 degrees from the hori- zon, and their relative rotation is 12 degrees. The cam- eras are rotated around the scene at a constant rate. Fig. 4(a) shows the initialized models using the same technique as before. Fig. 4(b) shows image potentials at an intermediate time frame where the aspects of some parts have changed and some parts have become partially occluded. Figs. 4(c-f) show that each object is still successfully tracked under these circumstances with the individual part models overlaid on the image potentials in Fig. 4(b). In the last experiment we demonstrate the applica- bility of our technique in case of object occlusion by another undetected object. We use the same sequence of stereo images as in the first experiment where there are two independently moving blocks, but we do not assume prior detection of one of the blocks this time. Fig. 5 shows the instant at which some of the image forces exerted on the active model nodes of the moving block exceed a threshold. It then triggers the qualita- tive segmentation system to resegment the scene and correctly group edges belonging to each of the blocks. After the models are reinitialized, tracking continues as before. Conclusion We have presented a new integrated approach to ob- ject tracking in 3D from 2D stereo image sequences. After initializing our deformable models based on a part-based qualitative segmentation system, we subse- quently track the objects using our physics-based ap- proach. We further used a Kalman filter for estimating the object’s shape and motion which allowed the pre- diction of possible visual events; thus we were able to determine where on the model, image forces can be exerted. We also demonstrated that our approach can deal with object occlusion from other independently moving objects by predicting each object’s motion in the scene. Occlusion due to previously unidentified objects can also be detected by monitoring changes to the image forces exerted on the models. Based on these changes, the qualitative shape segmentation sys- tem is invoked for scene re-segmentation and model re- initialization. We are currently extending our system to handle objects composed of more complex primitives than the ones we have assumed. 964 Perception -- Cd) Figure 4: Tracking multiple objects in a sequence of stereo(riages (a) initialized models, (b) ’ image potentials of an inter- mediate frame (both occlusions and visual events have occurred) (c-f) each object part correctly tracked with part models overlaid on the image potentials in (b). Note that only the active model nodes are marked, while the occluded ones are not. Figure 5: Unpredicted object occlusion: no knowledge of the 2nd block is assumed. It is detected by monitoring the forces exerted on the active nodes of the displayed model. References Blake, A.; Curwen, R.; and Zisserman, A. 1993. Affine- Invariant Contour Tracking with Automatic Control of Spatiotemporal Scale. In Proc. IEEE 4th International Conference on Computer Vision, 502-507. Broida, T. J.; Chandrashekhar, S.; and Chellappa, R. 1990. Recursive 3-D Motion Estimation from a Monocu- lar Image Sequence. IEEE Transactions on Aerospace and Electronic Systems 26(4):639-656. Deriche, R., and Faugeras, 0. 1990. Tracking Line Seg- ments. Image and Vision Computing 8(4):261-270. Dickinson, S.; Pentland, A.; and Rosenfeld, A. 1992a. From Volumes to Views: An Approach to 3D Object Recognition. Computer Vision, Graphics, and Image Pro- cessing: Image Understanding 55(2):130-154. Dickinson, S.; Pentland, A.; and Rosenfeld, A. 199213. Shape Recovery Using Distributed Aspect Matching. IEEE Transactions on Pattern Analysis and Machine In- telligence 14(2):174-198. Dickmanns, E. D., and Graefe, V. 1988. Applications of Dynamic Monocular Machine Vision. Machine Vision and Applications 1~241-261. Duncan, J. S.; Owen, R. L.; and Anandan, P. 1991. Mea- surement of Nonrigid Motion Using Contour Shape De- scriptors. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, 318-324. Gennery, D. 1992. Visual Tracking of Known Three- Dimensional Objects. International Journal of Computer Vision 7(3):243-270. Huang, T. S. 1990. Modeling, Analysis and Visualiza- tion of Nonrigid Object Motion. In Proc. IEEE 10th In- ternational Conference on Pattern Recognition, volume 1, 361-364. Kass, M.; Witkin, A.; and Terzopoulos, D. 1988. Snakes: Active Contour Models. International Journal of Com- puter Vision 1(4):321-331. Lowe, D. 1991. Fitting Parameterized Three-Dimensional Models to Images. IEEE Transactions on Pattern Analy- sis and Machine Intelligence 13(5):441-450. Metaxas, D., and Dickinson, S. 1993. Integration of Quan- titative and Qualitative Techniques for Deformable Model Fitting from Orthographic, Perspective, and Stereo Pro- jections. In P rot. IEEE 4th International Conference on Computer Vision, 641-649. Metaxas, D., and Terzopoulos, D. 1993. Shape and Non- rigid Motion Estimation Through Physics-Based Synthe- sis. IEEE Transactions on Pattern Analysis and Machine Intelligence 15(6):580-591. Pentland, A., and Horowitz, B. 1991. Recovery of Non- rigid Motion and Structure. IEEE Transactions on Pat- tern Analysis and Machine Intelligence 13(7):730-742. Szeliski, R., and Terzopoulos, D. 1991. Physically-Based and Probabilistic Modeling for Computer Vision. In Proc. SPIE Geometric Methods in Computer Vision, volume 1570, 140-152. Society of Photo-Optical Instrumentation Engineers. Terzopoulos, D., and Metaxas, D. 1991. Dynamic 3D Models with Local and Global Deformations: Deformable Superquadrics. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(7):703-714. Terzopoulos, D.; Witkin, A.; and Kass, M. 1988. Con- straints on Deformable Models: Recovering 3D Shape and Nonrigid Motion. Artificial Intelligence 36(1):91-123. Thompson, D., and Mundy, J. 1988. Motion-Based Mo- tion Analysis: Motion from Motion. Robotics Research: The Forth International Symposium 299-309. Verghese, G.; Gale, K.; and Dyer, C. 1990. Real-time, Parallel Tracking of Three-Dimensional Objects from Spa- tiotemporal Sequences. New York: Springer-Verlag. 3lO- 339. Perceptibn 965 | 1994 | 37 |
1,663 | Automatic Symbolic Traffic Scene Analysis Using Belief Networks* T. Huang, D. Koller, J. Malik, G. Ogasawara, B. Rao, S. Russell, and J. Weber Computer Science Division University of California Berkeley, CA 94720 {tthuang~koller~malik(ogasawara)bobbyrao~russell~jweber}~cs.berkeley.edu Abstract Automatic symbolic traffic scene analysis is essen- tial to many areas of IVHS (Intelligent Vehicle Highway Systems). Traffic scene information can be used to optimize traffic flow during busy pe- riods, identify stalled vehicles and accidents, and aid the decision-making of an autonomous vehi- cle controller. Improvements in technologies for machine vision-based surveillance and high-level symbolic reasoning have enabled us to develop a system for detailed, reliable traffic scene analysis. The machine vision component of our system em- ploys a contour tracker and an affine motion model based on Kalman filters to extract vehicle trajec- tories over a sequence of traffic scene images. The symbolic reasoning component uses a dynamic be- lief network to make inferences about traffic events such as vehicle lane changes and stalls. In this pa- per, we discuss the key tasks of the vision and reasoning components as well as their integration into a working prototype. Introduction An important task for progress in IVHS (Intelligent Ve- hicle Highway Systems) is the development of methods for automatic traffic scene analysis. All three major ap- plications of IVHS - ATIS (Advanced Traveler Infor- mation Systems), ATMS (Advanced Traffic Manage- ment Systems), and AVCS (Automated Vehicle Con- trol Systems) - could benefit from accurate, high-level descriptions of traffic situations. For example, an ATIS and an ATMS could use information about traffic con- gestion and stalls to warn drivers or to direct vehicles to alternate routes. An ATMS also could analyze local traffic at intersections to identify those with higher risk of accidents. Finally, an AVCS would need information about the actions of neighboring vehicles and the con- dition of traffic lanes ahead to control an automated car moving along a freeway (Niehaus & Stengel 1991). *This work was supported by the California Department of Transportation under the PATH project grant MOU-83. In this paper, we describe a prototype system in which we have successfully combined a robust, vision- based traffic surveillance system (Koller, Weber, & Malik 1994) with a dynamic belief network dedicated to analyzing traffic scenes. Unlike conventional loop detectors, which are buried underneath highways to count vehicles, video monitoring systems are less dis- ruptive and less costly to install. They also have greater range and allow for more detailed descriptions of traffic situations. Dynamic belief networks provide a flexible, theoretically sound framework for traffic scene analysis because they can easily model uncertainty and because they can provide high-level, symbolic descrip- tions by integrating low-level information from a vari- ety of sources. They also provide a natural framework for expressing knowledge about typical traffic behavior, allowing more accurate analyses from a given sensor stream. Symbolic traffic scene analysis using vision-based surveillance systems has been previously investigated by several research groups (Schirra et al. 1987; Koller, Heinze, & Nagel 1991; Heinze, Kriiger, & Nagel 1991; Huang, Ogasawara, & Russell 1993). The challenges of this approach include identifying vehicles despite im- precise video data and changing lighting conditions, tracking individual vehicles despite their overlapping with each other, and efficiently providing high-level de- scriptions based on evidence accumulated over time. We have achieved improvements in performance, reli- ability, and accuracy by applying a new approach for detecting and tracking vehicles, by explicitly reason- ing about vehicle occlusions (Koller, Weber, & Ma- lik 1994), and by devising techniques for fast belief network update, localized reasoning, and flexible node semantics. Low-Level Machine Vision-Based Surveillance Our traffic surveillance system is based on the block diagram shown in Figure 1. This section focuses on the tasks of feature extraction and tracking, and the next section focuses on the tasks of symbolic reasoning and incident detection. Perception From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Figure 1: Block diagram of the complete traffic surveil- lance system. Arrows denote the flow of information. As Figure 1 indicates, traffic scene analysis gener- ally proceeds from low-level processing of road traf- fic images to high-level descriptions of the traffic sit- uation (which can in turn be used to direct and dis- ambiguate low-level processing). Given a sequence of traffic images, a vision-based surveillance system must identify the vehicles in the scene and track them as they progress along the image sequence. This requires not only estimation of the moving vehicle shapes and positions, but also association one image to the next. of these estimates Two primary factors that complicate this task are noisy sensors, which yield imprecise measurements, and -vehicle occlusions, which make it more difficult to identify and disambiguate vehicles. To address these problems, we employ vehicle and motion models that are updated in a-Kalman filter formalism, thus yield- ing most likely estimates based on accumul ated obser- vations. Motion Segmentation A surveillance system initiates vehicle identification and tracking by determining what parts of each image belong to moving objects and what parts belong to the background. This is accomplished by examining the difference in pixel intensities between each new frame and an estimate of the stationary background. Reliable background estimation, which is critical for accurate identification of moving ‘blobs’, is made more difficult as lighting conditions change. We perform this initial- ization step by using a modified version of the moving object segmentation method suggested by (Karmann & von Brandt 1990) and implemented by (Kilger 1992). Our method employs a Kalman filter-based adaptive background model. This allows the background es- timate to evolve as the weather and time of day af- fect lighting conditions. The background is updated at each frame using the following update equation: &+1 = Bt + (Q1(1- Mt> + aaMt)B (1) Bt is the background model at time t , Dt is the dif- ference between the present frame and the background model, and n/rt is a binary mask of hypothesized mov- ing objects in the current frame. The gains a/l and a2 are based on estimates of the rate of change of the background. For a complete description, we refer the reader to (Koller, Weber, & Malik 1993). Vehicle Identification and Shape Estimation After identifying moving blobs, the vision system at- tempts to disambiguate individual vehicles and esti- mate their shapes. This helps with associating data over a sequence of images and with obtaining accurate vehicle trajectories. Our system performs these tasks by extracting closed contours enclosing each moving blob in each image. Contour extraction is based on mo- tion and gray-value boundaries, which are obtained by thresholding the spatial image gradients and the time derivatives of the images. For each moving blob, points that pass a threshold test are enclosed by convex poly- gons, and these are used as initial object descriptions. The top row of Figure 2 shows an image section with a car, the detected moving object patch corresponding to the image of the car, and the sample points made up of image locations with acceptable spatial gradients and time derivatives. The convex polygon enclosing all these sample points is shown in the bottom row. Our time-recursive shape estimation algorithm (Koller, Weber, & Malik 1993) cannot use convex poly- gons, since the number of vertices for a vehicle may change along an image sequence. We address this problem by using snakes, spline approximations to con- tours (Kass, Witkin, & Terzopoulos 1988; Curwen & Blake 1992). W e use closed cubic splines with 12 con- trod points to approximate each extracted convex poly- gon, and we obtain the locations of the control points by again employing a Kalman filter (Bartels, Beatty, & Barsky 1987; Koller, Weber, & Malik 1994). The bottom right image shows the spline approximation of the shape. 0th er examples of spline approximations can be found in Figure 6. Mot ion Estimation The final task of the video system is to track identi- fied vehicles from one frame to the next. To accom- plish this, we estimate vehicle motion with an affine motion model. For a sufficiently small field of view and for independently moving objects, the image ve- locity field U(Z) at some location z inside a detected image patch can be closely approximated by a linear Perception 967 Figure 2: The top row shows an image section with a moving car, the moving object mask provided by the motion segmentation step, and the image loca- tions with acceptable spatial gradients and temporal derivatives. The bottom row shows the convex poly- gon enclosing the sample points and the final contour description by cubic spline approximation of the poly- gon. (affine) transformation. Since motion is constrained to the road plane and since possible rotation components along the normal of the plane are small, the degrees of freedom can be reduced to the extent that we obtain a velocity equation of only a scale parameter s and a displacement vector ~0: u(z) = s(-%72)+~o, (2) For the scale parameter s, s = ‘ 0 indicates that there is no change in scale, while s < 0 and s > 0 indicate motion components along the optical axes away from and towards the camera, respectively. zm denotes the center of the moving image region, and uo denotes its displacement between two consecutive frames. The affine motion parameters e = (u, s) make up the state vector for motion estimation. We can use a third Kalman filter to estimate the motion parameters, since the measurement function can be expressed in a linear matrix equation. This tracker has been influenced by (Blake, Curwen, & Zisserman 1993), who successfully extended their real-time contour tracking system (Cur- wen & Blake 1992) by exploiting affine motion models. Complete details of the affine motion model can be found in (Koller, Weber, & Malik 1994). Occlusion Reasoning Because vehicles often overlap with each other in the road images, the extracted contours of vehicles will be- come distorted for some frames. This can cause ar- tificial shifts in vehicle trajectories, since tracks are obtained by connecting centers of contours along the image sequence. To avoid these artificial shifts and to obtain reasonable tracks, we employ an explicit occlu- sion reasoning algorithm, which compensates for over- lapping vehicles. The occlusion reasoning algorithm works because the traffic scene geometry is known and because mo- tion is assumed to be constrained to the ground plane (Koller, Weber, & Malik 1993). This knowledge makes it possible to determine a depth ordering among the objects in the scene, and this depth ordering defines the order in which objects are able to occlude each other. igh-Level easoning Using elief Networks We now address the task of using vehicle track infor- mation (e.g., their positions and velocities) to arrive at high-level symbolic descriptions of vehicles and the traffic scene. To accomplish this, our symbolic reasoner uses multiple, per-vehicle dynamic belief networks with fast rollup. Concepts Belief networks are directed acyclic graphs in which nodes represent random variables (usually discrete) and arcs represent causal connections among the vari- ables (Pearl 1988). A ssociated with each node is a probability table that provides conditional probabili- ties of the node possible states given each possible state of its parents. When values are observed for a subset of the nodes, posterior probability distributions can be computed for any of the remaining nodes. This updating takes place using a compiled form of the be- lief network that is more suitable to propagating the influence of evidence to other nodes. Belief networks offer a mathematically sound basis for making inferences under uncertainty. The con- ditional probability tables provide a natural way to represent uncertain events, and the semantics of the updated probabilities are well-defined. Knowledge of causal relationships among variables is expressed by the presence or absence of arcs between them. Fur- thermore, the conditional independence relationships implied by the topology of the network allow exponen- tially fewer probabilities to be specified than the full joint probability distribution for all the variables in the network. Dynamic belief networks allow for reasoning in do- mains where variables take on different values over time. Typically, observations are taken at regular ‘ slices and a given network structure is replicated for each slice. Nodes can be connected not only to other nodes within the same time slice but also to nodes in the previous or subsequent slice. As new slices are added to the network, older slices are removed. Before a slice is removed, its influence is ‘ into the next slice by recomputing probability tables for cer- tain nodes in that slice. Thus, evidence accumulated over time is always integrated into the current belief network model (Nicholson 1992; Kjaerulff 1993). 968 Perception Traffic network structure The symbolic reasoning component for our system is built on the HUGIN inference engine for belief net- works (Andersen et al. 1989). Figure 3 shows an example belief network fragment for a single vehicle. Figure 4 shows the fragment projected over one time slice. For each vehicle in a traffic scene, there is a sep- arate belief network corresponding to it. Ydot.t Figure 3: Belief network fragment for a single vehicle. Some of the nodes in Figure 3, such as Xp0s-sens.t and Xdotsens.t, correspond to discretized sensor val- ues that are set in each new slice when the slice is added to the network. For instance, the Xpos-sens.t node represents a vehicle’s left-right position among the lanes of a highway and can take on one of ten states indicating the vehicle’s distance from the right edge of the lanes. Other nodes, such as StaI1ed.t and LaneChange.t, correspond to high-level events. For ex- ample, the LaneChange.t node can take on one of three different states indicating if a vehicle is going straight, changing lanes to the left, or changing lanes to the right. The posterior probability distributions for these high-level events are affected by the sensor values in the current slice as well as the posterior probabilities of nodes in the previous slice. These distributions are then used to provide symbolic descriptions of the traffic scene. Figure 4 shows how nodes are replicated from time slice 0 to time slice 1, as well as how some variables in time slice 1 depend on variables in the previous time slice. For example, Ypos.tl (representing a vehicle’s forward position on the highway) depends on Ypos.tO (its previous position) and Ydot.tO (its previous veloc- ity). The probabilities associated with each node provide a natural framework to encode knowledge about traffic behavior and rules. For example, the probability table for Ydot.tl in Figure 4 contains probabilities for each Figure 4: Belief network fragment for a single vehicle projected over one time slice. Some nodes have been omitted for simplicity. of Ydot.tl’s possible states (e.g., 21-30 km/hr, 31-40 km/hr, etc.) given the states of Ydot.tO, Fwd-Clr.tO (the space in front of a vehicle), and Ydot-diff.tO (the difference in speed between a given vehicle and the ve- hicle in front of it). A driver is likely to slow down if there isn’t much distance between his vehicle and the vehicle in front and if his vehicle is going faster than the vehicle in front. Thus, the appropriate entries in the probability table will indicate a high probability that the vehicle’s speed at time tl will be lower than its speed at time to. Similarly, the other entries in the table encode probability distributions for the new velocity given the combinations of parent states. Ad- ditional traffic knowledge that is or will be encoded includes knowledge about lane-changing and braking behavior, the effect of road geometry and weather on driving behavior, and the significance of brake, hazard, and signal lights. Network Issues anclling multiple vehicles. As mentioned earlier, in each time slice the structure in Figure 3 is replicated for each tracked vehicle in the traffic scene. Clearly, the positions and velocities of different vehicles will affect each other. Thus, determining globally consis- tent probability distributions for each vehicle involves a large network consisting of changing interconnections between vehicle subnetworks. We have investigated this approach and found the cost of modifying and recompiling the network at each time slice too com- putationally expensive. Nevertheless, we plan to pur- sue this avenue further, perhaps using approximation methods. Our current approach is to assign each vehicle its own dynamic belief network. We incorporate the in- fluence of nearby vehicles on the current vehicle by assigning some nodes to those vehicles. For example, Front-Ypos.t and Front-Ydot.t in Figure 3 refer to “the vehicle in front of the current vehicle”. Since the ac- tual vehicle in front may change, these indexical nodes Perception 969 (Agre & Chapman 1987) do not correspond to a spe- cific vehicle. Instead, a preprocessing step uses sensor data to determine which vehicles are currently in front of each other and then sets those node states accord- ingly. Using multiple, per-vehicle belief networks with indexical nodes has yielded a reasonably inexpensive approach to achieving locally consistent high-level de- scriptions for each vehicle while considering the affect of nearby vehicles. Nodes with variable semantics. When a vehicle first stops on the highway, it could be for any number of reasons. The probability that the vehicle is stalled may be small at first, but it increases over time if the vehicle continues to remain stopped while no vehicles are stopped in front of it. To allow flexible represen- tation of how a vehicle being stalled relates to it being stopped for some time, we made it possible for nodes to have variable semantics, i.e. a node refers to a dif- ferent event in different time slices. This is accom- plished by modifying the node’s conditional probabil- ity table from one time slice to another. For example, the Stopped-n.t node has some value n associated with it, and the node refers to the event that the vehicle has been stopped for n time slices. The probability table for the node is modified according to the value of n associated with it. This can be computed with a simple function to simulate a counter (e.g., we can give vehicles positive probability of being stalled only if they’ve been stopped for over 50 time slices) or with any arbitrarily complex function. Rolling the network forward. Because the HUGIN system is geared toward standard rather than dynamic belief networks, we developed the facilities necessary for rolling the network forward. Essentially, this involves adding the capability to add new time slices to the network and to incorporate information from old slices to the rest of the network so that the old slices can be deleted. We developed two approaches to this problem. In the first approach, we generated and compiled a new network for each time slice, and we used a new network every time a slice was added. This approach seemed adequate and offered the opportunity to dynamically alter the actual network structure (which would be nec- essary for a global network of all the vehicles), but it suffered from the poor performance noted earlier. We currently use our second approach, which em- ploys two precompiled networks, each with two slices. As shown in Figure 5, the system alternates between the two networks. To introduce sensor information from a new time slice, the system incorporates the ev- idence from the oldest slice into the rest of the model through a series of straightforward matrix multiplica- tions. The resulting probability tables are stored in the first slice of the other network. The new sensor information is then added to the second slice of this 3) set and ,~~-____ pwacpte ( slice2 / gv ewdence Network A Network S NETWORK A IN USE 3) set and propagate new evidence Network A Netwdrk B NETWORK S IN USE Figure 5: Steps for rolling the dynamic network for- network, and their influence is propagated to obtain new posterior probabilities. This other network is then used until the next time slice, when the rollup proce- dure is repeated back to the first network. This ap- proach does not allow dynamic alteration of the belief network structure, but it greatly improves performance by eliminating the need for network-recompilation after every time slice. The dHUGIN package (Kjaerulff 1993) provides ex- tensions to HUGIN for dynamic belief networks, but it does not provide the flexibility of our first approach for changing the network structure from one time slice to the next, and it does not provide the performance speedup of our second approach. esults with @al- rld Traffic Scenes We have tested our system on real-world image se- quences, and we present here the results of one 270- frame sequence of a divided four-lane freeway. The image at the top of Figure 6 shows frame #40 of the sequence overlaid with contour estimates of the vehi- cles. The image at the bottom shows only the vehi- cle contour estimates and their tracks (starting from frame #O). The image at the top of Figure 7 shows frame #64 of the sequence, and the graphic on the bottom shows a reconstruction in the SmartPath traf- fic simulator’ ‘of the image (the geometry is slightly different due to the display of the SmartPath simula- tor). In the graphic, one vehicle has been identified by the symbolic reasoner as changing lanes, and the number in the signpost correctly indicates the number ‘SmartPath is a microscopic three-dimensional auto- mated highway simulator developed at UC Berkeley as part of the PATH (Partners for Advanced Transit and High- ways) program of the Institute for Transportation Studies. 970 Perception Figure 6: The upper image shows frame #40 of the image sequence with overlaid contour estimates of the cars. The bottom image shows the contour estimates with their tracks (starting from frame #O). of vehicles that have passed since the beginning of the image sequence. Running on a Sun SparcStation 10, the performance of the vision component reaches about two seconds per frame for simultaneous tracking of about 10 vehicles. A high-speed implementation on special purpose hard- ware using C-40 digital signal processors is in progress. The performance of the belief network varies greatly with the network design, but generally requires about one second per vehicle per frame. We expect to im- prove the performance of both components by an order of magnitude with various optimizations. Operation in real-time would require sampling image frames quickly enough for the affine tracker to associate vehicles be- tween frames and for the symbolic reasoner to detect short traffic events such as lane changes. We expect that operation at 10 Hz for the vision system and 3 Hz for the symbolic reasoner will be sufficient for real-time performance. Conclusions / Future Work In this paper we have described the successful combi- nation of a low-level, vision-based surveillance system with a high-level, symbolic reasoner based on dynamic Figure 7: The upper image shows frame #64 of the sequence. The bottom graphic shows a reconstruction in the SmartPath traffic simulator of this image. belief networks. This prototype system provides ro- bust, high-level information about traffic scenes, such as lane changes, stalled vehicles, and overall vehicle counts. We believe that the required accuracy can in the long run only be obtained using high-level reason- ing under uncertainty. The symbolic reasoner is already capable of using other vehicle features, such as vehicle type, turn sig- nals and brake lights, to improve its analytical perfor- mance. We are currently upgrading the vision system to detect these features, as well as to handle vehicle shadows (Kilger 1992). Furthermore, the inferences of the symbolic reasoner can be fed back to the tracker ’ Kalman filter to further increase its reliability. For ex- ample, if a vehicle is signalling left, its expected motion update should be biased toward leftward acceleration rather than a random perturbation. This allows for re- duced variance, and hence greater reliability in track- ing. In the extreme case, if the low-level tracker loses a vehicle (for example, in heavy rain), the high-level sys- tem can automatically “track” its most likely position by a combination of extended projection and inference from the behavior of other vehicles. Another benefit is the robust data fusion provided by Bayesian inference. This is especially important Perception 971 at dusk or dawn, when the surveillance system will see both vehicle outlines and vehicle tail lights. Fi- nally, by including a simple sensor failure model, the network can detect and diagnose sensor failure, while continuing to track vehicles using remaining sensor in- puts (Nicholson 1992). Besides continuing to refine the network design and to optimize its performance, we are investigating meth- ods for enabling the symbolic reasoner to handle mixed networks with both continuous and discrete variables (Lauritzen 1992; Shachter & Kenley 1989). This offers the opportunity for greater performance over purely discrete networks, and it seems reasonable, since sen- sor variables such as vehicle positions and velocities are adequately modelled as Gaussians. The symbolic rea- soner can also be enhanced to provide other types of descriptions, such as driver behaviors. Machine learn- ing techniques applied to a library of image sequences can be used to generate detailed probabilistic models of driver behavior, which are useful both in our own work and in analytical and simulation studies of high- way designs. We are currently moving the implementation of the prototype (running on single Sun SparcStations) to a heterogeneous system consisting of a host Sun Sparc- Station and special purpose hardware. This will im- prove the setup for large-scale experimentation and will improve performance to about 5Hz, which we believe will be adequate for traffic surveillance in sunny Cal- ifornia weather. To better assess the system’s useful- ness and accuracy, we plan to measure its performance on a more extensive collection of video sequences. Acknowledgments We gratefully acknowledge the help of C. McCarley and his group at Cal Poly, San Luis Obispo, for pro- viding us with video tapes of various traffic scenes. We also thank HUGIN Expert A/S for their generous doc- toral student license to use the HUGIN system. References P. Agre, D. Chapman. Pengi: An Implementation of a Theory of Activity, in Proceedings of the Sixth National Conference on Artificial Intelligence, 1987. S. Andersen, K. Olesen, F. V. Jensen, F. Jensen. HUGIN” - a Shell for Building Bayesian Belief Universes for Expert Systems, in Proceedings of the Tenth International Joint Conference on Artificial Intelligence, 1989. R. Bartels, J. Beatty, B. Barsky. An Introduction to Splines for use in Computer Vision, Morgan Kaufmann, 1987. A. Blake, R. Curwen, A. Zisserman. Affine-invariant con- tour tracking with automatic control of spatiotemporal scale, in Proc. Int. Conf. on Computer Vision, Berlin, Germany, May. 11-14, 1993, pp. 66-75. R. Curwen, A. Blake. Active Vision, MIT Press, Cam- bridge, MA, 1992, chapter Dynamic Contours: Real-time Active Snakes, pp. 39-57. N. Heinze, W. Kruger, H.-H. Nagel. Berechnung von Bewegungsverben zur Beschreibung von aus Bildfolgen gewonnenen Trajektorien in Strahenverkehrsszenen, In- format& - Forschung und Entwicklung 6 (1991), pp. 51- 61. T. Huang, G. Ogasawara, S. Russell. Symbolic Traffic Scene Analysis Using Dynamic Belief Networks, in AAAI Workshop on AI in IVHS, Washington D.C., 1993. Klaus-Peter Karmann, Achim von Brandt. Moving Object Recognition Using an Adaptive Background Memory, in V Cappellini (ed.), T ime- Varying Image Processing and Moving Object Recognition, 2, Elsevier, Amsterdam, The Netherlands, 1990. M. Kass, A. Witkin, D. Terzopoulos. Snakes: Active Con- tour Models, International Journal of Computer Vision 1 (1988) 321-331. M. Kilger. A Shadow Handler in a Video-based Real-time Traffic Monitoring System, in IEEE Workshop on Ap- plications of Computer Vision, Palm Springs, CA, 1992, pp. 1060-1066. U. Kjaerulff. User’s Guide to dHUGIN, Institute of Elec- tronic Systems, Aalborg University, 1993. D. Keller, N. Heinze, H.-H. Nagel. Algorithmic Character- ization of Vehicle Trajectories from Image Sequences by Motion Verbs, in IEEE Conf. Computer Vision and Pat- tern Recognition, Lahaina, Maui, Hawaii, June 3-6, 1991, pp. 90-95. D. Koller, J. Weber, J. Malik. Robust Multiple Car Tracking with Occlusion Reasoning, technical report UCB/CSD-93-780, University of California at Berkeley, October 1993. D. Koller, J. Weber, J. Malik. Robust Multiple Car Tracking with Occlusion Reasoning, in Proc. Third Eu- ropean Conference on Computer Vision, Stockholm, Swe- den, May 2-6, 1994, J.-O. Eklundh (ed.), Lecture Notes in Computer Science, Springer-Verlag, Berlin, Heidelberg, New York (to appear), 1994. S. Lauritzen. Propagation of Probabilities, Means, and Variances in Mixed Graphical Association Models, in Journal of the American Statistical Association, vol. 87, no. 420, 1992. A. Nicholson. Monitoring Discrete Environments Using Dynamic Belief Networks, PhD thesis, Oxford University, 1992. A. Niehaus, R. F. Stengel. Rule-Based Guidance for Ve- hicle Highway Driving in the Presence of Uncertainty, in Proceedings of the 1991 American Control Conference, 1991. J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann Pub- lishers, San Mateo, CA, 1988. J. R. J. Schirra, G. Bosch, C. K. Sung, G. Zimmermann. From Image Sequences to Natural Language: A First Step towards Automatic Perception and Description of Motion, Applied Artijicial Intelligence 1 (1987) 287-307. R. Shachter, C. Kenley. 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1,664 | Sensible Decisions: Towar Invariants eoretic Infor Keiji Kanazawa* Computer Science Division University of California Berkeley, California 94720 kanazawa@cs.berkeley.edu Abstract We propose a decision-theoretic notion of invariance in bounded rational decision making. We show how optimal decision making in sensory robotics can be approximately preserved under transformations of the decision rule. In par- ticular, we present a decision theoretic analysis of the use of visual routines in action arbitration in real-time robot soccer. In this domain, stochastic dominance, and therefore deci- sions, can be sensed approximately from the environment, and we exploit this in our decision making. Introduction The world demands behavior that is immediate, and yet guided by the anticipated consequences of observed events. As designers of autonomous agents, we seek robustness in agent behavior in the face of uncertainty. Decision theory and game theory (Savage 1954; von Neumann & Morgen- stern 1947) are normative theories of action with optimal prescriptions about rational behavior. Applying these theo- ries is often a battle with computational complexity (Cooper 1990). The space of possible contingencies is typically large, and guaranteeing an agent’s response time to external events often requires trading off the optimality of the agent’s decisions. For this reason, there is great interest in theories of qual- itative probability and decision theory incorporating, for example, technology from nonmonotonic reasoning (Gold- szmidt 1993). We propose a new point in the spectrum of qualitative decision-making, a continuous counterpart to symbolic qualitative reasoning. Our theory attempts to shed light on the informational utility of certain classes of geo- metric relations and perceptual cues. Sensors that detect *This work was performed while the author was at the Uni- versity of British Columbia and was supported by the Canadian Institute for Robotics and Intelligent Systems Group B5 and by Natural Sciences and Engineering Research Council of Canada Operating Grant OGP000928 1 awarded to Alan Mackworth. The author is currently supported by the State of California PATH MOU-130. Thanks to Rod Barman, Craig Boutilier, Tom Dean, Michael Horsch, Stuart Kingdon, Jim Little, Alan Mackworth, David Poole, and Michael Sahota for comments and useful sug- gestions about this work. these relations and aspects are seen as incorporating a kind of visual qualitative probability, enabling an agent to ap- proximately sense probabilities and relationships between probabilities from the environment. Using such virtual sen- sors for answering probability queries, an agent can sub- stitute sensing for expensive probability computations in decision-making. Rather than being a purely symbolic the- ory, our approach points the way toward the embodiment of qualitative probability in systems dynamically sensing and interacting with their environments in real-time. Concretely, we adapt visual routines (Ullman 1983) to extract geometric information that accurately or approxi- mately indexes optimal actions in the control of soccer- playing mobile robots. We exploit this under a notion of decision-theoretic information invariance, where approxi- mately optimal transformations in an agent’s decision rules can lead to improved performance with bounded loss in decision quality. The Soccer Domain The Laboratory for Computational Intelligence at the Uni- versity of British Columbia has been undertaking a project called Dynamo centering around mobile robot soccer (Bar- man et al. 1993). Soccer is a highly dynamic domain ideal for research in bounded rational decision-making. It is characterized by continual activity, direct physical ma- nipulation, distributed interacting agents (friendly, hostile, and neutral), and a high degree of uncertainty. Dynamo soccer involves small off-the-shelf radio- controlled toy cars, which we call Dynamites, playing on a ping-pong table-sized field (Figure 1). All sensing and computation is off-board. A ceiling-mounted camera tracks movements of the vehicles and the soccer ball. Color coding of the vehicles and ball simplifies tracking enabling frame rate (60Hz) measurement of position, orientation, and ve- locity of all objects. The vehicles can be commanded at 60Hz as well; actual lag depends on the controller used. Members of the Dynamo group’ have implemented a layered control architecture with vehicle and ball trajectory planning and demonstrated it in real games of Dynamite ‘Principally Michael Sahota, Rod Barman, and Stuart Kingdon. Perception 973 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Figure 1: Dynamites playing soccer. a soccer (Sahota 1994). The state of the art in this experimen- tation has been two robots playing against each other. This author is currently investigating algorithms to incorporate more players. In the remainder of this paper, we outline an analysis of work toward this end. Visual Routine Arbitration for Soccer We are interested in applying decision-theoretic and game- theoretic principles in Dynamite controllers. In this paper, we develop a simple visual routine-based decision rule for a soccer task, and contrast its decisions with probabilistic and decision-theoretic algorithms. In the process, we hope to show that adopting a biologically-inspired algorithm need not conflict with being a good Bayesian. The theory of visual routines is due to Ullman (Ullman 1983). Visual routines theory assumes the existence of a small set of primitive visual operators that perform com- putations on a scene or image. Examples of operators are line projection (drawing “ rays”), detecting intersections of rays, measuring distances, and filling regions with color. A visual routine is a pattern of activity of visual operators to extract intermediate-level information from an organism ’ surroundings. A visual routine is like a subroutine built out of the primitive computations of visual operators. A visual routine can, for example, detect if a point is in an enclosed region in an image by color-filling from the point outward (Chapman 1992). A visual routine might also, for example, help pool players with projection of ball trajectories. Visual routines theory was developed as a model of biological vision. It was applied to video game play- ing by Chapman and Agre (Agre & Chapman 1987; Chapman 1992). Dynamite soccer is similar to their video games, especially in our current configuration with a cam- era that has a complete bird ’ eye view of the game playing area. Thus it is at least plausible that Dynamites can apply visual routines fruitfully. After all, humans must use vision or at least some form of visually-mediated computation to play soccer. In this paper, we consider the use of visual routines in a Dynamite ’ decision2 to shoot the ball to score or pass to a team mate (Figure 2). 2As noted, all computation is off-board; we may loosely speak of a Dynamite ’ s decision to refer to the decisions of its off-board controller. Figure 2: The shoot-or-pass decision. Filled circles are friends, white circles enemies. M is me, F is friend, E is enemy, and G is goalie. B is the ball. The two longer arrows are projected trajectories for shoot and pass. In the shoot-or-pass scenario, a Dynamite is close to the ball, and it is trying to assess whether to aim directly for the goal to try to score, or to pass the ball to its team mate instead. Using visual routines, a Dynamite can roughly estimate the possibility of the enemy intercepting its shot or pass. The visual routineprocessor (VRP) is the actual “ that performs visual operations. The VRP is able, for exam- ple, to measure distances by the magnitude of the scan path from a point to another point. For the shoot-or-pass sce- nario, a VRP might compute the likely paths of the ball and vehicles by projecting rays on the basis of current direction and velocity (or other assumptions about the likely course of the objects). Intersections of the rays indicate likely points at which objects may collide. Thus we can use the VRP as an estimator of whether an enemy intercept has a chance of succeeding by comparing the projected times of the en- emy and ball to intersections of their possible trajectories. Such estimates are typically coarse; fine motion, actions by friends, and many other details are ignored by the VRP in its projections. In the following, we refer to the visual-routines based controller as the visuaZ routine arbitrator (VRA). A VRA decision rule might be: if el el fi then safe-for-shoot then shoot se if safe-for-pass pass se shoot-out-of-range where safe-for-shoot and safe-for-pass arevi- sual routines that act as oracles on the safety (unlikelihood of intercept) of different shots. Alternatively, a Dynamite could make its decision on the basis of a game theoretic model. Dynamite soccer is a perfect information zero-sum game; thus a maximin strategy is optimal. For example, we could assume that the enemy will compute its fastest path to the likely path of the ball 974 Perception and beeline for the intersection. Maximizing our expected utility on that basis yields our optimal action. A decision theoretic arbitrator (DTA) for such analysis might incorporate, for example, a Markov decision pro- cess model of the temporal behavior of friends, foes, and the ball. The Markov decision process model includes a stochastic model of the domain, a utility function modeling preferences over outcomes, and assumptions about enemy actions. The stochastic model involves state variables such as the position, orientation, and velocity of vehicles and the ball; the utility function may say that scoring is good, and that intercept is bad. The expected utility of an action a is c, P(w]a)U(w), where each w is a possible state result- ing from executing a. Decision theory prescribes a rational agent to undertake the action b that has the maximum ex- pected utility. The number of states w is of exponential order, and the problem of finding the action with maximum utility is NP-hard (Cooper 1990). Decision-theoretic Information Invariants The main thesis of this paper is that we can substituteexpen- sive decision-theoretic computation by simple visual com- putations with bounded loss in the optimality of the deci- sions made. We capture this with the notion of decision- theoretic information invariance. Recently, Donald and colleagues (Donald, Jennings, & Rus 1993) and Horswill (Horswill 1993) have introduced theories of program transformation focusing on the invari- ance of the input/output behavior of sensory-robotic control programs. Roughly speaking, two programs are informa- tionally invariant (borrowing Donald’s terminology) if they achieve the same results in the same situations. The idea is to determine what information and computation is actually important in executing a task. The theory proposed here is similar, but whereas previ- ous work focused on deterministic relations in computing decisions, we use decision theory and game theory as our basis for selecting control outputs. In the abstract, we can evaluate a program transformation on the basis of the ex- pected utility of adopting the transformation. In this paper, we assume that utility is defined in such a way that the expected utility is just the probability that a transformed control program agrees with an optimal deliberator. As an example, consider the shoot-or-pass decision. In the following, let s stand for shoot, p for pass, and i for intercept. In selecting the optimal action, a DTA compares the expected utilities of shoot and pass: EU[s] and EU[p]. Each EU is the expectation of the utility over possible out- comes, e.g., U[i]P[i(s] + U[li]P[+js] is the expected utility of shoot. Under the reasonable assumptions of zero utility for intercept and positive utility for no intercept, the DTA’s decision is based on the following: Jwsl L ~WPI U[+]P[+] 5 U[+]P[+lp] kP[+] < P[%lp] The constant k is the quotient of the utilities of no intercept Figure 3: Using the VRP to bound intercept probability. of shot and pass (in general, the utility of the no intercept outcome is dependent on the action). Let us suppose for now that k = 1: i.e., we interpret the utilities “myopically” as intrinsic utility of not getting intercepted. This assumption will be relaxed later on. Under this assumption, we find that, comparing two ex- pected utilities is equivalent to comparing two probabilities in our case. All we need then is a reliable and efficient ora- cle for the probability comparison.3 In the next section, we analyze the applicability of visual routines as such oracles. Analyzing the Visual In the following, we analyze an intuition that VRA decision rules based on distance measurement approximate more de- tailed intercept probability computations that a DTA might perform. Assume for now that the ball and enemy have constant velocity, and that the enemy is holonomic and can switch directions instantly. A VRP can then make projections about enemy intercept by (1) projecting a ray corresponding to the ball trajectory, (2) project a ray from the enemy to the ball trajectory, (3) mark the intersection, and (4) measure the distances of each line segment (ball and enemy) to the intersection (Figure 3; I is an intersection, D-E is enemy’s distance to the intersection, D-B that for the ball.). If the velocities of the enemy and ball are the same, then the distance approximates the probability of success or intercept of the shot relative to that intersection in the following sense: if the enemy is farther than the ball from the intersection, then the probability of success is higher than the probability of intercept. If enemy is closer than the ball to the intersection, then the probability of success is lower than that of intercept. If one is much greater than the other, then the probability accordingly changes. If the velocities of ball and enemy are not the same, then we adjust the distances with appropriate factors of proportionality. 3Depending on performance characteristics desired, and given rules whose reliability and efficiency are known, we can build a control system that approximates an optimal DTA with known error and performance. This is similar to control of inference using “anytime” and “contract” algorithms (Dean & Boddy 1988; Zilberstein 1993). Perception 975 Thus, in the soccer scenario, sensing of distance quali- tatively substitutes for probability assessment. In a loose sense, we sense probability approximately from environ- mental cues. Equally importantly, we approximately sense stochastic dominance and other relationships between prob- abilities. Thus, the VRA is an oracle for the expected utility comparison of the previous section. Just how approximate is the VRA as an oracle? It is easy to see that proportionality in the probabilities is not likely to be preserved except very roughly. In the following, we present an analysis of the accuracy of the VRA. Bear in mind that ours is but a coarse analysis with many simplifying assumptions. There are different criteria that apply in considering the competitiveness of decision rules for soccer; an objective criterion is that a decision rule win soccer games consis- tently. We propose to eventually obtain such experimental data, but first, we wouldlike to have an idea of what we hope to gain from experiments. In this paper, we restrict ourselves to analyzing inference quality not over whole games, but in the context of “plays” within games. We evaluate the VRA on its own terms, in terms of what it is trying to compute (namely, the likelihood of intercept or success) rather than its overall utility in soccer playing. To begin with, we assume holonomic vehicles and that the enemy will beeline to the shortest intercept path. We also assume that we are ready to hit the ball so that we do not need to worry about the time or path it takes to hit the ball in the first place. The analysis outlined below can be extended to incorporate this easily. Given the assumptions, the problem boils down to the following. The inputs are Db and De, the distances, respec- tively, of the ball and the enemy to their intersection point, computed by the VRl? How accurately does comparison of Db and D, reflect the probability of success and failure of the shot? The assumption, of course, is that a DTA would compute its decisions based on as accurate as possible an assessment of this probability. To estimate the robustness of the VRA, we need descrip- tions of likely ball and vehicle motion. In particular, we need their uncertainty to be captured by probability distri- butions. In our case, due to the large variability in speed, it is reasonable to assume normal deviates for these param- eters. As usual, a normality assumption simplifies certain aspects of analysis, but it is not a necessary one. We only require that there be some form of probabilistic estimate. What we wish to know is the likelihood that a VRA deci- sion rule is correct. We have analyzed this likelihood based on a variety of assumptions and also on several different VRA decision rules. We do not have the space to present all of our analyses. Instead we outline an important basic case to give a flavor of the analyses involved. Our basic analysis concerns the probability of a correct VRA prediction: P[VRA predicts success A success 1 a] + P[VRA predicts intercept A intercept 1 a] probability that the VRA predicts success for a shot and the shot actually succeeds. The other case can be derived from this case. The VRA’s decision algorithm is based on the relationship ^ ^ 4 < 3 where : is the VRA’s estimate of . . We can rewrite t&3 as bb . ve < be + vb. what We wish to estimate is P[& . Ve < De . vb A success la]. The conjuncts are conditionally independent given initial conditions and in this case, the desired probability is P[& . ri, < D, . rib ) a] x P[ success (a]. We assume that the VRA’s estimates given initial con- ditions are fixed. Thus the first conditional probability is simply either 1 or 0. How can we determine likelihood of success of a shot? It is reasonable, at least to a first approx- imation, to estimate this using the same relationship as the VRA (integrated with respect to Db, D,, Vb, V,): P[& * ve < D, + &,I&$,, vb, Ti,l = /J/J In the first integral, f is the joint density of all the random f(&,De, b, ve@brD^e, vb, ri,> Db. v,d),. vb variables. We can rewrite it as the second integral because = JJJJ all the random variables are conditionally independent, and f(Db Ifib>f(De I@df-(v, I Ijblf(ve I lie) &,.ve<De,vb each random variable is only dependent on its estimate. The resulting integral can be estimated, in principle, for any set of integrable densitiesf(.). In our case, we have assumed that eachf(VIv) is normally distributed. Each f(D I@ parameterizes the uncertainty in actual distance given a distance measurement. In the Dy- namo testbed, we have determined that the vision system estimates positions and distances accurately to l/lOOth of an inch. Thus it is reasonable to assume that each distance estimate is correct, thereby removing its uncertainty. Given the preceding, the VRA’s decision rule can be based on the relation %rie < vb where Db and D, are assumed to II be constants. OG probability estimate becomes JJ f(vb 1 vb)f(ve 1 li,)dvbdv, 2 ve<vb So what are thef(.)? The VRA has many choices on what to adopt as its speed estimate. Some reasonable ones are (1) initial velocity, (2) mean velocity and (3) lower or upper bound (lower bound for ball, upper bound for enemy). If the VRA uses mean velocity, then each conditional distributionf(V. IV.) is just the normal distribution that we have as the estimate of velocity. JJ N(/-b cb, Vb)N(/Je, ge, VeWbdVe @e<vb Although we cannot derive a closed it is trivial to estimate numerically. form for this integral, where a! are the initial conditions. We first analyze the 976 Perception 1”.“8 l”6 El oqeg Success Overall 0.85 0.90 Table 1: VRA accuracy: “Success” is the accuracy for only the success case, and “Overall” is the accuracy also including intercept. k Success Overall 0 0.85 0.90 1 0.96 0.85 2 0.99 0.75 Table 2: A “cautious” VRA predicts success well but it is poor overall. So now, we can estimate the probability that the VRA predicts success and actual success occurs for a particular initial condition. The probability of intercept is the comple- ment of the probability of success. The probability of VRA correctness for a particular initial condition is simply one or the other probability, depending on what the VRA predicts. The likely overall accuracy of the VRA is the expectation of VRA correctness over the possible initial conditions. In our analysis, we have simply assumed that all initial condi- tions are equally likely. We estimated the mean and variance for enemy speed as 3.0 and 0.5, and that for the ball as 1.8 and 0.6. Given these assumptions, our estimate of the VRA accuracy is 0.90. As we can see, provided that our assumptions are valid, the VRA’s estimate is quite competitive. Of course, what approximations are acceptable depends on the problem and the domain. Given that the VRA effectively ignores the variability in velocities, a 10% loss does not seem bad con- sidering the simplicity of the decision algorithm, and the computational complexity of decision theoretic inference. By varying speed parameters, it is possible to see that the VRA does best where the uncertainty in velocity is lowest. Conversely, if the mean velocity is a poor predictor of actual velocity, then the VRA will naturally not do as well (Table 1). Here is another estimate when the VRA is cautious, using a minimax criterion, assuming high speed for the enemy and low speed for the ball (Table 2). For example, we choose p f ka, where p and g are parameters for the normal density lower/upper bounds. The higher k is, the more “cautious” the estimate. More importantly, we can extend our analysis to derive the likelihood that a VRA will serve as a good oracle for the probability comparison of Section 4. We adopt the following as our VRA: if shoot-safer-than-pass then shoot else Table 3: VRA accuracy for probability comparison. pass fi This VRA computes the same decision as the DTA provided that the visual routine shoot-safer-than-pass is a reliable probability comparator. To compare shoot and pass, our inputs include distances of enemy and ball for both shoot and pass. Let Df be distance for shoot and L?’ be distance for pass. Then we have D& D”,, L$, @, and we also have velocity estimates as before. What we wish to estimate is the likelihood, given ini- tial conditions, that P[successIpass] < P[successlshoot] istruewhen shoot-safer-than-pass returns true, and P[successIpass] > P[successJshoot] when the visual routine returns false. The VRP estimates this by compar- ing likely travel times of ball and enemy to their intercept point. Let T = D/V be the time of travel. The VRP esti- mates P[successjpass] 5 P[successlshoot] by the relation 5 5 g. It is easy to see that this is equivalent to b b (1) Thus, the VRP estimate is independent of the velocities of the ball or enemy; it depends only on the distances. All that remains is to determine, given a VRP estimate by (I), if the predicted relation actually holds. The actual probabilities can be estimated, for example, by the same method as before. Under our assumptions about enemy and ball behavior, we find that the VRA is a highly accurate predictor of the probability relation, and thereby of the optimal decision (Table 3). If we use the VRA as an oracle for probability comparison, we achieve about 0.99 accuracy without having to engage in any probability computation (but at the expense of some vision computation). Thus, the optimality of an agent is almost invariant under substitution of a DTA with the VRA. Recall that earlier in the paper, we made an assumption that the utility of no intercept was the same for both shoot and pass, i.e., k was assumed to be 1 in the relation below: kP[successJshoot] 5 P[successlpass] It should be easy to see that it is straightforward to modify the visual routine decision rule in Equation 1 to incorporate k. Thus, for this problem, the visual routine decision rule can compute relations not only between probabilities, but between expected utilities as well. We are currently ex- tending the analysis of this paper so that the visual routine takes into account the probability of success of a shot by the friend, given that a pass succeeds. Perception 977 The analysis that we have performed here is for a special simple case. It is effectively an analysis of the sensitiv- ity of control output to the type of algorithm used. It is related to work in value of information (Howard 1966), “anytime” and “contract” algorithms(Dean & Boddy 1988; Zilberstein 1993), and approximation and abstraction in Bayesian networks (Provan 1993). In addition to work presented here, we have performed analyses using differ- ent assumptions about enemy and ball behavior and their uncertainty. For example, we have performed analyses in- corporating steering uncertainty in addition to uncertainty about vehicle velocity. As might be expected, the effect of this is not great unless there is a lot of uncertainty in the steering drift. We are currently in the process of extending our analysis to a case where the enemy simply servos to the ball position. Finally, we have evaluated both simpler and more complex VRA metrics, for example, comparing only the distance of the enemy to the ball trajectory (ignoring velocity and ball distance). In a longer version of the paper, we will present these results as well as proofs about the reliability of the VRA as a probability comparator for the shoot-or-pass decision. Conclusions What we have tried to do in this paper is to back our intuition about the suitability of visual routine-based algorithms for the soccer domain with formal analysis. In the process, we discovered that under certain assumptions, the visual routine arbitrator is a good approximation to an optimal rational decision-maker. In the problem we studied, we find that the essence of decision-theoretic optimization computation is captured by geometric relations that can be discovered by visual routines. Our analysis, although reassuring to the Bayesian in that it quantifies the robustness of different decision rules, is not meant as an end in itself. It is but a first step, and much remains to be done. First of all, although the VRA clearly involves simple computation, we need a concrete analysis of the performance gains obtained by using the VRA. Sec- ondly, we would like to remove various assumptions made about vehicle dynamics and enemy behavior. We would also like to extend our analysis to other domains where probability can be considered to be sensed both actively and peripherally. In general, we are interested in develop- ing tools for continuous game theory and control involving sensing and interaction with a dynamic environment. Last but not least, we are currently in the process of implement- ing a simple visual routines processor for testing the VRA in experiments. References Agre, P. E., and Chapman, D. 1987. Pengi: An implementation of a theory of activity. In Proceedings of the Sixth National Con- ference on Artificial Intelligence, 268-272. Seattle, Washington: AAAI. Barman, R.; Kingdon, S.; Mackworth, A.; Pai, D.; Sahota, M.; Wilkinson, H.; and Zhang, Y. 1993. Dynamite: A testbed for multiple mobile robots. In Proceedings of the 1993 ZJCAZ Work- shop on Dynamically Interacting Robots. Chamber-y, France: IJCAII. Chapman, D. 1992. Vision, Instruction, and Action. Cambridge, Massachusetts: MIT Press. Cooper, G. F. 1990. The computational complexity of proba- bilistic inference using bayesian belief networks. Artificial Zntel- ligence 42(2-3):393405. Dean, T., and Boddy, M. 1988. An analysis of time dependent planning. In Proceedings of the Seventh National Conference on ArtiJicial Intelligence, 49-54. Minneapolis, Minnesota: AAAI. Donald, B.; Jennings, J.; and Rus, D. 1993. Towards a the- ory of information invariants for cooperating autonomous mo- bile robots. In Proceedings of the International Symposium on Robotics Research (ISRR). Goldszmidt, M. 1993. Putting Qualitative Probability to Work Workshop. Horswill, I. D. 1993. Specialization of Perceptual Processes. Ph.D. Dissertation, MIT, Cambridge, Massachusetts. Howard, R. A. 1966. Information value theory. IEEE Transac- tions on Systems Science and Cybernetics 2( 1):22-26. Provan, G. 1993. Tradeoffs in constructing and evaluating tem- poral influence diagrams. In Proceedingsof the Ninth Conference on Uncertainty in Artificial Intelligence. Sahota, M. 1994. Reactive deliberation: An architecture for real- time intelligent control in dynamic environments. In Proceed- ings of the Twelfth National Conference on Artificial Intelligence. Seattle, Washington: AAAI Press. To appear. Savage, L. J. 1954. The Foundations of Statistics. Dover. Ullman, S. 1983. Visual routines. AI-Memo-723, MlT Artificial Intelligence Laboratory, Cambridge, MA. von Neumann, J., and Morgenstern, 0. 1947. Theory of games and economic behavior. Princeton: Princeton University Press, 2nd edition. Zilberstein, S. 1993. Operational Rationality Through Compi- lation of Anytime Algorithms. Ph.D. Dissertation, University of California, Berkeley, California. !I78 Perception | 1994 | 39 |
1,665 | irical luatio Henry Kautz and Bart Selman AI Principles Research Department AT&T Bell Laboratories Murray Hill, NJ 07974 (kautz, selman)@research.att.com Abstract Computational efficiency is a central concern in the design of knowledge representation systems. Compiling a knowledge- base into a more tractable form has been suggested as a way around the inherent intractability of many representation for- malisms. Because not all theories can be put into an equiva- lent tractable form, Selrnan and Kautz (199 1) have suggested compiling a theory into upper and lower bounds (one logi- cally weaker, the other logical stronger) that approximate the original information. A central question in this approach is how well the bounds capture the original knowledge. This question is inherently empirical. We present a detailed empirical evaluation of the compilation of two kinds of theories: computationally challenging randomly generated theories, and propositional encodings of planning problems. Our results show that one can answer a very high percentage of queries even using unit clause bounds, which are much easier to compute than more general tractable approximations. Furthermore, we demonstrate that many of the queries that can be answered by the bounds are expensive to answer using only the original theory: in other words, knowledge compilation does not just “skim off” easy queries. In fact, we show substantial total computational savings in using the bounds together with the original theory to answer all queries (with no errors) from a large benchmark set, over using the original theory alone. This study suggests that knowledge compilation may indeed be a practical approach for dealing with intractability in knowledge representation systems. Introduction In the design of knowledge representation systems, the tradeoff between expressive power and computational tractability has been studied extensively. Unfortunately, the languages that allow for efficient inference are often consid- ered too restrictive. One way around this issue is to employ some form of knowledge compilation. The idea is to let the user enter statements into the knowledge base (KB) in an unrestricted language, and have the system subsequently translate the information into a tractable form. Since an exact translation is often not possible, Selman and Kautz (1991) propose to approximate the original theory by using two bounds, one logically weaker (the upper bound) and the other logically stronger (the lower bound). As an example, they consider compiling general propositional theories into two approximating Horn theories. Certain queries can be answered quickly by using the bounds, as will be described below. Though theoretically appealing, the practical value of knowledge compilation will depend on how well the bounds approximate the original information. In other words, what fraction of the incoming queries can be answered quickly by using the bounds? We would also like it to be the case that among those queries that can be answered with the bounds, there are queries that cannot be answered easily using the original theory (i.e., the bounds are not just “skimming off” the easy queries). We will first show, by using a general complexity- theoretic argument, that there do exist theories for which answering certain queries using the bounds is much eas- ier than answering the same queries on the original theory. This argument reveals the existence of such theories and queries, but does not rule out the possibility that one would rarely encounter them in practice. We therefore also under- took an empirical evaluation of the knowledge compilation approach. We considered two classes of theories: hard random theories and propositional encodings of planning problems. We compile those theories, and give experimen- tal data which shows that the compilation leads to dramatic computational savings. In order to conduct our experiments, we needed theo- ries that were sufficiently challenging, so that answering queries would take a reasonable computational effort; oth- erwise there would be no need for compilation in the first place. For the random theories, we used the hard problem class as identified in Mitchell et al. (1992). For our plan- ning problems, we constructed a simple autonomous robot domain. To our surprise, planning problems that would intuitively appear quite hard were often answered almost instantaneously by the standard Davis-Putnam satisfiabil- ity procedure (Davis & Putnam 1960). In fact, we were able to prove that a very general class of such problems can be solved in linear time by unit propagation (a standard component of satisfiable procedures), even though many AI planning systems would find them very difficult. Af- ter identifying this class of “easy” planning problems, we were able to construct a planning domain that is provably computationally difficult, as was needed in our evaluation Automated Reasoning 155 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. of knowledge compilation. The form of knowledge compilation examined in this pa- per is based on approximations between logical languages that fall into different classes in the hierarchy of computa- tional complexity. The term “knowledge compilation” is used more broadly in the expert systems community to refer to a wide variety of work that aims to increase the efficiency of such systems. Much of this work develops techniques for transforming “deep” functional models of devices to “shallow” diagnostic rules (Chandrasekaran & Mittal 1983; Keller 1991). The output of such systems does not cor- respond to either an upper-bound or a lower-bound in our sense; while some information may be lost in the com- pilation process (as with our upper-bounds), the compilers themselves introduce domain-specific information about di- agnosis. Others view knowledge compilation as a kind of automatic programming, with the goal of converting a sys- tem specification to an implementation that exactly satifies it (Dietterich 1991). Bylander (1991) provides a high-level logical characterization of some different kinds of knowl- edge compilation; interestingly, he argues that forms of knowledge compilation based on approximations (as is ours) are unlikely to provide significant computational improve- ment. However, his argument is based on the assumption that the compilation process itself must be tractable, which we explicitly reject. Knowledge Compilation by Theory Approximation Selman and Kautz (1991) define knowledge compilation by theory approximation as follows. Assume that we have a logical theory Z=. One can approximate X by two theories &-, and Es& that are in a given tractable logical language. The approximation is such that xglb b Z= + &b. So, xslb is logically stronger than the original theory, and is called a greatest lower bound (GLB); and &ub is logically weaker than the original theory, and is called a least upper bound (LUB).l The bounds are the best ones possible, given the particular tractable language. This means, for example, that there does not exist a tractable theory 2 that is not logically equivalent to the xglb and is such that x:glb b Xc’ b Xc. The LUB of a theory is unique, but there can be several distinct GLBs. Let us consider an example of approximating a general propositional theory by two bounding Horn theories. We take X = (la V c) A (lb V c) A (a V b). (a, b, and c are propositional letters.) The Horn theory a A b A c is an example of a Horn lower-bound; both a A c and b A c are GLBs; ( TZ V c) A (lb V c) is an example of a Horn upper- bound; and c is the LUB. These bounds can be verified by noting that KC-Query(a) if xi&, k Q! then return “yes” else if xgib k Q! then return “no” else determine whether Z b a! using a general theorem prover and the original theory. Figure 1: Fast querying using theory approximation. The original theory is Z; X lub and &lb are its approximations; and a! is the query. Moreover, there is no Horn theory ;C’ logically distinct from a A c such that (u A c) k Z’ b Z. Similar properties hold of the other GLB and of the LUB. Instead of compiling into Horn theories, one can choose to compile into other tractable propositional theories, such as a set of unit clauses (i.e., a conjunction of literals) or a set of binary clauses. Our experiments below show that even unit bounds lead to substantial computational savings. Fig. 1 shows how the bounds can be used to improve the efficiency of a knowledge representation system. The system first tries to obtain an answer quickly by using the bounds, which can be done in linear time for Horn (Dowl- ing & Gallier 1984) or unit bounds. In case no answer is obtained, the query is tested directly against the original theory. Note that KC-Query thus remains a complete pro- cedure. A time-saving alternative would be for the system to simply return “don’t know” if the bounds do not answer it. The system can thus answer certain queries in linear time, resulting in a improvement in its overall response time. Ex- actly how many queries can be handled directly by the ap- proximations depends on how well the bounds characterize the original theory. Computational Savings The key question concerning knowledge compilation is whether it will lead to an actual savings in computational effort. For example, it could be the case that queries an- swered by the approximating bounds can also be answered quickly using the original theory. An obvious counterex- ample is any inconsistent theory. Compilation yields an inconsistent upper bound. Any query against this bound would quickly return “yes” (see Fig. 1). However, evalu- ating a query against the original theory would in general involve proving that the theory was inconsistent, which is NP-complete. Of course, most interesting knowledge bases will be con- sistent. Let us therefore consider a consistent theory that is equivalent to a Horn theory, but is not in Horn form. Clearly, all queries can be answered efficiently against the bounds. However, it is not the case that a theorem prover could also answer queries efficiently against the original theory. This can be shown using a result by Valiant and Vazirani (1986). They show that even if a propositional theory has a single model (and is thus trivially equivalent to a Horn theory), finding the model is still intractable (unless NP # (a A b A c) j= (u A c) + X + c b ((la V c) A (lb V c)). ‘The terminology is based on a model-theoretic view of the approximations. Note that the models of, for example, the &lb form a subset of the models of X. We are interested in a largest possible subset. For another approach to approximating logical theories, see Dalal and Etherington (1992). 156 Automated Reasoning RP, which is unlikely). Therefore, there cannot exist a theo- rem prover that efficiently handles this special case, because such a prover could be used to find the unique model of the non-Horn theory (by repeatedly testing whether each literal followed from the theory). This complexity theoretic argument shows that there ex- ist theories where compilation gives a provable computa- tional savings. Of course, this still leaves open the ques- tion whether one would encounter such theories in practice. In the next two sections, we therefore present an empiri- cal evaluation of knowledge compilation of two classes of theories. In both cases, we will demonstrate substantial computational savings. Empirical Evaluation I: Hard Random Theories In this section, we consider the compilation of hard, randomly-generated propositional theories. Mitchell et al. (1992) show that most randomly-generated theories are easy to reason with. Such theories tend to be either very over- constrained or very under-constrained; in either case, exper- iments show that answering queries is easy using the stan- dard Davis-Putnam procedure (Davis & Putnam 1960).2 However, Mitchell et al. also described how to generate computationally challenging theories. The key is to gener- ate formulas with a particular ratio of clauses to variables. For random 3CNP formulas, the ratio is about 4.3. We con- sider hard random 3CNF theories containing between 75 and 200 variables. In order to simplify the following anal- ysis, we computed bounds that consisted of conjunctions of unit clauses. Note that unit clauses are a restricted case of Horn clauses. Therefore, these bounds are not as tight as the full Horn bounds. We will show that even these bounds are useful for answering a high percentage of queries. Because the full Horn bounds are tighter, they would answer an even higher percentage of queries. However, by considering the unit clause bounds we are able to provide a simple exact analysis. We began by generating a set of 40 random 3CNF theo- ries, with 10 each based on 75100,150, and 200 variables. Then we computed the unit LUB and a unit GLB of each. Table 1 gives the median size, in literals, of the LUB and GLB for each size theory. The bounds were computed us- ing the algorithms as given in Selman and Kautz (1991), adapted for generating unit bounds. We generated the op- timal bounds. Computation time for the unit LUBs ranged from 5 minutes for the 75 variable theories, to one hour for the 200 variable theories. (All experiments were run on a 1OOMhz SGI Challenge.) Computation of the unit GLBs ranged from 1 minute to 5 minutes each. 21f the theory is over-constrained, it is generally unsatisfiable, so that all queries trivially follow. If it is under-constrained and the CNF query contains short disjunctions, then the query almost certainly does not follow. Finally, if the theory is under-constrained and the CNF query contains only long disjunctions, then the query almost certainly does follow, which can be easily shown by adding the negation of the query to the theory and using the Davis-Putnam procedure with unit propagation to show inconsistency. vars clauses size unit size unit percent queries answered LUB GLB unit binary ternary 75 322 53 71 100% 85% 88% 100 430 57 93 100% 76% 79% 150 645 62. 139 100% 66% 66% 200 860 132 188 100% 83% 85% Table 1: Statistics for compiling and querying hard random 3CNF theories. The percentage of queries that could be answered by these bounds, as given in Table 1, is computed using some basic probability theory. We assume that we are dealing with single-clause queries drawn from a uniform fixed-clause length distribution. The simplest case is the unit clause queries. All unit clause queries can be answered using only the unit LUB, because this bound is complete for such queries. Thus this column is 100% for every size theory. Next, let us consider the more interesting case of binary queries. Let a V y be a random binary clause, where x and y are distinct and not complements. We wish to compute the probability that the bounds answer the query, given that the unit LUB is of size 1 and the unit GLB is of size m, and there are N variables in the theory. That is, we wish to k X v Y) or &lb Y 25 v Y)) compute pr( (xlub which equals P$&b t- - x v y) + p?‘(xglb y x v Y> because the two possibilities are disjoint. A disjunction is entailed by a set of literals if and only if one of the disjuncts is so entailed. Thus, p~(&ub i- x v Y) = Pr((&ub t- xc> or (&ub t- Y)) This quantity is equal to p+lub t- a) + @lub t- Y) - (&ub + z A Y) The first and second terms are equal to the odds of picking a random literal that is in the LUB, namely 1/( 2N). The third term is equal to the number of ways of choosing two distinct literals from the LUB, divided by the number of ways of choosing two distinct, non-complementary literals, namely 1(1 - 1)/((2N)2(N - 1)). Thus, P?-&b I- a: v y) = 4+-- I? l(1 - 1) 2N 2N 4N(N- 1) using a similar calculation, we can calculate Pr(&b t- x V y). Combining the probability that the LUB answers the query with the probability that the GLB answers the query results in the expression 1 4N( m-1)-3(m-1)+12-m2 - 4N(N - 1) The value of this expression was used to complete the “bi- nary” column of Table 1. Automated Reasoning 157 Table 2: Time in seconds to answer 1000 random queries. The probability that the bounds answer a random ternary query can be similarly derived, and was used to complete the final column of the table. As we can see from Table 1, the percentage of queries that can be handled by the unit clause bounds is quite high. Note that the queries handled by the bounds can be answered in linear time. The Davis-Putnam procedure, however, scales exponentially on the queries considered in the table (this follows from the experiments in Mitchell et al. (1992)). Thus, this suggests that knowledge compilation on such hard randomly-generated theories should have a clear payoff. We verified the computational savings suggested by the preceding analysis by implementing the fast querying al- gorithm shown in Fig. 1, and testing 1000 random binary and 1000 random ternary queries against each of the 40 test theories. In case both bounds failed to answer a query, it was tested against the original theory using an efficient implementation of the Davis-Putnam procedure called “tableau”.3 Table 2 lists the average time to run each batch of a 1000 queries, using the bounds together with tableau versus using tableau alone. Thus, in both cases all queries were answered. We see that knowledge compilation reduced the overall time by over two orders of magnitude on the largest theories. This eliminates the remote possibility that the bounds are only answering the “easy” queries. Earlier we invoked complexity theory to argue that in general the bounds are not limited to easy queries; these experiments verify that the bounds answer hard queries against a computationally interesting distribution of random theories. As an aside, we observe that even when we take into ac- count the time required to compile the theories, we obtain an overall time savings. For example, on the 200 variable theories, computing the bounds takes about an hour and five minutes; thus, the total time to compute the bounds and answer 1000 binary queries is 3,955 seconds, versus 12,962 seconds not using the bounds. (Note that differ- ence in overall time would increase even further when we would consider, for example, 10000 queries.) Thus in this case we have gone beyond the main objective of knowledge compilation, namely to speed query answering by shifting computational effort from on-line to off-line (compilation), and have actually reduced the total amount of work required. 3The Davis-Putnam procedure is currently the fastest known complete procedure for propositional satisfiability testing and theorem-proving on the class of formulas considered here (Buro & Biining 1992; Dubois et al. 1993). Tableau (Crawford & Auton 1993) is one of the fastest implementations of the algorithm. Finally, we observe that these positive results for random theories are quite surprising, since one would expect that their apparent lack of structure would make them hard to approximate by simpler theories. Empirical Evaluation II: Planning Formulas Planning has traditionally been formalized as first-order deduction (Green 1969; McCarthy & Hayes 1969). In this approach, a plan is basically a proof that a state- ment asserting the existence of a goal state is valid. Kautz and Selman (1992) develop an alternative formalization of planning as propositional satisfiability. They show how planning problems in typical domains, such as the blocks world, can be axiomatized so that every model of the ax- ioms corresponds to a plan. The satisfiability formaliza- tion makes it easy to state facts about any state of the world (not just the initial and goal states) and is closer in spirit to modem constraint-based planners (Stefik 1981; Chapman 1987) than is the deductive approach. We decided to evaluate knowledge compilation within the planning as satisfiability framework. The particular problems described in the Kautz and Selman paper all have unique models, corresponding to a single solution. Com- piling such formulas provides no benefit beyond finding the single satisfying model. Therefore we developed a class of planning problems that each have many different solutions. Compiling these problems allows one to evaluate quickly various queries about what must hold in all solutions, as well as to pose queries that impose additional constraints on the possible solutions. We call this domain the “mapworld”. In the basic version of the mapworld, we imagine that a robot is moving between nodes of a graph, such as the one shown in Fig. 2. (Ignore for now the section of the figure labeled “MAZE”, which will be explained later.) At each time step the robot can either stay in place or move to an adjacent node. An instance of the mapworld consists of axioms that describe a particular such graph, as well as constraints on the location of the robot at various times, up to some final instance; for example, that the robot be at node a at time 0 and at node g at final time 10. One can then pose queries to answer against these axioms, such as “Can the robot be at node f at time 2?” (obviously, no), or “Does the fact that the robot goes through node c imply that it does not go through node k?” (less obviously, this implication does indeed hold, because it takes at least 11 steps to reach g when going through both c and k). One application in which the ability to answer queries of this sort is useful is plan recognition (Schmidt, Sridharan, & Goodson 1978; Allen & Perrault 1980; Kautz 1986). For example, one may have partial knowledge about the goals and actions of another agent, and want to be able to infer the possible states the agent could be in at various times. An- other interesting application is in reactive planning systems (Agre & Chapman 1987; Schoppers 1987; Kaelbling 1988; Kabanza 1990). An important issue in such systems is how to combine reactive behaviors (e.g. move to a node if it contains food) with more global plans (e.g. visit nodes x and y before the end of the day). A possible architecture 158 Automated Reasoning a b . . : * .m..... Figure 2: The mapworld domain. for a combined system would have a reactive module that proposed actions (e.g. move to node c), which are however rejected if the axiomatization of the global planning prob- lem entails the negation of the action (i.e., the action would be incompatible with the global goals). This proposal is similar to Bratman, Israel, and Pollack’s (1988) view of plans as Jilters, but note that we suggest filtering against the whole set of possible solutions (models) of the plan- ning problem, rather than against a single one. Clearly it requires the ability to check rapidly if the proposed action is consistent with at least one solution to the global problem. The basic mapworld can be captured by the following kinds of axioms. The proposition that the robot is a node x at time i is written xi. First, there are movement axioms M, that state that the robot always stays put or moves to an adjacent node; for our example, these would include ai 1 (%+l V h+l V di+l) for 0 5 i < 10. Second, there are disjointedness axioms V, that state that the robot is only at one node at a time; for example, Ui > (lbi A *a* A lki). Finally, there are assertions that constrain the robot to be at certain locations at certain times; such positive assertions (such as (a~, 910)) are designated P, while negative asser- tions (such as {ifs}) are designated n/. Finally, we define propositions of the form aever by Xever E (⌧:0 v Xl v l * * v Xl() ) . Given these axioms, the first query above becomes “Does M U 2) U n/ U P b lf2?“, and the second becomes “Does M U V U n/ U P i= cover > l&ver?” Surprisingly, it turns out that aZZ CNF queries against a basic mapworld problem can be answered quickly, using a standard theorem- prover.4 One can prove that a simple rule of inference 41t is not surprising, of course, that an efficient algorithm ex- ists for these queries, because the lengths of the shortest paths between all points in a graph can be determined in polynomial time (Aho, Hopcroft, & Ullman 1974). What is unexpected is that the SAT encoding of the problem allows an efficient solution by a completely general theorem-prover, that does not employ a special shortest-path algorithm. called “unit propagation” is complete for such theories. Unit propagation is takes only linear time, and is part of all resolution-style theorem proving procedures, such as the Davis-Putnam procedure. In general unit propagation by itself is not a complete decision procedure. However, one can prove the following theorem (Kautz & Selman 1994): Theorem: For any basic mapworld problem and clausal query Q, we have MuVu~uP+cr if unit propagation proves that M U D U nf U P U (xx) is inconsistent. Thus, knowledge compilation is not needed in this case: unit propagation yields a linear-time decision procedure. This indicates that there are interesting computational advantages to using a satisfiability encoding for planning. For example, a standard STRIPS-style planner (Fikes & Nilsson 1971) would end up exploring (in general) an exponential number of paths before realizing that certain sets of nodes cannot be reached within a fixed time-bound. To make our mapworld more computationally challeng- ing, we generalize it by adding constraints that say that certain pairs of nodes are forbidden to appear on the same path. Such constraints often occur in real-life planning problems, where for example going through a node repre- sents consuming some limited resource. An example of such a constraint is -fever V ljever, which states that the robot cannot pass through both nodes f and j on its way to g. This change makes planning much harder - in fact, answering CNF-queries becomes NP-complete, as can be shown by a reduction frompath withforbiddenpairs (Garey & Johnson 1979, page 203). This also greatly increases the applicability of our results, because most interesting planning problems are NP-complete (Gupta & Nau 1991; Erol, Nau, & Subrahmanian 1992) and thus can be effi- ciently encoded as mapworld problems. In Fig. 2, the area labeled “MAZE” is a 30-node subgraph constructed so that all paths through it are blocked by vari- ous forbidden pairs of nodes. Disregarding these pairs, the shortest path through the maze is 5 steps long. By count- ing alone, then, one would think that was possible to go Automated Reasoning 159 11 RandBin 1 RandEver 1 Hand number queries theory oniy II 500 I 400 I 5 time 2013 8953 1071 KC-Query time 464 3748 439 Z+LUB time 580 840 6.9 KC using X+LUB time 283 617 6.8 bounds only time 5 6 1 num. answered by bounds II 376 1 144 1 2 1 Table 3: Statistics on querying mapworld with and without knowledge compilation. Time in seconds. from a to g by traversing the maze in no more than 10 steps (the time limit on the problem). It is computationally hard, however, to determine that these paths are blocked, and that in fact the robot must traverse the edge from d to e. Any query that depends on realizing this fact is also quite hard to answer. We therefore compiled the problem instance, effec- tively moving the most computationally difficult part of the reasoning off-line. (As we will see, the bounds also contain a great many other non-trivial conclusions concerning the mapworld example.) The SAT encoding of the mapworld in Fig. 2 contains 576 variables and 29,576 clauses. It takes about 4400 seconds to compute both the unit LUB and a unit GLB. The unit LUB determines the values of 341 of the variables. The GLB we found was a single model, which nonetheless was useful in query-answering. We then created three different test sets of queries: Rand- Bin is a set of 500 random binary queries; RandEver is set of 400 random binary queries, where the propositions are taken just from the “ever” predicates; and Hand is a small set of hand-constructed queries that are intuitively interesting and non-obvious, such as fever V iever. Table 3 compares the results of various ways of running the queries. For “theory only” the queries were simply tested against the uncompiled problem using tableau. The “KC-Query” row is the time required to answer all queries using the query algorithm presented in Fig. 1 that uses both the bounds and the original theory. In all cases we see a significant speed-up. In fact, the savings for the RandEver test set more than pays off the entire cost of computing the bounds. We then experimented with several variations on the ba- sic knowledge-compilation querying algorithm. For the “X+LUB” row we conjoined the original theory with its unit LUB, and then ran all queries using tableau. Note that the conjoined theory is logically unchanged (since the orig- inal theory entails its LUB), but is easier to reason with. For the RandBin test se4 this approach is not as good as the plain “KC-Query” algorithm; however, for RandEver and Hand it is considerably faster. Next, in the “KC using X+LUB” experiments we first tested each query directly against the bounds, but if they did not answer it, we then answered it using tableau with the conjoined theory. In every case this was the fastest complete method. Finally, we ran the queries against the bounds only, leav- ing some of them unanswered. In all cases this took only a few seconds for hundreds of queries. About 75% of the RandBin queries, 36% of the RandEver queries, and 2 out 5 of the Hand queries can be answered in this way. However, the great difference in speed (e.g., 5 seconds on the RandBin queries, versus 283 seconds for the fastest complete method) suggests that using the bounds alone may be most practi- cal for many real-time applications. For example, in many domains instead of relying on expensive theorem proving a system may try to obtain information by direct sensing of its environment. Conclusion We have evaluated the computational savings that can be gained by compiling general logical theories into a pair of tractable approximations. We first argued on complexity- theoretic grounds that on certain theories knowledge com- pilation must result in computational savings. We then con- sidered the compilation of two kinds of theories: hard ran- dom CNF theories, and propositional encodings of planning problems. In both cases our experiments showed that a high percentage of queries can be answered using the tractable bounds, and that the approach leads to a dramatic decrease in the time required to answer a large series of queries. This indicates that the knowledge compilation approach is useful for both unstructured, randomly generated theories, and highly structured theories such as encodings of plan- ning domains. In this paper, we obtained good performance with unit clausal approximations. An open question that we will address in future work is whether it is worthwhile to compute the more accurate, but more expensive to obtain, Horn approximations. In any case, this study has shown that knowledge compilation by theory approximation is in- deed a promising approach for dealing with intractability in knowledge representation systems. 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1,666 | Basic Meanings of Spatial Computation and Evaluation in 3D Space Klaus-Peter Gapp Cognitive Science Program, Dept. of Computer Science Universitat des Saarlandes D-66041 Saarbriicken, Germany gapp@cs.uni-sb.de Abstract Spatial relations play an important role in the re- search area of connecting visual and verbal space. In the last decade several approaches to seman- tics and computation of spatial relations in 2D space have been developed. Presented here is a new approach to the computation and evalu- ation of basic spatial relations’ meanings in 3D space. We propose the use of various kinds of ap- proximations when defining the basic semantics. The vagueness of the applicability of a spatial relation is accounted for by a flexible evaluation component which enables a cognitively plausible continuous gradation. For validating the evolved methods we have integrated them into a work- bench. This workbench allows us to investigate the structure of a spatial relation’s applicability region through various visualization methods. Introduction An important part of research in artificial intelligence deals with connecting visual and verbal space, that is, the translation of visual information into natural language descriptions. The advantage of linguistic de- scriptions in certain situations is based on the more compact possibilities of language for the transmission of information, compared to a graphical representation with the same content of information (cf. (Wahlster 89)). For generating a scene description in natural language a correct treatment of the spatial relations is essential. Spatial relations are independent from a particular language and act on a higher abstract level as a connecting link between visually perceived data and natural language. The linguistic representatives for the spatial relations are prepositions in their spa- tial meanings (cf. (Retz-Schmidt 88)). Prepositions combined with descriptions of placement, an object to be localized (LO) an a reference object (REDO), build d the class of localization expressions (Herskovits 86). Today, research and applications in 3D space are in- creasing in import ante. Thus the old definitions of spatial relations, which were mainly for 2D space, need to be extended. For example, a localization expression like “the cur in front of the house” implies not neces- sarily that the car is at exactly the same height as the house. A purely geometrical representation of the seman- tics of spatial relations is not appropriate (cf. (Miller & Johnson-Laird 76)), b ecause functional dependen- cies and pragmatic principles are not considered. We therefore propose the use of a multilevel model (cf. (Gaw 93)). 0 n a low level, just the geometrical prop- erties of the objects (basic meanings) are considered. The higher levels provide the possibility to include functional dependencies and pragmatic aspects. Our objective here is to present a computational model for the basic meanings of spatial relations which proposi- tionally describes the relationships between geometri- cal objects in 2D and 3D space. In the definition of the basic semantics of spatial relations we agree with the thesis of (Landau & Jack- endoff 93), that if people are applying spatial relations they do not account for every detail of the objects in- volved. We are therefore able to use an approxima- the algorithm, which considers only the essential shape properties of an object. The evaluation of a spatial re- lation’s applicability differs from one person to another (cf. (Kochen 74)). This phenomenon is accounted for by integrating a flexible evaluation component. The exact specification of the gradation functions will be determined through psychological experiments, which are currently in progress. To obtain a validation of the developed algorithms they have been integrated into a workbench. This al- lows us to investigate the structure of a spatial rela- tion’s applicability region through various visualization methods (Gapp 94). The workbench is part of the VI- Z’RA (Visual TRAnslator) project which deals with the relationship between vision and natural language (cf. (And& et al. 89)). Related work HanRmann (HanBmann 80) developed in the SWYS project (HuBmann & Schefe 84) a module which an- swers queries about a 2D scene in German. To express the vagueness of the spatial relations, he uses the func- Spatial Reasoning 1393 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. tions SFUNK and PF UNK of Zadeh’s Fuzzy-Set The- ory (Zadeh 65). Carsten and Janson (Carsten & Jan- son 85) developed a component in the NAOS project (Neumann 82) for classifying spatial prepositions in 3D traffic scenes. They used a hierarchy for each prepo- sition to generate more specified localization expres- sions like exactly behind. The range of applicability of a spatial relation was fixed, therefore no gradation was supported. Systems which used differentiated values for the applicability of spatial prepositions were the CITYTOUR and the SOCCER system of the VITRA project (Andre et al. 88). Both systems worked in a 2D environment. A local coordinate system, which de- pends on the outline of the reference object, is initially defined. The distance between the object to be local- ized and the referent measured on the local coordinate system is then mapped to a fixed evaluation function (e-2). (Abella & Kender 93) presented a framework for a system that describes qualitatively 2D objects using spatial prepositions. They define a preposition by a set of inequalities. A fuzzification procedure us- ing Monte Carlo Simulation was used to account for the vagueness of prepositions. Some prerequisites for the prepositions applicability appear to be too restric- tive, for example, the applicability of near requires an intersection of the objects’ bounding boxes. In the approach presented here, we use an extended local coordinate system to approximate the reference object’s extension. Furthermore, we assign high prior- ity to the possibility of a cognitively plausible evalua- tion of the spatial relations’ applicability. Before turning to the computation, we briefly de- scribe the input of the algorithms - the objects’ shape descriptions - and the hierarchy of idealizations used for calculating the basic semantics. Object representation and idealization We need a geometrical representation of the observed objects in order to establish spatial relationships be- tween them. The object descriptions we use as input for our algorithms are described in terms of their sur- face boundaries, i.e., they are specified as collections of faces. The geometrical representation is currently re- stricted to the following types of faces: planar polygon, box, disc, ring, cylinder, and sphere. The geometrical model can have a hierarchical structure for grouping objects into a new object. The definition of types of objects, which might be instantiated several times, is also supported. In (Herskovits 86) Herskovits proposed employing various kinds of object idealizations, e.g., object ap- proximations to a point, a line, a surface, a horizontal plane, etc. Landau and Jackendoff also confirm that spatial relations depend mainly on boundedness, sur- face, or volumetric nature of an object and its axial structure (Landau & Jackendoff 93, p. 226). Therefore it seems reasonable to consider only ap- proximated shape properties of an object when com- puting spatial relations. In most cases, it is sufficient to approximate the object to be localized with its cen- ter of gravity, since only position is required for the applicability of the spatial relation. In our system the following idealizations are used: (1) Center of gravity. (2) Bounding rectangle (BR): The bounding rectangle of an object with respect to a direction vector v’ is the minimal rectangle which is aligned to v’ and contains the 2D representation of the object. (3) 20 representation: The base of each object (Necessary when perceiving objects from a bird eye’s view, e.g., maps). (4) B ounding right purullelepiped (BW (5) 30 P re resentution: The complete geometri- cal description of an object. Computation of spatial relations Three distinct classes of spatial relations are consid- ered, the topological relations, the projective relations, and the relation between, which takes an exceptional position in the group of spatial relations. Their ba- sic meanings with respect to their use in the German language, are described first, followed by explanations of the computational procedures. Accounting for the vagueness of the applicability of spatial relations, the result of a computation always lies in the interval [O. .l]; the endpoints stand for not and fully applicable respec- t ively . Topological relations The topological prepositions in German considered are an (engl. at) and bei (engl. near) in their local use.’ The semantics of “at” and “near” The topo- logical relations at and near both refer to a region proximal to an object. Their range of applicability therefore often overlaps. Differences appear mainly on the pragmatic level. If one has the choice between near and at to describe a spatial constellation, near is never preferred to describe a spatial situation with a direct contact between two objects. Therefore the following definition of the basic semantics is used: At localizes an object in the proximal exterior of a REFO. Contact is not necessary. For the applica- bility of the relation near contact between objects is explicitly prohibited. But note, in a question like “Is object A located near object B? “, it is still possible that contact between A and B exists. The computational procedure The computa- tional procedure for the topological relations at and near attempts to reflect the definitions as described above. Depending on the prevailing dimension, the REFO is approximated by either its BR or BRP, ‘In the sequel only the English expressions for the Ger- man prepositions are used. Slight differences between the German and the English may appear. 1394 Spatial Reasoning aligned to its intrinsic front and the LO by its cen- ter of gravity CG( LO). If the REFO has no intrinsic front it may acquire an accidental front by virtue of its location (cf. (Miller & Johnson-Laird 76)). If a con- textual induced accidential front is also not available, then the deictic orientation is used. In the following, only the 3D case is considered. The 2D case can be treated analogously. Figure 1: Definition of the local coordinate system Based on the BRP of the REFO, a local coordinate system, as shown in Figure 1, is defined. The intrin- sic orientation of the REFO ZREFO, projected onto the plane orthogonal to gravitational force (horizon- tal), and the direction of gravity (vertical), determine the BRP’s alignment. Thus, the REFO should be in its intrinsic vertical position. If this is not the case at the time of calculation, a transformation of the ob- ject relative to its vertical alignment is necessary. The scaling along a single axis corresponds to the extension of the REFO along the prevailing dimension. To find the local coordinates of the LO, the BRP is aligned to the positive y-axis of the world coordinate system with the help of a rotation ROT, around the z-axis and then shifted to the origin. Expressing the rotation and the translation in matrix notation, the transformation matrix ~~~~~~~~~~ yields: MTransform := MTranslation *W~,(~REFO) Applying the matrix of transformation ~~~~~~~~~~ to CG( LO) results in the transformed center of grav- ity CGt ..,,r(LO) and thus, the Iocaldistance DISlj,, between LO and REFO with respect to the local ref- erence system. CGtransd~O) := MTransform * CG(LO) DISTloc(~O) := IlC%ransf(~Ohc The local coordinate system therefore ensures a scal- ing of the distance between LO and REP0 depending on the prevailing external dimensions of the REFO. The approximation of the LO by its center of grav- ity provides a appropriate evaluation if the two LOS have different sizes. Therefore, two buildings would typically not stand as near as a building and a fire hydrant. Using this method, topological relations can be com- puted in the 2D as well as 3D. Even instances in differ- ent dimensions, e.g., the LO is a parking lot and the REFO is a building, can be handled appropriatly. The local distances of different REFOs are compa- rable, i.e., object-independent, and this is a require- ment for defining a evaluation function, which maps the distances to the interval [O..l] of the degrees of applicability. The evaluation functions used here are cubic spline functions SpdincR,,. They ensure a conti- nous evaluation and, furthermore, a flexible definition of the graph. Figure 2 shows a possible definition of the evaluation functions for at and near. In partially instantiated queries incontiguity between regions of ob- jects involved is necessary for a successful evaluation. This is taken into account by the definition of the eval- uation function Splinenea,-. If the query is fully spec- ified (see the note above), then a curve shape like the one of at must be used. By means of modification, addition, and deletion of spline footings the evaluation can be adapted to the prevailing user’s perception. AT/NEAR I-"AWE Figure 2: Evaluation functions of the proximal region concerning at and near Given two objects LO and REFO, the function DA~el,,,o > which computes the degree of applicabil- ity Red(L0, REFO), can now be specified as: D*R%lpO : (LO, REFO) H SPLINERe~t,p,(DISTI,,(LO)), with Reltopo E {at, near} For the case local distance equal to 0, i.e., the LO is inside the BRP or BR, but not inside the REFO, a special scaling factor is applied to the evaluation func- tion, which is also dependant on the extension of the REFO. More details concerning the handling of the so-called critical ureas can be found in (Gapp 93). Projective relations The relations considered are in front of, behind, right, above, below, and as a special case the relation beside, which can be viewed as the disjunction of the relations right and Ieft. First a description of the basic meanings is given. The semantics of projective relations To eval- uate spatial relations with respect to the projective Spatial Reasoning 1395 (a) world coordinate system (b) transformed world coordinate system (c) local coordinate system (4 transformed world coordinate system Figure 3: Role of the the coordinate system in angle calculation prepositions, the computational procedure described above must be extended. The algorithm developed thus far can be used as a basis because using a projec- tive relation as well as topological ensures a localization of an object proximal to a reference object.2 Conse- quently, there is an initial requirement for the struc- ture of a projective relation’s region of applicability: If the distance from the L 0 to the REDO increases, then the degree of applicability decreases. Addition- ally the factor direction must be accounted for in the evaluation. This yields a further segmentation of the proximal region into relevant areas, i.e., areas in which the LO reaches a degree of applicability greater than zero. The reference system, which is necessary for the computation, depends on the different ways of looking at the REDO (intrinsic, extrinsic or deictic use). In summary, basic meanings of projective relations localize, with respect to a reference system, an object depending on the proximal region of the REDO and the canonical direction implied by the relation. The larger the direction deviation or distance, the smaller the applicability of a projective relation. The relation beside is the only projective relation with an orientation involving two opposite directions, which correspond to relations right and left. Because the use of beside always implies an alignment of the REP0 it is reasonable to define the region of applica- bility for beside as the union of the applicability regions of the relations right and left. The extended evaluation procedure As men- tioned before, the existing method for evaluating topo- logical relations can also be used for getting the prox- imal region of the REDO depending on its extension in each dimension. Additional requirements for pro- jective relations are the determination of a reference system (depending on the perspective used), and the 2This holds in any case for questions using where. If the query is fully specified it is possible that the requirement of proximity is not necessary. But this will have to be determined in future research. 1396 Spatial Reasoning inclusion of the canonical direction implied by the pre- vailing relation. The conceptual system must deter- mine which perspective is to select in a specific case. In intrinsic use, every transformation that has already been applied to the REDO, must be reversed and then applied to the REP0 and the LO. This is very im- portant producing the correct result, e.g., using this procedure the computation of “the thigh is above the knee” still holds even if the person is sitting on a chair, with the thighs in a horizontal position. To calculate a reference system for extrinsic/deictic use, the gravitational force determines the vertical axis and the horizontal part of the extrinsic/deictic orienta- tion vector v’ determines arrangement of the two hor- izontal axes. Dependant on this reference system, the local coordinate system is built up as described above. With respect_ to this reference system the local dis- tance DISTC, is computed from the local coordinates of the center of gravity and mapped to the evaluation function SPLINEproj. In contrast to the evaluation of topological relations, the deviation of the LO from the canonical direction, implied by the projective re- lation, is taken into account. Therefore, let 7 be the direction vector implied by the projective relation and -# s = CG(L0) - CG(REF0). Then a = L(s’,?J de- notes the deviation of LO from the canonical direction r’referring to the world coordinate system (Figure 3a). Let r’tran8f = Mtransf(r9 and Srtransf = Wransf(s9, the transformed vectors of r’ and s’ are referring to the local reference system. The angular deviation is not affected by the transformation (Figure 3b). Let ,;lroaensf = CGtran,f(LO) - CGtransf(REJ’O) be the vector between the two transformed centers of gravity (referring to the local coordinate system). Hence, ,8 = L(s;fP,e,,f, r’&,,f) is the local angular de- viation, referring to the local reference system, and p # CY. This is important because the angles referring to the world coordinates do not consider the extension of the REFO. However, computing the angle using the local coordinates, as shown in Figure 3c, includes the reference system in the evaluation of the direction de- viation. The distinction between the two variants will be obvious when the local coordinates are transferred to the world coordinate system (Figure 3d). Like the local distance, the angle is mapped to a spline function SPLINEan,ze, which results in a value between 0 and 1. The inclusion of the direction, with the help of the direction deviation, can be applied to 2D as well as to 3D data. In the 3D instance, the angular devia- tion /? increases, corresponding to a larger or smaller z-coordinate of the vector v’ and hence the value of SPLINE,,,l,(P) also increases. Given two objects, LO and REFO, and an orientation vector c, the de- gree of applicability DAR~~,,,,~ of a projective relation Re&oj can now be defined as: DARelproj : (LO, REFO,3) n SPLINEprox(DISTIJ,c (LO)) . SPLINE,,,l, (P)) with Rdproj E (behind, left, above, . ..} Figure 4 is a visual example of the 3D applicability structure of above (a) and right (b) using a building as REFO. The darker the grey areas of the relation’s region of applicability are, the higher is the degree of applicability. Figure 4: Cross-sections of the 3D applicability struc- ture of above and right The relation “between” The relation between occupies an exceptional position among the static relations considered because it refers to two reference objects. The semantics of “between” The basic meaning of between is defined by the structure of its region of applicability. The location with the highest degree of applicability is normally exactly midway between the two REFOs (provided no other object lies inside the interspace) Increasing the distance to this location de- creases the applicability, depending on the extension of the REFOs. This dependence on the REFO is ex- pressed by a displacement of the region of applicability towards the REFO with the smaller extension. The structure of the region of applicability is specified pic- torially in Figure 5. Figure 5: 2D Applicability structure of between The computational procedure Approaches for computing the applicability of between can be found in (Hanfimann 80; Habel 89). A cognitively plausi- ble gradation was not supported by these approaches. Because of this, we use a new method to compute the applicability of between; it is as follows: Four essential variables need to be considered: 1. The distance between the two REFOs 2. The angle WGLO CGREFO~~CGREFO~ CGREFO~) 3. The angle L(CG~O CGREF02pCGREF02 CGREFOd 4. The extension of the REFOs. Neglecting the second REFO in the requirements given above and taking into account the vector which results from building the difference of the REFOs’ cen- ter of gravity, there are the same requirements that have to be met by the evaluation of the projective re- lation in front of. So it is natural to make use of the computation in front of to obtain the semantics of between. Hence between is defined as: An object LO is located between two reference ob- jects REFOl and REFOZ, provided it is extrinsic in front of REFOl, using REFOd as point of view, and vice versa. Mathematically such a double dependency can be expressed by taking the arithmetic mean of both de- grees of applicability: DAbetween : (LO, REFOl, REF02) w with J1 = CG(REFOi) - CG(REF02) and 3 2 = CG(REF02) - CG(REFO1) Figure 6 shows that the 2D structure of applicability for the relation between fulfills the exact requirements of the semantics above. Figure 6: The structure of applicability of between Spatial Reasoning 1397 Implementation The presented computational model was fully imple- mented and tested. For validation purposes different visualization methods (cf. (Gapp 94)) are used to get an idea of the spatial relations’ region of applicabil- ity (Figure 4 and 6). The system proceeds from a geometrical scene description and answers questions in natural language about the constellation of the ob- jects involved in a cognitively plausible manner. Using an object indexing method permits an immediate ob- ject access to accelerate answering partially instanti- ated queries. Presently every possible applicable spa- tial relation has been generated. The construction of a component which decides what spatial relation or compositions in a certain situation should be used is currently under investigation. The computational model is integrated in a work- bench which serves as a basis for the incremental event recognition component of the VITRA project. Conclusion and future work In this paper methods were developed for computing the basic meanings of spatial relations with respect to geometrical object properties. We have proposed an approximative algorithm which represents a reason- able compromise between simplification and necessary exactness. The described methods for computing the relations between objects in 2D and 3D space consider the extension of the REFO and permit a plausible eval- uation dependant on the user’s perception. The eval- uation procedures are applicable to 2D as well as 3D scene data. Even the application of a spatial relation to objects with different dimensions, e.g., a parking lot and a house, is supported. The next step is to acquire psychological evidence of the applicability of basic spatial relations’ mean- ings. For this purpose, empirical studies have been designed. Subsequently further phenomena can be considered, e.g., the influence of intervening objects or borders. Acknowledgements I would like to thank Gerd Herzog for his support, ad- vice, and criticism. Thanks also to Anthony Jameson, Amy Norton, and Dagmar Schmauks for improving the readability of this paper. References A. Abella and J. R. Kender. Qualitatively Describ- ing Objects Using Spatial Prepositions. In: Proc. of AAAI-93, pp. 536-540, Washington, DC, 1993. E. Andr6, G. Herzog, and T. Rist. On the Simultu- neous Interpretation of Real World Image Sequences and their Natural Language Description: The System SOCCER. In: Proc. of the 8 th ECAI, pp. 449-454, Munich, 1988. E. Andr6, G. Herzog, and T. Rist. Natural Lan- guage Access to Visual Data: Dealing with Space and Movement. In: F. Nef and M. Borillo (eds.), Proc. of the lSt Workshop of Logical Semantics of Time, Space and Movement in Natural Language. Hermes, 1989. I. Carsten und T. Janson. Verfuhren zur Evaluie- rung rdumlicher Prtipositionen anhand geometrischer Szenenbeschreibungen. Diplomarbeit, FB Informatik, Univ. Hamburg, 1985. K.-P. Gapp. Berechnungsverfahren fir rliumliche Re- lationen in 3D-Szenen. Diplomarbeit, FB Informatik, Univ. des Saarlandes, Saarbriicken, 1993. Auch als: Memo 59, SFB 314, 1993. K.-P. Gapp. Einsatz von Visualisierungstechniken bei der Analyse von Realweltbildfolqen. In: Proc. of the 1 st Workshop of Visual Computing, Darmstadt, 1994. C. Habel. Zwischen-Bericht. In: C. Habel, M. Her- weg, and K. Rehkamper (eds.), Raumkonzepte in Verstehensprozessen: Interdisziplinare Beitrage zu Sprache und Raum, pp. 37-69. Tiibingen: Niemeyer, 1989. K.-J. Hanfimann. Sprachliche Bildinterpretation fir ein Frage-Antwort-System. Ifi-hh-m-74/80, FB Infor- matik, Univ. Hamburg, 1980. A. Herskovits. Language and Spatial Cognition. An Interdisciplinary Study of the Prepositions in English. Cambridge, London: Cambridge University Press, 1986. M. HuBmann and P. Schefe. The Design of SWYSS, a Dialogue System for Scene Analysis. In: L. Bolt (ed.), Natural Language Communication with Pictorial Information Systems, pp. 143-201. Miinchen: Hanser/McMillan, 1984. M. Kochen. Representations and Algorithms for Cognitive Learning. Artificial Intelligence, 5:199-216, 1974. B. Landau and R. Jackendoff. “What” and “where” in spatial language and spatial cognition. Behavioral and Brain Sciences, 16:217-265, 1993. G. A. Miller and P. N. Johnson-Laird. Language and Perception. Cambridge, London: Cambridge Uni- versity Press, 1976. B. Neumann. Bildverstehen. In: W. Bibel und J. Siekmann (Hrsg.), Kiinstliche Intelligenz, pp. 285- 355. Berlin, Heidelberg: Springer, 1982. G. Retz-Schmidt. Various Views on Spatial Prepo- sitions. AI Magazine, 9(2):95-105, 1988. W. Wahlster. One Word Says More Than a Thou- sand Pictures. On the Automatic Verbalization of the Results of Image Sequence Analysis Systems. Com- puters and Artifial Intelligence, 8:479-492, 1989. L. A. Zadeh. Fuzzy Sets. Information and Control, 8:338-353, 1965. 1398 Spatial Reasoning | 1994 | 40 |
1,667 | Automatic Depiction of Spatial Descriptions* Patrick Olivier Toshiyuki Maeda Jun-ichi Tsujii Centre for Intelligent Systems Central Research Laboratories Centre for Computational Linguistics University of Wales Matsushita Electric Ind. Co. Ltd. University of Manchester Aberystwyth 3-4, Hikaridia, Seika-cho Institute of Science and Technology Dyfed, SY23 3DB, UK Soraku-gun, Kyoto 619-02, Japan Manchester, M60 l&D, UK plo@aber.ac.uk maechan@crl.mei.co.jp tsujii@ccl.umist.ac.uk Abstract A novel combination of ideas from cognitive linguis- tics and spatial occupancy models in robotics has led to the WIP (Words Into Pictures) system. WIP au- tomatically generates depictions of natural language descriptions of indoor scenes. A qualitative layer in the conceptual representation of objects underlies a mechanism by which alternative depictions arise for qualitatively distinct interpretations, as often occurs as a result of deictic/intrinsic reference frame ambigu- ity. At the same time, a quantitative layer, in conjunc- tion with a potential field model of the semantics of projective prepositions, is used in the process of cap- turing the inherently fuzzy character of the meaning of natural language spatial predications. Introduction People often relate their visual experiences to one an- other by means of verbal descriptions. Relying on a commonality of perceptual experience of the world about us. For example, the size and orientation of ob- jects can be captured using dimensional predications such as “the pole is high”. The relative positions of objects are communicated by, amongst other means, static spatial predications such as “a chair is in front of the desk”. Adequate representation of the meaning of spa- tial prepositions and dimensional adjectives must be grounded in our cognitive model of three-dimensional space, which in turn is structured based on the func- tionality of our perceptual system. Such a represen- tation should distinguish qualitative ambiguities (eg. the deictic, intrinsic and extrinsic interpretations of a preposition (Retz-Schmidt 19SS)), but also quanti- tative differences (for example, that certain regions in space are more typically “in front of” a reference object than others). Further, the qualitative and quantitative components of meaning are dependent on the entities that are the objects of the spatial predications. Drawing on the work of Lang (Lang 1993) (Lang, Carstensen, & Simmons 1991) (Bierwisch & Lang *This research was kindly funded by the Matsushita Electric Industrial Company Limited. 1989) and incorporating ideas originating in the field of robot manipulator path planning (Khatib 1986), the WIP (Words Into Pictures) system automatically generates such a representation for natural language scene descriptions in English, and produces depictions of quantitatively likely, but qualitatively distinct, in- terpretations. The Domain The WIP system addresses the problem of understand- ing and generating depictions of room descriptions. As such, it is a prototype application under the um- brella of research into natural language interaction with multi-media systems. Users are initially required to specify the type of room and their vantage point (ie. their position and orientation within the room). They can then specify the room’s contents and the locations of the contents using dimensional and prepositional ex- pressions. In this paper we restrict ourselves to de- scribing the semantic representation and processing of spatial prepositions, in particular projective preposi- tions. Spatial Prepositions Projective prepositions place a constraint on the prox- imity of the located object and the reference object. Predications such as “the chair is in front of the desk” constrain the “desk” and “chair”, to some degree, to be proximal to each other. Conversely projective preposi- tions such as “away from” predicate a distal relation- ship between the located and reference object. Further, the degree of the proximity expressed in any projective prepositional predication varies according to a number of considerations including: the spatial context (the spatial extent and content of the scene described); and the absolute and relative sizes of the located object and reference object. This last consideration can be illustrated by contrasting the the predications: “a car is to the left of a lorry” and “an apple is to the left of the orange ” . Whilst the preposition used here is the same in both cases, the pieces of fruit will be closer to each other than will the “car” and “lorry”. Spatial Reasoning 1405 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Figure 1: Intrinsic, deictic and extrinsic ambiguity In addition to the constraint on the proximity of the located object and reference object, projective- prepo- sitions place a constraint on the position of the located object relative to a particular side of the reference ob- ject. In the case of the intrinsic interpretation of a medication such as “the stool is in front of the desk”, the “stool” is located in some spatial region defined by the half-plane that is the intrinsic front of the “desk”. Intuitively, the closer the “stool” is to the region de- fined by the projection of the desk’s dimensions, the more the spatial arrangement conforms to the proto- typical interpretation of the predication. Intrinsic, deictic and extrinsic interpretations of pro- jective prepositions qualitatively differ according to the reference frame with respect to which the directional constraint is characterized (Retz-Schmidt 1988). In the intrinsic case the reference frame is centered at the reference object and adopts the intrinsic orientation of the reference object. In figure 1, stool number 1 is in- trinsically “in front of the desk”. The reference frame for a deictic interpretation is centered at the speaker and adopts the speaker’s orientation; deictic readings can be invoked explicitly with qualifications such as “from where we are standing”; when the reference ob- iect has no intrinsic or extrinsic sideness relating to ihe preposition used; or when intrinsic or extrinsicin- terpretations are ruled out on other grounds (eg. the impossibility of spatially arranging the objects as re- quired by the interpretation). In figure 1 stool number 2 is deictically “in front of the desk”. Extrinsic readings can occur when the reference ob- ject has no intrinsic sides relating to the locative prepo- sition (eg. trees) but is in close proximity to another object ‘that is stkmgly sided (such-as a house); in which case the reference frame capturing the intrinsic orien- tations of the stronger sided object can be adopted by region-2 region-3 Figure 2: A qualitative model of space the reference object. Referring to figure 1 the chair is extrinsically “in front of stool number 3”; the stool has inherited an extrinsic front from the right wall. Typically an object is located with respect to more than one reference object by the means of multiple spatial predications. Consequently, a requirement on meaning representation for spatial predications is that they must being easily combined to giving rise to a cumulative meaning. Related work Past work has failed to construct a computational se- mantics rich enough to capture the phenomena men- tioned so far, due to a concentration either on a purely qualitative model or an overly simplistic quantitative model of spatial predicates. Early efforts such as (Winograd 1972) and (Waltz & Boggess 1979) are defi- cient as a result of their commitment to a purely quali- tative model of constraint, though in the case of (Waltz & Boggess 1979) th e resulting representation is analog (quantitative). More recently, Kalita (Kalita & Badler 1991) uses Talmy’s geometric-relation schema (Talmy 1983) and Douglas’ qualitative spatial model (Douglas & Novick 1987). Spatial predications specify inclusions in rect- angular regions that are outward projections of the ex- tents of the reference object. Figure 2 depicts the two-dimensional case for such an approach, inclusion in regions 1 to 4 corresponds respectively to “in front of”, “right of”, “behind” and “left of” predications. In addition to being too restric- tive (clearly point X is “left of” the object), intrinsic and deictic sides are not distinguished, and any point within a particular region, regardless of its distance from the reference object, equally satisfies the con- straint. Lang (Lang, Carstensen, & Simmons 1991), (Lang 1993) uses a similarly qualitative model but distinguishes deictic and intrinsic sides in his object schema representation of objects, with reference to 1406 Spatial Reasoning which t,he corresponding competing interpretations are captured. Yamada uses the concept of a potential field to capture North-South and East-West directional con- straints (Yamada, Nishida, & Doshita 1988). For ex- ample, if object A is North of B, this spatial constraint is modeled using a torsion spring-like function. Any further constraint on A (which might cause it to be lo- cated other than due North of B) is similarly modeled with a potential function. The most likely interpreta- tion is computed as the minimum energy configuration of the objects and springs. Schirra uses the inversely related concept of a normalized typicality field in which the potential is highest for more prototypical configu- rations (Schirra & Stopp 1993). Whilst Schirra’s typi- cality fields can capture both direction and proximity constraints, only intrinsic interpretations are catered for. Both Schirra and Yamada idealize reference ob- jects as points and fix the magnitude of fields for par- ticular prepositions, regardless of the reference object’s dimensions. Conceptual Representation The WIP system represents spatial predications as ei- ther geometric or potential field constraints over two layered conceptual representations of objects consist- ing of a qualitative spatial and perceptual represen- tation, coupled to a quantitative object model. This allows it to differentiate between interpretations rela- tive to different reference frames, and also to vary the degree of constraint depending on the reference and lo- cated objects concerned. The resulting representation facilitates the depiction of the ‘most plausible’ inter- pretations. Qualitatively modeling objects The qualitative layer of the object representation is based on Lang’s object schemata (Lang 1993). The desk of figure 3( ) a is represented as in figure 3(b). In this first schema a, b and c label three orthogonal axes centered at the object, each of which is instantiated by one or more dimensional assignment parameters (DAPs)’ ; al-a2, bl-b2 and cl-c2 are corresponding half-axes. Each half axis is labelled either nil or with an intrinsic side (eg. i-front). If the object has been constrained in the scene as a result of some spatial predication, WIPS infers the object’s deictic side as- signment. For example, if the desk of figure 3(a) is aga,inst a wall in a room to the left of the observer then its object schemata will be as given in figure 3(c). The explict representation of deictic and intrinsic sides allows the identification of the actual face of an 1 DAPs are not of direct interest here although they are fundamental to the process of dimensional designation and where dimensional assignment might result in a reorienta- tion of the conceptual object (eg. assigning verticality in the process of interpreting “the pole is high”). (a) a2 (b) a: max b: vert c: obs al: i-left bl: i-bottom cl: i-front a2: i-right b2: i-top c2: i-back Figure 3: Object schemata object rel strutted. ative to which a spatial constraint is con- Quantitatively modeling objects The quantitive model of the objects in WIP is com- prised of: o the graphical description of the parts (GDP), con- structed from a finite set of geometric primitives o the mapping from the geometric axis qualitative axis system system to the The set of graphical primitives in the WIP system is currently restricted to lines and quadrilaterals, which are specified relative an object’s geometric axis system (GAS). The mapping between the GAS and the quali- tative axis system is specified in terms of the alignment of the x, y and z axes of the GAS and the qualitative half-axes al-a2, bl-b2 and cl-c2. The GDPs for each object are located relative to the speaker/viewer as a result of intepreting spatial predictions over the object, although the elements of the background scene (the in- ternal walls) are located in the process of defining the speaker’s vantage point on the scene. The magnitudes of the extents of an object can be calculated from the configuration of the GDPs that comprise the object. Spatial Reasoning 1407 Figure 4: Field for intrinsic “in front of the desk” Figure 5: Combined potential fields Potential Fields Spatial predications are interpreted as constraints on the orientation and the position of the located object relative to the reference object. The qualitative dis- tinction corresponding the use of either the deictic and intrinsic reference frames is captured by identifying the different deictic and intrinsic sides of the qualitative conceptual representation of the object. Having iden- tified any ambiguity, a potential field (originating from the half-plane relevant to the particular interpretation) is used to capture the fuzzy character of the constraint imposed by spatial prepositions. easily computed by gradual approximation (Yamada, Nishida, & Doshita 1988). Figure 4 shows a region of the field corresponding to the intrinsic interpretation of “in front of the desk”. Quantitative variations in proximity and directional constraints are dependent on reference object and lo- cated object dimensions. Modifying the potential func- tion constants on the basis of object dimensions is the mechanism by which this dependency can be captured. The the shape and extent of the potential field P(x, y) Originating in robot manipulator path planning (Khatib 1986), we use the potential field model (PFM) to capture the proximity and direction components of the spatial constraint imposed by certain prepositions, particularly projective prepositions. In general, for a preposition that imposes a projective constraint rela- tive to the face of a reference object, the normal of which extends in the x-direction, we use a potential function P(x, y), where: is governed by the three constants: 1. q.wox 2. 3. Directly proportional to the proximity localisation of the minimum energy configuration. L prox The distance of the minimum energy configuration from the reference object. Jyx:, Y) = $rox(x, Y) + h-(x, Y) (1) Pprox(z, Y) = +y@zjj - Lprox)” (2) Directly proportional to the directional localisation of the minimum energy configuration. In WIP values for I(prox, Lprox, and K&r are lin- early dependent on the dimensions of the reference ob- ject and located object, which gives rise to intuitively more plausible depictions for the same preposition with different reference and located objects. d, = (z - x0) (4) 44 = (Y - Yo) (5) The y axis when combined with the x axis defines the plane in which the constraint applies; (x0, ya) is the Cartesian coordinate of the reference object rel- ative to the speaker/viewer. The lower the value of P(x, y) for a point (x, y), the better the spatial con- straint is satisfied. The minimum for the field can be MO8 Spatial Reasoning Multiple spatial predications over an object are sim- ply accommodated by the linear addition of the com- ponent fields. Figure 5 illustrates the cumulative po- tential field resulting from the expression “in front of the desk and near the cabinet”. An Overview of WIP WIP has been implemented using Prolog and Smalltalk/Objectworks. After specifying the dimen- sions of the room and the speaker/viewer’s vantage / input Figure 6: Intrinsic interpretation of “a chair is in front Figure 7: Adding the predication “the chair is near the of the left desk” back desk” point, natural language descriptions are parsed to log- ical forms. Spatial predicates and their arguments in- stantiate potential field specifications and the two-layer models of objects from the conceptual lexicon; and the cumulative potential fields for a description are con- structed. Where qualitative ambiguities arise (such as competing deictic and intrinsic interpretations of a preposition) parallel intepretations are generated. Unconstrained degrees of freedom are set on the ba- sis of default assumptions, for example, if a chair is de- scribed as being “in front of” a desk, then the vertical position of the chair is constrained to keep its bottom on the floor. Lastly the minima of the potential fields for each interpretation are computed and the now fully constrained graphical model of the objects used to ren- der the depictions. Figures 6 and 7 illustrate example outputs from WIP. In figure 6 the chair in the scene is only con- strained to be in front of the left desk. In figure 7 the constraint that the chair is near the back desk has been added. Concluding Remarks Past attempts at addressing the problem of relating natural language description of spatial scenes to phys- ical referents (through depiction or otherwise) have been deficient in one or more of the following: o the ability to distinguish competing deictic and in- trinsic interpretations , i/ 1 Input L, o a probabilistic model of the possible location de- noted by projective prepositions. e an automatic tuning of the degree of proximity and directional constraint imposed by prepositions, in accordance with the dimensions of the reference and located objects. WIP encompasses all of these, and generates intu- itively reasonable depictions of natural language de- scrip tions of scenes. Deictic and intrinsic interpreta- tions are distinguished by the qualitative representa- tion; the potential field model provides the ability to assign a likelihood to the different possible locations of a located object; and by making the constants of the PFM dependent on the extents of the reference and located objects automatic tuning of the PFM is guar- anteed. The preposition processing component of WIP is currently being developed to account for more sub- tle effects, such as, extrinsic interpretations and dis- allowing interpretations for which a located object is obscured in the resulting depiction. References Bierwisch, M., and Lang, E. 1989. Dimensional Ad- jectives: Grammatical Structure and Conceptual In- terpretation. Berlin Heidelberg New York: Springer- Verlag. Douglas, S., and Novick, D. 1987. Consistency and variance in spatial reference. In Proceedings of the Ninth Annual Cognitive Science Society Meeting, 417-426. Spatial Reasoning 1409 Kalita, J., and Badler, B. 1991. Interpreting prepo- sitions physically. In Proceedings AAAI-91, 105-110. Khatib, 0. 1986. Real-time obstacle avoidance for manipulators and modile robots. The International Journal of Robotics Research 5( 1):90-98. Lang, M.; Carstensen, K.; and Simmons, G. 1991. Modelling Spatial Knowledge on a Linguistic Basis. Berlin Heidelberg: Springer-Verlag. Lang, E. 1993. A two-level approach to projec- tive prepositions. In Zelinsky-Wibbelt, C., ed., The semantics of prepositions: from mental processing to Natural Language processing. Berlin: Mouton de Gruyter. Retz-Schmidt, G. 1988. Various views on spatial prepositions. AI Magazine 9(2):95-105. Schirra, J. R. J., and Stopp, E. 1993. Antlima - a listener model with mental images. In Proceedings of IJCAI, 175-180. Talmy, L. 1983. How language structures space. In Pick, H., and Acredolo, L., eds., Spatial Orienta- tion: Theory, Research, and Application. New York: Plenum Press. 225-282. Waltz, D. L., and Boggess, L. 1979. Visual analog representations for natural language understanding. In Proceedings of IJCAI, 926-934. Winograd, T. 1972. Understanding Natural Language. New York: Academic Press. Yamada, A.; Nishida, T.; and Doshita, S. 1988. Fig- uring out most plausible interpretation from spatial descriptions. In Proceedings of the 12th International Conference on Computational Linguistics, 764-769. 1410 Spatial Reasoning | 1994 | 41 |
1,668 | A Model for Integrated ualit at ive Spat ial and Dynamic easoning about Physical Systems * Raman Rajagopalan Artificial Intelligence Laboratory Department of Computer Sciences University of Texas at Austin Austin, Texas 78712 raman@cs.u,texas.edu Abstract Qualitative spatial reasoning has many applications in such diverse areas as natural language understanding, cognitive mapping, and reasoning about the physical world. We address problems whose solutions require integrated spatial and dynamic reasoning. In this paper, we present our spatial representation, based on the extremal points of objects, and show that this representation is useful for modeling the spatial extent, relative positions, and orientation of objects, and in reasoning about changes in spatial relations and orientation due to the translational and rotational motion of objects. Our theory has been implemented to support a magnetic fields problem solving applica- tion using the QPC and QSIM systems for qualita- tive modeling. The issues encountered in integrating spatial and dynamic reasoning in the context of these systems are also discussed. Introduction Spatial reasoning has been studied in Artificial In- telligence from many perspectives, including natural language understanding [Freksa 92, Mukerjee and Joe 90, Retz-Schmidt 881, cognitive mapping [Kuipers and Levitt 881, and qualitative reasoning about physical systems [Forbus, et. al. 91, Joskowicz and Sacks 91, Nielsen 88, Weinberg, Uckun, and Biswas 921. A fun- damental starting point for spatial reasoning is the rep- resentation of the spatial extent of an object. Problems which require knowledge of the exact shapes of objects, such as determining whether two gears will mesh to- gether, will require a numerically precise spatial repre- sentation, such as the configuration space [Forbus, et. al. 91, Joskowicz and Sacks 911. For many problems, knowledge of the approximate extent of objects is sufficient, or that could be only information available. Several spatial reasoning meth- ods, based on the use of simplifying abstractions to *This work has taken place in the Qualitative Reason- ing Group at the Artificial Intelligence Laboratory, The University of Texas at Austin. Research of the Qualita- tive Reasoning Group is supported in part by NSF grants IRI-8904454, IRI-9017047, and IRI-9216584, and by NASA contracts NCC 2-760 and NAG 9-665. approximate the actual extents of objects [Abella and Kender 93, Cui, Cohn, and Randell 92, Mukerjee and Joe 901, have been developed to address these cases. None are sufficiently rich to simultaneously model all of the following properties: the spatial extents, relative positions, and orientations of objects, and the effects of translational or rotational motion on the spatial state. For example, Cui, Cohn, and Randell [1992] use con- vex hulls as an abstraction method. They present techniques for reasoning about the relative positions of objects, but do not discuss the orientation of ob- jects. They also do not provide a qualitative method to describe the convex hull itself, or how to compute its changing location or orientation if the underlying object translates or rotates. They assume that an ex- ternal function will provide this information. We consider problems whose solutions require in- tegrated spatial and dynamic reasoning. Specifically, we are implementing a magnetic fields problem solver, which, given a diagram to describe the initial spatial state and text to describe any dynamic changes taking place, solves the problem through qualitative simula- tion. An input processing specialist, The Figure Un- derstander [Rajagopalan and Kuipers 941, is used to integrate the information in the text and diagram in- put into a unified model of the initial state. A library of model fragments, for spatial reasoning and for the magnetic fields domain, is used by the &PC [Crawford, et. al. 90, Farquhar 941 qualitative modeling system to detect spatial configurations that could lead to dy- namic processes. The effects of any active processes are determined using the QSIM [Kuipers 861 qualita- tive simulation system. Our problems cover the operation of such commonly used devices as motors, generators, and transformers. Relative position and orientation information is used to study the effects of changing the magnetic flux pass- ing through a closed conducting object. The change in flux can be due to a time-varying magnetic field (trans- former), or to the translational or rotational motion of the conducting object (motor, generator). Forbus, Neilsen, and Faltings [1991] and Joskowicz and Sacks [1991] 1 a so address the issue of integrated Spatial Reasoning 1411 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. l Diagram: l Text: The loop is rolling along the block into a magnetic field. Figure 1: A magnetic fields problem involving transla- tional motion: What happens as the conducting loop (white) rolls across the magnetic field (gray)? The rectangular bounding box abstraction shown for the loop is not included in the input to the problem solver. spatial and dynamic reasoning, but the characteristics of our problems are not well suited for the configura- tion space-based approach they have adopted. They work with domains where objects cannot share the same physical space, and objects cannot be dynami- cally created or destroyed. In such cases, the config- uration space must be computed only once, and the boundaries of the forbidden regions can be used to de- tect the points at which two objects are in contact. In our problem set, the most interesting spatial relation is overlap between objects, and since magnetic fields can be created simply by establishing a current flow in a wire, we must allow for the dynamic creation and destruction of spatial objects. In the following sections, we describe our spatial rep- resentation and its use in reasoning about the relative positions between objects and the orientation of convex objects, particularly in dynamically changing worlds. We will also discuss the issues encountered in integrat- ing spatial and dynamic reasoning in the context of the &PC and QSIM systems. Example Magnetic Fields Problems Consider the scenarios in Figures 1 and 2. In Figure 1, a conducting loop is rolling into a magnetic field. In Figure 2, a conducting loop is rotating inside a mag- netic field. The problem is to describe what happens as the specified motions take place. We have to recognize changes in the redutive posi- tion (figure 1) or orientation (figure 2) of the loop rel- ative to the field to determine when the magnetic flux through the loop is changing. During those periods, an induced emf will be established in the loop such that the resulting current flow will produce a magnetic field that opposes the change in flux through the loop. Mag- netic forces can then act on the loop, and orientation information can be used to determine the net magnetic force/torque and its effects (e.g., the loop in Figure 1 will slow down as it enters and exits the field). o Diagram: o Text: The loop is rotating in a coun- terclockwise direction about the X-axis. L Figure 2: A magnetic fields problem involving rota- tional motion: A rudimentary generator. The Figure Understander The Figure Understander works with text input and a numerical description of a diagram, a PostScript file produced by the Interviews drawing editor, to output a qualitative, constraint-based description of the initial state. A picture description language is used to define a semantics for diagram objects, greatly simplifying the task of processing the input. For example, for Figure 2, given that white objects are conducting loops, The Figure Understander easily associates the direction of rotational motion with the smaller rectangular object. The diagram-based input method serves two pur- poses. Fir&, it is a more- natural and less error-prone method of entering the initial spatial state than us- ing a special purpose text form. Second, it allows numerically-precise spatial data to be extracted for _ - solving problems where such information is necessary. For example, The Figure Understander includes heuris- tics for selecting frames of reference, and when appro- priate, numerically rotates the diagram before extract- ing the initial spatial state. The Figure Understander corrects minor human errors in drawing the diagram by assuming that coordinate values within a given epsilon measure are equal. The Spatial Representation When an abstraction is used to approximate the actual spatial extent of an object, there can exist real distinc- tions that can no longer be reasoned about without additional case-specific information. If a maximally covering abstraction is used, such as a convex hull, one can auuruntee non-intersection conclusions based on examining only the approximate shapes, but not intersection conclusions. For example, if the convex hulls of two objects are not intersecting, then the un- derlying objects cannot be intersecting. However, it’s possible that the underlying objects do not intersect even if the convex hulls intersect. Similarly, if an ab- stract shape is fully contained within the actual shape, then one can guarantee intersection conclusions, but not non-intersection conclusions. Our problems require reasoning about what can hap- pen if two objects are intersecting or if one object is fully enclosed inside another. We enforce the con- 1412 Spatial Reasoning straint that a shape abstraction should fully enclose an underlying object at all times, to guarantee when it is at all possible for two objects to be intersecting. We also wish to minimize the need for quantitative information in describing the initial spatial state and to maintain the spatial state as objects translate and rotate. The goal is that a qualitative solution should apply to any physical scenario that fits the initial state description. The generality of the solution will degrade with the requirement for precise numerical information in describing the initial spatial state or in determining subsequent spatial states. Modeling Spatial Extent We describe the spatial extent of an object qual- itatively in terms of its extremal points: the topmost (tm), rightmost (rm), bottommost (bm), and leftmost (lm) points [Rajagopalan 931. To reason about three dimensional objects, we add the frontmost and rearmost points. We use two abstractions, a rectangular bounding box drawn around the extremal points of an object, and a bounding circle, as described below, to approx- imate the region occupied by the object. For problems in three-dimensional space, we use a bounding cube and a bounding sphere respectively. In Figure 3, we illustrate our abstraction method on two polygons. We draw a bounding circle around object A and a rectan- gular bounding box around object B. The radius of the bounding circle is the maximum distance from the cen- ter of gravity of an object to any point on its perimeter. The bounding box abstraction is sufficient for rea- soning about problems involving static worlds or only translational motion. The bounding circle/sphere ab- straction is used for problems involving rotation about the center of gravity. The latter abstraction provides the guarantee that an underlying rotating object will always remain within the bounding abstraction, and that the abstractions will have a fixed shape. The bounding circle/sphere abstraction is, in gen- eral, weaker than the bounding box abstraction. Con- sider the real possibilities that a rotating object could come into contact with another object, and that rota- tion could remove an existing contact. If two bounding spheres are not intersecting, we can conclude with cer- tainty that the underlying objects cannot come into contact after any rotation of either object about its center of gravity. If two bounding spheres intersect, they will continue to intersect after any rotation of the underlying objects. Additional information, such as the distances between the objects, their sizes, and rel- ative orientations, will be required in that case to de- termine with certainty if rotation can create or remove contacts between the underlying objects. Modeling Relative Positions/Orientation We describe the relative positions of objects through inequality relations between their extremal points. If tda) ‘I tm(b) - VI +- rm(b) v2 Ma) bMW v3 A B A: Bounding Circle B: Rectangular Bounding Box Figure 3: Examples of the rectangular bounding box and bounding circle as methods of shape abstraction for two polygons. the rectangular/cubic bounding box abstraction is used, the extremal points of the shape abstraction and the underlying object are the same. If the bounding circle/sphere abstraction is used, the extremal points used are those of the bounding abstraction, and not the underlying object. For example, for the objects in Figure 3, the inequality relation rm(A) < Zm(B), represents the fact that A is to the left of B. Although we can conclude that objects are intersect- ing with certainty in some special cases (such as over- lap across an extremal edge), in general, for relations involving intersections between objects, we can prove only the weaker relation that the bounding abstrac- tions of the objects satisfy the desired property. For example, object A bounding-abstraction-encloses object B if (am(A) 5 /m(B)) A (rm(A) 2 rm(B)) A (h(A) 2 h(B)) A (h-n(A) 5 bm(B)). We define the orientation of a surface of an object with respect to a global Cartesian frame of reference through its surface normal direction, as used by Nielsen [1988]. In our representation, this may be obtained through knowledge of the identities of the extremal points between which a surface lies. For example, the orientation vector of edge El for object B in Figure 1 has positive X and Y components since it lies between Vertices Vl and V2, the topmost and rightmost points. Rectangular bounding boxes and bounding circles are powerful abstractions for qualitative spatial reason- ing: numerically precise information is not required, even in a dynamically changing world, to maintain the bounding boxes and bounding circles. All we need are the inequality relationships between the extremal points of the bounding abstractions that are used. The use of circular/spherical abstractions for rotating ob- jects ensures that only translational motion can change the position of the extremal points of the shape ab- stractions and thus, the relative positions of objects (assuming that objects have fixed shapes). Orientation information, as required to determine the direction of current flow in an edge of a conducting loop, may be obtained if the connectivity of an object Spatial Reasoning 1413 and its extremal points are known. Only rotational motion can change the identities of the vertices and edges that form the extremal points of an object, and thus, its orientation. Translational Motion Our model of relative positions, based on inequality relations between the extremal points of objects, allows us to recognize that a qualitatively interesting event will occur when the inequality relation changes (e.g., when m-n(A) = am(B) in Figure 3). This can be used to study the effects of translational motion. The values of the rightmost and leftmost points of an object will change over time if the X-velocity of the object is non-zero, and the values of the topmost and bottommost points will be affected by the Y-velocity. In Figure 3, if the X-velocity of object A is positive, the coordinate value of its rightmost point will increase over time, and we can recognize that a qualitatively interesting state will occur once m-n(A) = im(B). Rot at ional Mot ion To maintain the orientation of a rotating object, we must determine the changes in the identities of the vertices and edges that form its extremal points as it rotates. Currently, we only consider the rotation of two dimensional objects about an axis that passes through their center of gravity. Rotation can also change the projected area of an object onto another object in a different plane, a property of great interest for the gen- erator problem described in Figure 2. The projected area of an object rotating about the X or Y axis onto another object in the XY plane is a function of the area of overlap between the two objects (as if both were in the XY plane) and the cosine of the angle between the plane of the rotating object and the XY plane. We independently model the effects of rotation about the X and Y axes, and use qualitative addition to determine the net change in the projected area. We model the extent of rotation about the X and Y axes, respectively, through two angles measured counterclockwise from the XY plane to the plane of the object: 6y, the angle between the plane of the object and the Y axis, and 19x, the angle between the plane of the object and the X axis. When 8~ or t9y is equivalent to 90 or 270 degrees, the projected area of an object onto the XY plane is zero. These angles also mark the point at which the orien- tation of the object changes. During counterclockwise rotation about the X-axis, when By is in the interval 90 degrees to 270 degrees, the identities of the topmost and bottommost points will be reversed. During rota- tion about the Y-axis, the identities of the leftmost and rightmost points can be reversed. In Figure 3, consid- ering object B, if the object has a value for By in the interval 90 to 270 degrees, then the orientation of edge El would have a positive X-component and a negative Y-component since vertex Vl would be a point instead of a topmost point. bottommost Rotation in the XY Plane Rotation about the Z- axis can only change the orientation of an object, and not the projected area onto the XY plane. Given, as in Figure 3, that vertex Vl is the topmost point of an object rotating in the counterclockwise direction, and that vertex V2 follows Vl, V2 will be the next topmost point. The difficult problem is to determine which ex- tremal point will change first. Given that V2 is the rightmost point and that V3 follows V2, the question now becomes will V2 become the topmost point before V3 becomes the rightmost point? Since the bottom- most and leftmost points may also change, there is always a four-way race condition. For a general polygon, we would require quantitative knowledge (e.g., the internal angles of the polygon) to avoid intractable branching during a qualitative simu- lation. However, for such commonly encountered spe- cial shapes as circles, rectangles and parallelograms, qualitative solutions do exist. For example, rectangles have the property that all four extremal points change simultaneously, eliminating the race condition. Integrating Spatial and Dynamic Reasoning We have implemented our spatial reasoning methods using the &PC [Crawford, et. al 90, Farquhar 941 qualitative modeling system, which in turn uses the QSIM [Kuipers 861 qualitative simulation system. We encountered two difficulties in integrating spatial and dynamic reasoning in the context of these systems - the need to model piecewise continuous variables, and the need to model variables with circular quantity spaces. Modeling Piecewise Continuous Variables Several qualitative modeling tools, such as &PC and QPE [Forbus 901, q re uire model variables to be contin- uous. In problems involving both spatial and dynamic reasoning, it’s possible for certain model variables to be piecewise-continuous. Figure 1 shows a conduct- ing loop, whose abstracted shape is a rectangle, mov- ing into a rectangular field. As the loop enters, the derivative of the area of overlap between the two ob- jects is positive and is proportional to the X-velocity of the loop. Once the loop is enclosed in the field, the derivative of the area of overlap drops discontinuously to zero. This derivative is a piecewise-continuous vari- able - one whose value is continuous within a given world model, but which may change discontinuously at a transition point, when a new world model is com- puted to reflect a qualitatively significant change in the world state. &PC inherits the values of model variables from the previous model when determining the new model af- ter a transition point. Discontinuous changes in the values of variables could lead to contradictions in the 1414 Spatial Reasoning new model. In our implementation, we allow the &PC model builder to explicitly declare that a variable is piecewise-continuous within a &PC model fragment description, and prevent their values and any inequal- ity relations involving such variables from being inher- ited at a transition point. This technique may be used for any dependent variable, since the new value for the variable may be recomputed in a subsequent model, or for any independent variable whose new value is explic- itly given in the subsequent model.’ Variables that are dependent on piecewise continuous variables must also be modeled as piecewise continuous since their values could also change discontinuously. Modeling Circular Quantity Spaces A second modeling restriction imposed by the exist- ing qualitative reasoning systems is that the range of values for a model variable is given through a linear quantity space. For modeling such phenomena as ro- tation, it is beneficial to model some variables through a circular quantity space to directly model the fact that the behavior of the system is cyclic. Consider the variable 0y for the example of Figure 2. This measures the extent of rotation around the X-axis. The qualitatively significant values for 0~ in- clude 0,90, 180,270, and 360 degrees. We would like to directly state that the value of 360 degrees is function- ally equivalent to zero degrees (resulting in a circular quantity space), instead of having to model, in a linear quantity space, that 450, 540, etc., are also significant values. We cannot model this fact in a linear quantity space since we would have that (0 < 270)) (270 < 360), and (0 = 360), which leads to a contradiction. We use the circular-quantity-space declaration - (circular-qspace-quantity theta-y convex-2-d-objects (theta-y-0 theta-y-90 theta-y-180 theta-y-27011 to define the variable theta-y as a quantity for the domain class convex-2-d-objects. It has a circular quantity space with four qualitatively significant val- ues represented by theta-y-O, theta-y-go, theta-y-180, and theta-y-270. After theta-y-270, the quantity space wraps back to theta-y-O. Note that each of these values actually represents a set. We maintain the inequality relationships between 0y and each of t?$c, &so, ey 180, and 0y270 to model the relative value of 0y. The same inequality relations, (0y > t!Jyo) and (By < &so), are used to capture the fact that 0y is between 0 and 90 degrees or 360 and 450 degrees. We avoid contradictions in the model by asserting only a linear subset of the circular quantity space into each &PC model. Assuming that each of the qualita- tively significant values in a circular quantity space is associated with a model transition condition, in any &PC model, we only have to consider the relationship between the circular-valued variable (ey) and three of those values. For example, in the initial state of the problem described in Figure 2, we have that By is equal to ~9~0, is less than &go, and is greater than eyz70. We may model t9y to be greater or less than By isc, and not both, to linearize the circular quantity space since we know that I+ cannot equal Oylso without first cross- ing through t!?ygO or 0y270, when a model transition is required to occur. We use the piecewise-continuous variable feature to model the fact that the inequality relationships be- tween ey and any of Oyo, eygo, Oylso, and 0~270 can change discontinuously at a transition point. The appropriate inequality relations are automatically as- serted into the subsequent model. For example, in Figure 2, the loop is rotating in a counterclockwise direction about the X-axis and the next qualitatively significant change occurs when 19y equals Bygo. Then, we ignore all previous inequality relations between 0y and its possible values, and insert into the model that (0~ = eygo), (0y < eylso), and (ey > eye). The re- lationship between By and 0y2To is insignificant, and may be modeled as ‘<’ or ‘>’ since the relationship in the previous model (>) will not have been inherited. Qualitative Behavior for the Examples in Figures I and 2 To illustrate both solutions, we have artificially com- bined the problems in Figures 1 and 2 into a single problem: As in Figure 1, the loop moves to the right until it is entirely enclosed in the magnetic field. At that point, its translational motion stops, and it rotates around the X-axis as in Figure 2. This was done by treating translational and rotational velocity as piece- wise continuous variables, and resetting their values once the loop was enclosed in the field. During translational motion (denoted by time points to, tl, and t2), as the loop enters the field (tl to t2), the area of overlap, and thus, the magnetic flux through the loop, increases steadily (steady due to the use of the rectangular bounding box abstraction for the con- ducting loop). During this period, an induced emf is established in the loop, which results in a steady cur- rent flow. The current flow is negative to show that it opposes the increase in the flux through the loop. The direction of current flow may be either clockwise or counterclockwise depending on the direction of the magnetic field, a property we ignore for the purposes of this example. The variables DIF-<F.LM-XVAL>-<L.RM-XVAL> and DIF-<F.LM-XVAL>-<L.LM-XVAL> are generated by &PC to encode the inequality relations between the rightmost and leftmost points of the loop and the left- most point of the field. Note that a qualitatively in- teresting change occurs in the relative positions of the loop and the field whenever one of the DIF terms is zero (i.e., an inequality relation changes). When the former DIF variable is zero, the loop begins to enter the field. When the latter is z,ero, the loop is fully enclosed in the field. Note also that the value of the derivative of the Spatial Reasoning 1415 L.X-VELOCITY L.X-ROT-VELOCITY DLr-~C.U(-XVAL>-‘L.RY-XV~> L.SIN-TIBTA-Y L.INDUCBD-EMF-NM Figure 4: Qualitative behavior produced by QPC/- QSIM for the problems in Figure 1 (up to time t2) and Figure 2 (after time t2). The shape abstrac- tion for the loop is assumed to be rectangular in the models for translational motion, and is assumed to be circular in the models of rotational motion. The values of L.AREA-OF-OVERLAP (constant after t2) and L.AREA-OF-OVERLAP-DERIV (constantduringtl-t2)re- fleet these assumptions. area of overlap between the loop and the field changes discontinuously from a positive value to zero at time t2. The variables dependent on this derivative, such as the derivative of the flux passing through the loop, the magnitude of the induced emf, and the current flow in the loop, also change discontinuously. At time point t2, translational motion stops and ro- tational motion begins. We show the output for two complete, counterclockwise rotations of the loop. Each time interval after t2 corresponds to an additional 90 degree increment in the value of 0~. Theta-Y has a positive value equivalent to zero in the initial state (I.e., the actual value may be 360, 720, etc.). It is con- tinuously increasing after time t2 since the rotational velocity of the loop is positive and constant. The magnetic flux through the loop is proportional to the projected area of the loop onto the mag- netic field, which is given by Proj-Area = (Area- Loop)(cos t9y). The rate of change of flux through the loop, &B/c&, is proportional to the rate of change of the projected area of the loop onto the field, which is given by dProj-Area = (Area-Zoop)(- sin &)(dBy). The induced emf in the loop is proportional to -d@/dt. The simulation output shows the sinusoidal behavior of the model variables as the loop rotates around the field. The last four DIF variables encode the inequality relationships between theta-Y and its possible values. The qualitatively interesting changes (in orientation) occur whenever one of the DIF terms crosses zero. Note that at time t3, when the value of theta-Y is equiva- lent to 90 degrees (the difference term dif-<l.theta-y>- <l.theta-y-90> is zero), the projected area of the loop onto the XY plane becomes zero. The projected area is then negative through time point t5, when theta-Y becomes equivalent to 270 degrees (the difference term dif-<l.theta-y>-<l.theta-y-270> is zero). This repre- sents the period when the orientation of the loop is reversed due to the identities of the topmost and bot- tommost points being reversed. Note the discontinuous changes in the values of the last four DIF variables. These occur when a newly as- serted inequality relation (after a transition) between theta-Y and any of eye, eygo, OylsO, and &-270 is dif- ferent from that in the previous model. This demon- strates not only the operation of the circular quantity space mechanism, but also the usefulness of the ability to model piecewise continuous variables. Summary and Conclusions Forbus, Nielsen, and Faltings [1991] have conjectured that there exists no purely qualitative, general pur- pose, representation of spatial properties. Their con- clusions are based on the need to reason about the exact shapes of objects in reasoning about mechanical devices, a spatial property that is indeed difficult to describe in a qualitative fashion. Many qualitative formalisms have since been devel- oped to support spatial reasoning {Mukerjee and Joe 90, Cui, Cohn, and Randell 92, Abella and Kender 931. They share the property that simplifying abstruc- tions are used to approximate the actual shapes of objects. The authors describe how abstractions such as the convex hull, collision parallelograms, or inertia tensor-based bounding boxes may be used for qualita- tive spatial reasoning, but do not describe how these abstractions can be represented internally in a qual- itative fashion, or how to qualitatively compute the changes in the positions and orientations of the ab- stractions as the underlying objects translate or rotate. We discussed the advantages and fundamental lim- itations of using shape abstractions for spatial rea- soning, and presented an extremal point-bused spatial representation that requires little information to com- pute and maintain even as objects translate and rotate. With this method, we can describe the relative posi- tions of objects through inequality relations between their extremal points, and easily determine the effects of translational motion on the spatial state. We showed that the orientation of a convex object with respect to 1416 Spatial Reasoning a global Cartesian frame of reference could be deter- mined given just the connectivity of the object and the identities of its extremal points, and discussed meth- ods for maintaining the orientation if the object rotates about an axis passing through its center of gravity. We are applying our spatial reasoning methods in a problem solver for the magnetic fields domain. The remaining work in this ongoing project will cover the use of orientation information to compute and reason about the effects of magnetic forces, and will address methods for modeling dynamically created spatial en- tities, such as magnetic fields due to current flow in a wire. We have also tested the utility of our spatial representation for use in natural language understand- ing, including reasoning about objects with intrinsic fronts, by considering problems involving the use of spatial reasoning to isolate objects in a complex scene to name them [Rajagopalan 941. Acknowledgements I thank Professor Benjamin Kuipers for his many sug- gestions in developing the ideas presented in this paper, and Bert Kay, James Lester, Toyoaki Nishida, Sowmya Ramachandran, and Lalitha Rajagopalan for providing valuable comments on earlier drafts. References [Abella and Kender 931 Abella, A. and J. Kender. Qualitatively Describing Objects Using Spatial Prepositions. In: AAAI-93, Washington, DC, 1993. [Crawford, et. al. 901 Crawford, J., A. Farquhar, and B. Kuipers. &PC : A Compiler from Physical Models into Qualitative Differential Equations. In: AAAI-90, Boston, MA, 1990. [Crawford and Kuipers 911 Crawford, J. and B. Kuipers. Algernon - A Tractable System for Knowledge-Representation. AAAI Spring Sympo- sium on Implemented Knowledge Representation and Reasoning Systems, Palo Alto, CA 1991. [Cui, et. al. 921 Cui, Z., A. G. Cohn, and D. Randell. Qualitative Simulation Based on a Logical Formalism of Space and Time. In: AAAI- 92, San Jose, CA, 1992. [Egenhofer and Al-Taha 921 Egenhofer, M. and K. Al-Taha. Reasoning about Gradual Changes in Topological Relationships. In: A. Frank, I. Campari, and U. Formentini, Eds., Theo- ries and Methods of Spatio-Temporal Reasoning in Geographic Space, Springer-Verlag, Berlin, 1992. [Farquhar 941 Farquhar, A. A Qualitative Pro- cess Compiler. In: AAAI-94, Seattle, WA, 1994. [Forbus, et. al. 911 Forbus, K., P. Nielsen, and B. Faltings. Qualitative Spatial Reasoning: the CLOCK Project. Artificial Intelligence 51, 1991. [Forbus 901 Forbus, K. The Qualitative Process Engine. In Weld, D., and de Kleer, J., eds., Read- ings in Qualitative Reasoning about Physical Sys- tems. Morgan Kaufman, Los Altos, CA, 1990. [Ereksa 921 Freksa, C., Using Orientation Infor- mation for Qualitative Spatial Reasoning. In: A. Frank, I. Campari, and U. Formentini, Eds., Theo- ries and Methods of Spatio-Temporal Reasoning in Geographic Space, Springer-Verlag, Berlin, 1992. [Galton 931 Galton, A., Towards an Integrated Logic of Space, Time, and Motion. In: IJCAI-93, Chambery, France, 1993. [Joskowicz and Sacks 911 Joskowicz, L., and E. Sacks. Computational Kinematics. Artificial Intelligence 51, 381-416, 1991. [Kuipers 861 Kuipers, B. Qualitative Simulation. Artificial Intelligence 29, 289-338, 1986. [Kuipers and Levitt 881 Kuipers B., and T. Levitt. Navigation and Mapping in Large-Scale Space. AI Magazine, 9(2), 25-43. [Mukerjee and Joe 901 Mukerjee, A. and G. Joe. A Qualitative Model for Space. In: AAAI- 90, Boston, MA, 1990. [Nielsen 881 Nielsen, P. A Qualitative Approach to Mechanical Constraint. In: AAAI-88, Saint Paul, MN, 1988. [Rajagopalan 931 Rajagopalan, R. A Model of Spatial Position Based on Extremal Points. In Proceedings: ACM Workshop on Advances in Geographic Information Systems, Arlington, VA, 1993. [Rajagopalan 941 Rajagopalan, R. Integrating Text and Graphical Input to a Knowledge Base. In Working Notes: AAAI Workshop on Integra- tion of Natural Language and Vision Processing, Seattle, WA, 1994. [Rajagopalan and Kuipers 941 Rajagopalan, R. and B. Kuipers. The Figure Understander: A System for Integrating Text and Diagram Input to a Knowledge Base. In Proceedings: The Seventh International Conference on Industrial and Engi- neering Applications of Artificial Intelligence and Expert Systems (IEA/AIE-94), Austin, TX, 1994. [Resnick and Halliday 881 Resnick J. and D. Halliday. Fundamentals of Physics, 3rd. Edition, John Wiley and Sons, 1988. [Retz-Schmidt 881 Retz-Schmidt, G. Various Views on Spatial Prepositions. AI magazine, g(2). [Weinberg, et. al. 921 Weinberg, J., S. Uckun, G. Biswas, and S. Manganaris. Qualitative Vec- tor Algebra. In: B. Faltings and P. Struss, Eds., Recent Advances in Qualitative Physics, pp. 177- 192, The MIT Press, Cambridge, MA, 1992. Spatial Reasoning 1417 | 1994 | 42 |
1,669 | A Theory for Qualitative Spatial Reasoning Based on Order Relations Ralf Riihrig Laboratory for Artificial Intelligence University of Hamburg Vogt-Kolln-Str. 30 22527 Hamburg, Germany email: roehrigQinformatik.uni-hamburg.de Abstract What is needed for an analysis of the existing approaches to qualitative spatial reasoning and for a deeper understanding of the domain of space is a unifying theory that explains all of the concepts used for the representation of the different aspects of space by some primitive but well understood relations. In order to provide such primitive relations it will be shown that the concepts used in the existing approaches can be explained by simple order relations between points on some low-dimensional structures. One of the properties of an order relation is transitivity. It will be shown that this property alone is sufficient to explain all the inferences described in the various approaches to qualitative spatial reasoning. Motivation Several approaches to qualitative spatial reasoning have been developed recently. A major problem with these approaches is the lack of comparability between them. One difficulty is that the approaches deal with different aspects of the spatial domain. Each of them provides some concepts for spatial relations, but most of the concepts differ in a substantial way. An overview of the dimensions of qualitative spatial reasoning is given in (Freksa & Rohrig 1993). Another difficulty in the comparison of the various approaches is that most of them use look-up tables for the explication of possible inferences instead of using the properties of the concepts involved. Even though look-up tables may have computational advantages, they include only very specialised rules that are not likely to be compared with properties of concepts from other approaches. What is needed for an analysis of the existing approaches and for a deeper understanding of the domain of space is a unifying theory that explains all of the concepts used for the representation of the different aspects of space by some primitive, but well understood, relations. In order to provide such primitive relations it will be shown that the concepts used in the approaches to qualitative spatial reasoning can be explained by simple order relations between points on some low-dimensional structures. For some of the approaches these low- dimensional structures are one-dimensional axes to which the spatial scenes are projected. For other approaches, those using orientation relations as basic spatial concepts, the low-dimensional structures are circles around the objects, and other objects are projected to those circles. Since it is not possible to define a binary order relation on a circle, a ternary relation with similar algebraic properties will be introduced. This relation is a sort of a cyclic order, and will therefore be called CYCORD. For the approaches using topological relations the low-dimensional structure is a system of subsets of space that is partially ordered by set inclusion. One of the properties of an order relation is transitivity. It will be shown that this property alone is sufficient to explain all the inferences described in the various approaches to qualitative spatial reasoning. The Theory Although the existing approaches to qualitative spatial reasoning differ substantially, they have some aspects in common: they deal with objects in 2, 3, or n-dimensional space, they refer to spatial scenes by spatial relations between those objects, and they use composition of spatial relations for doing inferences. The thesis of this paper is that for all approaches, 1) objects can be projected to 1418 Spatial Reasoning From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. points on some low-dimensional structures that are ordered by an order relation 2) spatial relations can be expressed in terms of these order relations, 3) transitivity can be used to do inferences, and 4) the inferred facts can be translated back into the original terms, ending up in exactly the same inferences as are described in the approaches. The low-dimensional structures are axes, circles, and, for the topological approaches, partially ordered systems of subsets of space. There is a limitation to this theory: in some approaches, spatial relations require a theory of equality of points on the low-dimensional structures. For the sake of simplicity, and because the introduction is straightforward, equality is not included here. Order relations In this section, the algebraic properties of a binary order relation are recalled to provide a basis for the definition of a ternary order relation on cyclic structures. An order relation is known to be asymmetric, non-reflexive, and transitive. Now, a relation with similar properties will be defined on the points of a circle. There is a problem defining a binary order relation on a circle, even when committing to a clockwise orientation for example; if any point A appears on a circle before a point B, then it is also true that B appears before A, when starting between A and B (cf. Figure 1). This problem can be fixed by defining a starting point for each pair of points and adding this point as a third argument to the order relation. The resulting relation will be called CYCORD, which is short for Cyclic ob’ects: re ation: r’ points on a circle CYCORD : point X point X point Properties Asymmetry A-B-C ==> 1 (A-C-B) Non-Reflexivity 1 (A-B-A) boundedTransitivity A-B-C, A-C-D ==> A-B-D Revolving A-B-C ==> B-C-A Figure 1: Properties of a cyclic order relation ORDer. The interpretation of CYCORD (A, B, C) (or A-B-C for short) is that in a clockwise direction, B appears before C when starting at A. Another valid interpretation of A-B-C is that B is between A and C, when committing to a clockwise direction. There is no restriction regarding additional points between A and B or B and C. Still another view of CYCORD is that the circle is cut in A, resulting in an open interval from A to A on which a normal binary order is defined for any two points that are unequal to A. Each of the algebraic properties of a binary order relation has a correspondence in a property of the cyclic order. CYCORD is asymmetric: if B is between A and C, then B should not be between C and A. CYCORD is non-reflexive: A-B-A holds for no A, B; this property ensures that CYCORD does not collapse into a binary order. CYCORD is transitive, but not in the expected way, which would be: if A-B-C and B-C-D, then A-B-D. Even though this property seems to hold in Figure 1, it does not hold in the general case. This may be verified by the same picture in Figure 1: A-C-D holds, and C-D-B holds too, but it is not the case that A-C-B holds. The problem is that the circle must not be traversed more than once, when transitivity is applied. Therefore, a property called bounded transitivity is imposed here, which is a more conservative form of transitivity, based on a constant starting point: if A-B-C and A-C-D, then A-B-D, in words, if B is before C when starting from A, and C is before D when starting from the same point A, then also B is before D when starting from that point A. This property is very intuitive and is valid, because it is guaranteed that the circle is not traversed more than once. There is one additional property that holds for CYCORD: since CYCORD is a relation over three arbitrary points on a circle, the three points may change places in a revolving manner: if B is between A and C, then also is C between B and A. The revolving property offers some very intuitive enhancements to the other properties of CYCORD. First, in combination with asymmetry it ensures that no two arguments of the CYCORD relation may be switched. Second, in combination with non-reflexivity it ensures that no two arguments of the CYCORD relation are the same. Third, in combination with bounded transitivity, it allows for other transitivity schemes, where the bound is not necessarily the first argument. And fourth, Spatial Reasoning 1419 applying the revolving property more than once makes the arguments of a CYCORD relation a cyclic list. Applications In this section, the theory will be supported by several examples. Approaches to qualitative spatial reasoning are divided into three major classes, those using orderings, those using orientation information, and those using topological relations for the description of spatial relations between objects. Ordering approaches In some of the approaches, such as (Jungert 1988), (Giisgen 1989), or (Mukerjee & Joe 1991), the projection step is done explicitly: objects are projected to multiple one-dimensional axes. Since there is no interaction between the axes, an inference calculus can be applied on each axis independently. Projection of objects results in intervals on each axis, and spatial relations are represented by interval relations. Since intervals are defined by their start and end points, it is straightforward to translate the interval relations to relations between points. For example, an A before B becomes a simple end(A) c start(B), while B overlaps C becomes a more complex formula: start(B) < start(C) and start(C) c end(B) and end(B) < end(C), where “start” and “end” are functions from intervals to their start points and their end points, respectively. Using transitivity of “4’ it can be inferred from the two facts above, that end(A) < start(C) . The inferred fact can be translated back into terms of interval relations as A before C. This inference corresponds to the one Gusgen stated in his composition table (Giisgen 1989). Since there is no loss of information, when translating intervals to points and interval relations to order relations on points, all inferences valid in one formalism have to be valid in the other one. Orientation approaches Some of the approaches, such as (Frank 1991) and (HernBndez 1992), use sector models for a description of orientation relations between objects. In these approaches, objects are considered to be points, and each object induces several sectors around it which are each bounded by two globally oriented lines (cf. Figure 2). Information about a point being on either side of a straight line can be reduced to an order relation on a one-dimensional axis perpendicular to that line, where the point and the line itself are projected to points on that axis. Since each orientation relation in the approaches corresponds to one sector, it can without loss of information be translated to order relations on each of the axes perpendicular the bounds of that sector. 1 2 Figure 2: Representation of orientations in (Hernrindez 1992) For example, in the sector model of (HernZindez 1992), A front B becomes A < B on the axis perpendicular to bound 1, and B c A on the axis perpendicular to bound 2. In the same manner, B front C becomes B < C on the axis perpendicular to bound 1, and C < B on the axis perpendicular to bound 2. Since a global system of orientations is used, the bounds are oriented in the same way in every object. Hence, the axes perpendicular to the bounds are the same for any bound with the same index. Using transitivity, from the facts above we can conclude A < C on axis 1, and C < A on axis 2. These inferred facts correspond to A front C in terms of orientations, which is one type of inference included in the composition table in (Hernandez 1992). Some other approaches, such as (Schlieder 1992), (Freksa 1992), and (Latecki & Rohrig 1993), use locally oriented sector systems for the description of orientation relations. Since the orientation of the bounds of the sectors is determined locally by another object instead by a global reference orientation as before, the corresponding axes are distinct for most orientation relations, and hence, transitivity cannot be applied here. Instead of global axes, locally defined structures can be used for the projection step: on a circle around an object, the projection of any other object results in a point on that circle. Additional points are induced by each object depending on the theory in the 1420 Spatial Reasoning corresponding approach. In (Schlieder 1992), for example, a complementary view is induced, and in (Freksa 1992) and (Latecki & Rohrig 1993), a model of four sectors induces four points on the circle, one for each bound between the sectors (cf. Figure 3). Figure 3: In a local sector model with four sectors, an object A induces four points on a circle around another object B. - An orientation relation in these approaches corresponds to one sector defined by two objects, i.e. a third object is between the corresponding bounds, which can be expressed by a CYCORD relation on the circle. In Figure 3, for example, Object A induces four points AO, Al, A2, and A3 on a circle around B, and an orientation relation C right- front B w.r.t. A can be translated to A2-CO-A3. Accordingly, D right-front B w.r.t. C can be translated to C2-DO-C3. Using bounded transitivity, one of the properties of CYCORD, AO-DO-A2 can be inferred from the two facts above, which in the example in Figure 3 corresponds to D left B w.r.t. A, which in turn is short for the disjunction D Zeft-front B w.r.f. A or D left-back B w.r.t. A. This type of inference can be found in the composition tables of (Freksa 1992), or can be calculated by the inference rule in (Late&i & Rohrig 1993). Topological approaches Some of the approaches to qualitative spatial reasoning are based on topological considerations. The basic assumption is that objects are embedded in a given space of any dimension. Each object separates the space- into disjoint regions. (Egenhofer 1989), for example, uses the boundary of an object to distinguish its interior, boundary and exterior. The same division of space is used by (Hernandez 1992), whereas (Cohn et al. 1993) use a cling film to establish the convex hull of the space occupied by an object. From that they get a further subdivision of the space: the interior of an object is separated into the space that is properly inside the object, and that which is inside the convex hull, but not inside the object. Spatial relations between objects are represented by comparison of the subsets of space induced by the objects. While in some of the topological approaches the empty or non-empty intersection of each pair of subsets is used for the definition of spatial -relations, set inclusion is equally well suited for the same definitions. Figure 2 shows for the relation A disioin t B a comnlete transformation from the g-intersection model of (Egenhofer 1989) into a representation using set inclusion. interior(A) c exterior(B) boundary(A) c exterior(B) interior(B) c exterior(A) exterior 1pI -@j -@ I boundary(B) c exterior(A) Figure 4: Representation of the disjoint relation in the 9-intersection model of (Egenhofer 1989), and transformation of a 9-intersection into set inclusions The set of subsets of space induced by the objects together with set inclusion forms a lattice, where the empty set is the bottom element, and the whole space is the top element. Even though this lattice is not a proper one-dimensional structure, it is still the case that all spatial relations can be expressed by a binary order relation, set inclusion, and transitivity is the only property needed to explain the inferences in the topological approaches. For example, if A disjoint B and B includes C, then interior(B) c exterior(A), and interior(C) c interior(B) and boundary(C) c interior(B), so interior(C) c exterior(A) and boundary(C) c exterior(A) can be inferred. These facts can be translated back to topological terms as A disjoint C , which is one of the inferences in (Egenhofer 1989) and in (Hernandez 1992). Spatial Reasoning 1421 Comparison of existing approaches Even though the various approaches to qualitative spatial reasoning deal with different aspects of space, all of their spatial concepts can be expressed in terms of simple order relations. While it is hard to see the differences and the common ground of the spatial relations when analysing composition tables, the new theory offers a way of a direct comparison of spatial concepts on the level of the basic structures. Existing as well as new approaches can be classified by the structure on which of their concepts can be expressed in terms of order relations. One class of approaches can be explained by linear axes, such as, of course, approaches using orderings for the definition of spatial concepts, but also the orientation approaches of (Frank 1991) and (Hernandez 1992). Approaches in this class can be compared by analysing the axes and the possible interaction between the axes. While in the approaches of (Jungert 1988) and (Gusgen 1989) the axes are totally independent, in the approach of (Hernandez 1992), information about order relations on two axes may be used to infer information about orderings on the other axes: in Figure 2, for example, if an object B is to the right of bound 1, and is to the left of bound 2, then it is also above bound 3 and above bound 4. It is also easy to see how different approaches of the same class may be combined: by the identification of axes. If, for example, it happens to be that one of the bounds in the approach of (Hernandez 1992) is pointing to the north, then two of the axes are the same as in the approach of (Jungert 1988), and so, information given in one system can be used by the other. Also some differences become obvious: although in both approaches, that of (Jungert 1988) and that of (Frank 1991), the cardinal directions north and east are used for the definition of spatial concepts, the axes are different; while in the first approach the distinction whether some object is to the north or to the south of another object is made by an axis heading exactly to the north, the same distinction is done in the latter approach by a sector model consisting of two axes, one heading north-west, and the other heading north-east. In another class of approaches, the basic structure for the expression of spatial concepts in terms of order relations is a set of circles around every object. On this level it can be observed, for example, that the concepts in the approach of (Latecki & Rohrig 1993) are expressed by the same CYCORD relations as the concepts in (Freksa 1992), and therefore, a direct translation can be given: if, for example, ABC forms a positively oriented obtuse angle in (Latecki & Rohrig 1993), the information is the same as C Zeflt-front AB in (Freksa 1992). Still another class of approaches requires a system of subsets as their basic structure for the expression of spatial concept in terms of set inclusion. Since this system is not a spatial structure, there will not be any flow of information between concepts from this class and concepts of either of the other classes. In (Hemandez 1992), for example, his concepts projection and orientation are disintegrated because they refer to basic structures from different classes, namely, spatial axes and systems of subsets of space. iscussion From a knowledge representation theoretic point of view, any inference rule can be seen as a property of the concepts involved. Since composition tables, as they are found in most of the approaches to qualitative spatial reasoning, are a collection of inference rules, these approaches formally describe their spatial concepts by a lot of properties. There have been attempts to reduce the amount of properties by compacting the composition tables using symmetry and redundancy (Freksa 1992b). The theory described in this article provides a single property, transitivity, which is not applied to the original spatial concepts in the approaches, but is applied to concepts that are a result of a transformation from the original concepts. Since this transformation can be done without loss of information, the properties of the transformed concepts can be seen also as properties of the original concepts. Describing spatial concepts by a single property is not only useful for a comparison of the various approaches, but also provides a simple mechanism for all of the inferences included in the calculi of the approaches. While for the description of these inferences a single property, transitivity, is sufficient, there are two more properties of an order relation, asymmetry and non-reflexivity. These properties can be used to introduce negation and to infer 1422 Spatial Reasoning negative facts. For example, if A before B in (Gusgen 1989), then end(A) < start(B), and since start(X) < end(X) holds for any interval X, using transitivity we can infer start(A) < end(B). Now, asymmetry can be used to infer 1 end(B) < start(A), which corresponds to not B before A in terms of the original concepts. For another example, in (Hernandez 1992) non-reflexivity can be used to infer 1 A<A on any axis. This negative fact can be used in the back transformation step to conclude not A front A, not A right A, and so on, for every orientation relation used in Hernandez’ theory. These negative facts can be very useful in large spatial data bases, and are necessary for natural language understanding. Acknowledgement I would like to thank Christian Freksa and Geoff Simmons for a critical review of the final version of this paper and for correcting my English. I would also like to thank the anonymous referees for their detailed comments on the first version of this paper. References Allen, J.F. 1983: Maintaining Knowledge about Temporal Intervals, CACM 26 (11): 832-843. Cohn, A.G., Randell, D.A., Cui, Z. 1993: A Taxonomy of Logically Defined Qualitative Spatial Relations. In Proceedings of International Workshop on formal Ontology, Padova, Italy Egenhofer, M. 1989: A Formal Definition of Binary Topological Relationships. In W. Litwin and I-I.- J. Schek eds. Third International Coqference on Foundations qf Data Organisation and Algorithms, vol. 367 of Lecture Notes in Computer Science, 457-472. Springer, Berlin. Frank, A.U. 1991: Qualitative Spatial Reasoning With Cardinal Directions. In Proc. Seventh Austrian Conference on Artificial Intelligence, Wien, 157- 167, Springer, Berlin. Freksa, C. 1992: Using Orientation Information for Qualitative Spatial Reasoning. In: A. U. Frank, I. Campari, U. Formentini eds. 1992 Theories and Methods of Spatio-Temporal Reasoning in geographic space, Springer, Berlin. Freksa, C. & Rohrig, R. 1993: Dimensions of Qualitative Spatial Reasoning. In Piera Car-ret& N., Singh, M.G. eds. 1993 Qualitative Reasoning and Decision Technologies, Proc. QUARDET’93, CIMNE Barcelona. Gtisgen, H.W. 1989: Spatial Reasoning Based on Allen’s Temporal Logic. Technical Report, TR- 89-049, International Computer Science Institute, Berkeley. Hemtidez, D. 1992: Qualitative Representation of Spatial Knowledge. Doctoral Dissertation, Technische Universitit Miinchen. Jungert, E. 1988: Extended Symbolic Projections as a Knowledge Structure for Spatial Reasoning. Pattern Recognition, Kittler, J. ed. 1988, Cambridge, U.K. Latecki, L. & Rohrig, R. 1993: Orientation and Qualitative Angle for Spatial Reasoning. In Proceedings of the 13th International Joint Conference on Artificial Intelligence, 1544- 1549. Chambery, France. Mukerjee, A. & Joe, G. 1991: A Qualitative Model for Space. In Proceedings of AAAI-90, 721-727. Schlieder, C. 1992: Anordnung und Sichtbarkeit. Eine Charakterisierung unvollstandigen raumlichen Wissens. Doctoral Dissertation, Universittit Hamburg. Freksa, C. 1992b: Temporal reasoning based on semi- intervals. Art@cial Intelligence 54: 199-227 Spatial Reasoning 1423 | 1994 | 43 |
1,670 | Liu Zhang Artificial Intelligence University of Georgia Athens, GA 30602 lzhang@ai.uga.edu The purpose of this research is to develop an adaptive tutoring system which uses AI techniques to explore how to diagnose student’s misconceptions in problem solving and generate relevant instructions from the context. The system is called StatSim. StatSim is an expert system for teaching basic concepts of statistics such as standard deviation, normal distribution and standard scores. It simulates three types of knowledge: statistics domain knowledge, diagnostic knowledge and tutorial knowledge to guide students in problem solving. At the beginning of the tutorial, the student is given a case as a statistics problem to solve, produced by the problem generator based on the student’s record. The consultation program (domain expert) solves the problem first and saves the results and reasoning process in working memory. The diagnosis program (diagnosis expert) interprets the student’s behavior by comparing the student’s behavior in solving the sarne problem with the expert’s behavior. The tutoring program (teaching expert) responds to the student’s behavior on the basis of what the student knows and his goals for the tutorial session. It can take the initiative by offering orientation when a new concept is introduced or by interrupting a student when it finds some explanation is necessary. The purpose of this tutorial is to use the context of an actual problem to make the student aware of gaps and inconsistency in his knowledge and to correct these deficiencies. The whole tutoring process consists of two Donald Potter Artificial Intelligence University of Georgia Athens, GA 30602 dpotter@ai.uga.edu sessions: a consultation session and a tutorial session. During the consultation session, the Problem Solver program applies domain knowledge production rules to derive a solution. It reads in a problem text, converts it into a set of keywords in the form of attribute-value pairs and saves them in working memory. The rule interpreter fires all the rules whose conditions are satisfied and saves the results as a text file. During the tutorial session, the Tutor program maintains and updates a student model and a record of the communication between the tutor and student. A set of tutorial rules are used to control what to teach and how to teach on the basis of what the student knows. A template-based user interface is designed to keep track of the student’s mental activity. It serves both as an external memory and a source of input to the system. The student’s problem-solving behavior is recorded in performance history. A special module (performance interpreter) which simulates the diagnostic expertise of a teacher is developed to reconstruct the student’s model of domain knowledge on the basis of the student’s performance history. The input to the performance interpreter comes from the generic template and working spreadsheet. Each move in the student’s behavior on the screen is recorded whenever an input textbox is out of focus. The interpreter keeps its observations until it collects enough information to update the student model. Interpretation rules are employed to decide when to intervene and how to intervene, one of the major issues in ITS. The system is sensitive to every step in the student’s problem solving process but at the same time lets him explore the solution to the problem. StatSim has four major features: 1) it uses multiple faulty diagnosis techniques to locate student’s misconceptions; 2) it employs graphics, animation, menus, windows and other interactive techniques in instruction delivery to enhance understanding and motivation; 3) it uses production rules to control the intervention so that the user has enough control of the system; 4) it uses planning to refine the explanations and instructional acts to maximize the teaching effects. Student Abstracts 1501 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 44 |
1,671 | Synthetic Robot Language Development Holly A. Yanco* MIT Artificial Intelligence Laboratory 545 Technology Square, Room 741, Cambridge, MA 02139 holly@ai.mit.edu (617)253-7884 Cooperating robots can benefit from communica- tion. Our robots create their own adaptable synthetic robot languages (ASRLs). We have shown that robots can develop “basic”, context dependent, and composi- tional ASRLs using reinforcement learning techniques. (See (Yanco 1994) for a complete description of this work.) We have demonstrated that the robots are able to develop ASRLs using two different reinforcement schemes: task-based reinforcement and individual re- inforcement. In task-based reinforcement, the robots only receive positive reinforcement when the task is completed properly. This reinforcement method is preferable in situations where it can not be determined who performed the correct actions to reach the goal, but it is clear that the goal was reached. Individual reinforcement is better suited to tasks where it is clear which of the robots helped to reach the goal. This determination is used to give the robots that helped reach the goal good reinforcement while penalizing the robots that did not contribute toward the group goal. In our model, the robots are able to learn more quickly using the individual reinforcement, but at the expense of convergence. However, most tasks can not easily be decomposed to determine which members of the group acted correctly, and even for those tasks that can be easily decomposed, the overhead necessary to make the determination is often costly. While task-based rein- forcement results in longer learning times, it only re- quires a one-bit decision in allocating reinforcement. The basic ASRL is a simple one-to-one mapping of robot signals to robot actions. The development of this ASRL in simulation and with robots demon- strated that robots could learn to communicate and could adapt their language to changing circumstances. Simulated robots have also created a context depen- dent ASRL. In a context dependent language, robot words can have different meanings depending on the *This research is supported by the NSF under Profes- sor Lynn Andrea Stein’s NSF Young Investigator Award No. IRI-935’7’761, Digital Equipment Corporation, the Gor- don S. Brown Fund, and ARPA ONR contract N00014-91- J-4038. Any opinions, findings, conclusions or recommen- dations expressed in this material are those of the author and do not necessarily reflect the views of the NSF. 1500 Student Abstracts state of the world as perceived through sensor read- ings. For example, the robots could learn a command for DO, where they should DO recharge in the presence of a charging station, DO gather when sensors indicate that objects are present that should be collected, or DO sleep when the lights are turned out. The context de- pendent language requires shorter learning times than the basic experiment because the robots need to learn fewer ASRL signals. The simulated robots have also developed a com- positional ASRL. A compositional language combines words with ways for the words to be put together to form higher level concepts. For example, you have probably never read a sentence exactly like this one before; however, you are able to understand the sen- tence because you know the meanings of the words in this sentence and understand English grammar. In the basic ASRL, whenever the robots encounter a new sen- tence (or concept), they must start the learning process from scratch, even if the concept only varies slightly from a previously learned concept. In compositional ASRLs, the robots can use what they have already learned as they encounter new sentences containing old words. Therefore, the learning times for the composi- tional ASRL are dramatically faster than for both the basic ASRL and the context dependent ASRL. Adaptable synthetic robot languages developed by the robots themselves have several advantages. They allow the robots to create languages that will be well- suited to specific tasks and to the capabilities of the robot hardware. ASRLs require less human involve- ment than pre-programmed robot languages. The robots are able to adapt to changing circumstances without outside assistance. In a dynamic environment where robots must work continuously without human assistance, adaptable synthetic languages are the com- munication method of choice. References Yanco, H. A. 1994. Robot communication: issues and implementations. Master’s thesis, Massachusetts Institute of Technolgy. Also available as MIT-AI-TR 1478. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 45 |
1,672 | Fuzzy Irrigation Decision Support System Hong Xiang AI Programs The University of Georgia Athens, GA 30602 xhong@ai.uga.edu Brahm P. Verma Gerrit Hoogenboom Department of Biological Department of Biological and Agricultural Engineering and Agricultural Engineering The University of Georgia The University of Georgia Athens, GA 30602 Griffin, GA 30223 bverma@gamma.bae.uga.edu ghoogen@gaes.griffin.peachnet.edu Water is a limiting factor in agriculture and when improperly managed reduces the yield potential of crops. The objective of this study is to develop a Fuzzy Irrigation Decision Support System (FIDSS) to opti- mize water management for soybean production. Management of irrigation systems for greatest ben- efit requires an understanding of many physical, bio- logical and chemical processes, and economical factors. Such processes are very complicated and involves many uncertainties. During the last 20 years, considerable progress has been made in developing computer crop growth simulation models. These models are devel- oped with the desire to incorporate quantitatively the fundamental mechanisms controlling the above pro- cesses. However, this objective has been compromised by simplifying the mechanisms’ representations by gen- eral process descriptions which use empirical relation- ships determined from experimental data. In most cases, it is not possible to collect and correlate data for all conditions due to the nature of these processes. For example, variables such as soil water uptake by roots, soil water content at various depths and water lost by evapotranspiration interact with each other in a complex way making it hard to determine fundamental quantitative relationships among these variables. This study is therefore undertaken to begin the de- velopment of a mechanistic model using qualitative rather than quantitative relationships of the most im- portant variables for making irrigation decisions. The Fuzzy set theory introduce by Lofti Zadeh in 1965 provides the framework to cope with ambiguity and unnaturalness of the traditional crisp method in this domain. Fuzzy expert systems utilize human experi- ence and decision methods, and they have proven to be valuable when dealing with non-linear and complex relationships. In FIDSS we have developed membership functions for 21 important variables of three primary compo- nent s: 1) variables for plant, such as, leaf area in- dex (LAI) and evapotranspiration (EP); 2) variables for water status and flow in soil, such as, soil-water content in a layer (0~) and infilteration (IN); and 3) variables for weather, such as, maximum temperature (TM) and solar radiation (RAD). FIDSS has 163 rules in its knowledge base specified as follows: PF (LA1 IS HIGH) AND (RAD IS HIGH) AND (TM IS HIGH) THEN (EP IS HIGH) FIDSS is organized to receive crisp daily values of all state variables from an existing crop model, fuzzify the received inputs, perform evaluation with the knowl- edge base to give a fuzzy output, defuzzify the output to a crisp value which is then compared to a predeter- mined threshold condition for irrigation decision. The existing soybean crop growth simulation model SOYGRO V5.42 developed at the University of Florida by James Jones et al. was used to update state vari- ables. SOYGRO also has an irrigation management model in it which provided us an opportunity to com- pare decisions made by FIDSS with the ones of SOY- GRO. The important additions in FIDSS are that it includes two days’ predicted weather data for estimat- ing soil water content and more additional variables for making decisions. At this early stage of FIDSS development, only lim- ited attempts have been made to tune the rules. How- ever, the following comparison of FIDSS output with the outputs of SOYGRO shows promise for this ap- proach. The output shown below is for soybean (cul- tivar ‘Bragg’) grown in Millhopper Fine Sandy soil for 1978 weather condition (for which field data is avail- able). A further tuning of rules and a systematic eval- uation of FIDSS is planned. Table 1: Irrigation Outputs of SOYGRO and FIDSS MODEL Irrigation days (from planting) and final resultes 73,77,82,87,93,98,115 SOYGRO Yield = 3386.6(kg/ha) Total Water = 211(mm) 8,15,68,72,76,80,84,88,92,96,110 FIDSS Yield = 3406.8( kg/ ha) Total Water = 275(mm) Student Abstracts 1499 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 46 |
1,673 | Utility-Directed Planning Mike Williamson Steve Hanks Department of Computer Science and Engineering, FR-35 University of Washington, Seattle, WA 98195 Classical AI planning has adopted a very narrow no- tion of plan quality, namely that a plan is good just in case it achieves a specified goal. Goals provide a valu- able point of computational leverage: despite the fact that planning is intractable in the worst case, goal- satisfying planning algorithms can effectively solve classes of problems by using the goal to focus the search for a solution (using backward-chaining techniques), and by exploiting domain-specific heuristic knowledge to control search. But as the sole description of a planning problem, goals are in several regards inadequate. Goals pro- vide neither a means of representing partial satisfac- tion (either a plan succeeds in achieving the desired world state or it does not), nor a way of describing the value of the specified world state relative to the cost of achieving it. In short, goals provide insufficient information to measure plan quality in any satisfying way. Decision theory has been proposed as a solution to this problem. It provides a rich theoretical frame- work for the construction of utility models captur- ing precisely the notion of partial satisfaction and the cost-benefit tradeoff mentioned above. But the plan- ning community has been slow to adopt utility models for the description of planning problems, since plan- ning with utility models requires optimization, com- monly thought to be less tractable and less amenable to heuristic control than classical goal satisfaction. We claim that optimal planning can be made heuris- tically tractable for a class of utility models that is sig- nificantly more expressive than simple goal formulas. We extend the definition of plan quality to take into account partial satisfaction of the goal and the cost of resources used by the plan, while at the same time building an effective planning algorithm by exploiting classical planning techniques like backward chaining and knowledge-based search control rules. We have adopted a goal-directed utility model similar to proposals by (Haddawy & Hanks 1993). This util- ity model allows the description of soft deudline goals whose value is a function of the time when the goal is satisfied. A goal is represented by a propositional goal formula, a temporal decuy function, and a goal-vulue coeficient. The temporal decay function must, be uni- formly 1.0 until the deadline, and decrease monotoni- cally thereafter. The goal-value coefficient determines the relative value of achieving the goal. The cost of the plan is captured with a residual utility function, a function of the resources consumed by a plan. Like temporal decay, the residual utility must be monotoni- cally decreasing with respect to increased consumption of any given resource. We have implemented PYRRHUS, a planning algo- rithm which finds optimal plans for the utility model described above. PYRRHUS is a synthesis of branch- and-bound optimization with a least-commitment, plan-space planner. The underlying planning mech- anism is based on the UCPOP planning system (Pen- berthy & Weld 1992), with extensions to provide sup- port0 for time and metric resources. In addition to the sort of search control knowledge employed by classical goal-satisfying planners, PYRRHUS uses the structure of the utility model to compute an upper bound on the utility of partial plans, possibly allowing them to be pruned from the search space. Our initial empirical results are encouraging. We have conducted a number of experiments in a simu- lated transportation domain, comparing classical goal- satisfying planning to optimal planning with various utility models. PYRRHUS is able to employ the same heuristic search control knowledge as a classical plan- ner to solve problems that would be intractable oth- erwise. We found the difficulty of optimal planning depends strongly on the nature of the utility model; in some cases the additional structure of the utility model makes optimal planning much easier than sim- ple goal-satisfying planning, while in other cases it is more difficult. We are in the process of developing a formal characterization of the relationship between the structure of the utility function and the difficulty of optimal planning. eferences Haddawy, P., and Hanks, S. 1993. Utility Models for Goal-Directed Decision-Theoretic Planners. Techni- cal Report 93-06-04, Univ. of Washington, Dept. of Computer Science and Engineering. Submitted to Ar- tificiul Intelligence. Penberthy, J., and Weld, D. 1992. UCPOP: A sound, complete, partial order planner for ADL. In Proc. 3rd Int. Conf. on Principles of Knowledge Representation und Reusoning, 103-114. 1498 Student Abstracts From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 47 |
1,674 | A Modular Visual Tracking System Mike Wessler* MIT Artificial Intelligence Laboratory 545 Technology Sq. NE43-803 Cambridge, MA 02139 wessler@ai.mit.edu I am currently building an active visual tracking sys- tem for a real world robot. The hardware is being built at MIT under the supervision of Professors Rod Brooks and Lynn Andrea Stein, and is humanoid in form. The software is also humanoid: I am basing its organization on models of early vision in the human brain. Most of the software is still in the design phase; what I describe here is the part of the system that is already up and running. The robot, named Cog, has roughly the same degrees of freedom in the waist, neck, arms and eyes as a hu- man and is designed with similar proportions in mind. The eyes sport a simulated fovea - each eye consists of two cameras mounted in the same plate, one with a wide field of view, and one with a much narrower view. Both cameras produce 128 x 128 gray scale im- ages. The narrow one is used for tracking, and can be used for object recognition, while the wider view will be used for motion detection and peripheral vision. I have written a visual tracking system that will eventually be hooked up to the motors in Cog’s neck and eyes. For now, tracking is simulated by moving a small 16 x 16 “attention window” around the larger image from one of the cameras. On startup, the sys- tem memorizes the 16 x 16 segment in the center of the full image as a “reference” image. For the rest of the run, the system moves the window around to maintain whatever was initially present within its view. The tracking system runs as follows. Once a new frame is grabbed, the system makes a guess about where the new window location should be, based on its previous velocity. Next, a portion of the image slightly larger than the attention window is selected, and the derivative of this region is computed.’ Finally, a sim- ple correlation is performed between the memorized reference image and the nine 16 x 16 windows centered around the pixel position nearest the guess. The one *This research is supported by an NSF Graduate Fel- lowship and by ARPA ONR contract N00014-91-J-4038. Any opinions, findings, conclusions or recommendations ex- pressed in this material are those of the author and do not necessarily reflect the views of the NSF. 10rigina.lly, I had taken two derivatives in the 3: and y directions, but it turns out that a single derivative runs twice as quickly, with very little decrease in reliability. with the best correlation becomes the new center of the attention window. The entire sequence of grab, process, and correlate runs at 15 Hz on one of the Mo- torola 68332 processors that make up Cog’s “brain”. The system can track anything that accelerates less than one pixel (0.15 degrees for the narrow-angle cam- era) per frame per frame. This becomes a problem only for objects that jerk suddenly; the system does very well with objects like hands and faces moving at normal speeds. Furthermore, by examining the result of the best correlation, the tracker knows exactly when it has “lost” the image, and should request the coordi- nates of a new region to track. The tracking routines form the heart of a much larger system that models Stephen Kosslyn and Olivier Koenig’s view of early vision in human brains. Instead of tracking whatever happened to be in the center of the camera view on startup, the full architecture will have an attention shift module to direct the gaze from one object to another. This module receives inputs from other modules that detect motion, faces or other ‘~pOpOUtS” in the field of view. An opposing forces model, described by Marcel Kinsbourne, implements the decision of when to switch attention: if one of the “watchers” detects a very strong stimulus, or when the tracking system has lost the image or has gotten “bored” with the image, the attentional system will prompt a tracking change. Further up the line, information from the tracking window will be fed to a system that keeps a represen- tation of location. This system gradually builds up a map of the world as attention is yanked from one ob- ject to another. Furthermore, by watching its hands and arms, Cog can learn to associate certain arm posi- tions with certain locations in space, in effect learning hand-eye coordination. Finally, because the image within the tracking win- dow is relatively constant, a moving background can be segmented out simply by averaging one image with the next. This yields extremely useful data for an object recognition system, which can then put “labels” on the locations that the location system is recording. Infor- mation from the object recognition system can also be used to guide attention around the image, for example from a face to the eyes or mouth. Student Abstracts 1497 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 48 |
1,675 | Learning by Observation and Practice: A Framework for Automatic Acquisition of Planning Operators Xuemei Wang * School of Computer Science Carnegie Mellon University Pittsburgh PA 15213-3891 wxm@cs.cmu.edu The knowledge engineering bottleneck is a central prob- lem in the field of Artificial Intelligence. This work ad- dresses this problem in the context of planning systems. It automatically learns planning operators by observing ex- pert agents and by subsequent knowledge refinement in a learning-by-doing paradigm. Our learning method is im- plemented on top of the PRODIGY architecture(Carbonel1 et al. 1992). The learning system is given at the outset the description language for the domain, which includes the types of objects and the predicates that describe states and operators. The observations of an expert agent consist of: 1) the sequence of actions being executed, 2) the state in which each action is executed @e-state), and 3) the state resulting from the execution of each action (post-state). Our planning system uses STRIPS-like operators and the goal of this work is to learn the preconditions and the effects of the operators. We assume that the operators have conjunctive precondi- tions and no conditional effects, everything in the state is observable, and there is no noise in the state. The architecture for learning by observation and practice in planning includes the observation module, the learning module, the planning module, and the plan execution mod- ule, as illustrated in Figure 1. Operators for the domain are learned from these observa- tion sequences in an incremental fashion utilizing a conser- vative specific-to-general inductive generalization process. When an operator is observed for the first time, the system creates the corresponding operator such that its precondi- tion is the complete pre-state and its effect is the differ- ence between the post-state and pre-state. Operators thus learned may have extra preconditions that correspond to the irrelevant features in the state. These extra preconditions are removed incrementally if they are not present in the pre-states of the new observations. In order to further re- fine the new operators to make them correct and complete, and to evaluate the new operators, the system uses them to solve practice problems. The system first generates an appoximate plan to solve the practice problem using the par- *Thanks to Jaime Carbonell for his suggestions and support in this work. This re- search is sponsoredby the Wright Laboratory, Aeronautical Systems Center, Air Force Materiel Command, USAF, and the Advanced Research Projects Agency (ARPA) under grant number F3361593-1-1330. Views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily rep- resenting official policies or endorsements, either expressed or implied, of Wright Laboratory or the United States Government. 1496 Student Abstracts Expert Agent actions Environment Figure 1: Overview of the data-flow among different modules of the learning system, The observation module provides the learning module with observations of the expert agent. The learning mod- ule formulates and refines operators in the domain. The planning module is essentially the PRODIGY planner modified to use some heuristics for planning with incomplete and incorrect operators as well as for plan repair, it generates tentative plans to solve practice problems. The plan execution module executes the plans, provid- ing the learning module with the execution traces, and passing the plan failures to the planning module for plan repair. tially incorrect and incomplete operators, then it executes the plan. When an operator fail to apply, it repairs the plan and continues execution, until the problem is solved or a re- source bound is exceeded. The system also refines operators based on the executions. oIn summary, operators are refined through a process which integrates learning, planning, plan repair, and execution. See (Wang 1994) for more details of this research. This learning method has been partially demonstrated in the extended-strips domain and the process planning domain. We are currently performing more exten- sive tests in these domains. We plan to extend the algorithm to handle situations when part of the state is not observable, and there is noise in the state. References Carbonell, J. G., and The PRODIGY Research Group. 1992. PRODIGY4.0: The manual and tutorial. TR CMU-CS-92-150, Carnegie Mellon University. Wang, X. 1994. Learning Planning Operators by Observation and Practice. In Proceedings of the Second International Conference on AI Planning Systems. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 49 |
1,676 | ModGen: Theorem Proving by Model Generatio Abstract ModGen (Model Generation) is a complete theorem prover for first order logic with finite Herbrand do- Sun Kim Hantao L&hang Department of Computer Science The University of Iowa Iowa City, IA 52242, U.S.A {sunkim,hihang}@cs.uiowa.edu mains. ModGen takes first order formulas as input, and generates models of the input formulas. ModGen consists of two major modules: a module for trans- forming the input formulas into propositional clauses, and a module to find models of the propositional clauses. The first module can be used by other re- searchers so that the SAT problems can be easily rep- resented, stored and communicated. An important issue in the design of ModGen is to ensure that trans- formed propositional clauses are satisfiable iff the orig- inal formulas are. The second module can be easily replaced by any advanced SAT problem solver. Mod- Gen is easy to use and very efficient. Many problems which are hard for general resolution theorem provers are found easy for ModGen. Introduction Many theorem proving problems are difficult for to- day’s theorem provers not because these problems are really hard but because the methods are not suitable to these problems. For example, one of test problems in Larry Wos’ thought-provoking book (Wos 1988) (Test Problem 6) asks one to prove that any group of order 7 is commutative. Using OTTER (McCune 1990), one of the best resolution-based theorem provers, this prob- lem cannot be solved in hours. However, if we code this problem in the propositional logic, the problem can be solved in a couple of seconds. The test problem mentioned above involves func- tions of finite domains. For this kind of problems, the constraint solving methods are better tools. The FINDER program (Stanley 1992) developed by John Slaney is a well-known program for model generation based on a constraint solving method. The goal of our project is to create a subroutine of OTTER which has similar functionality as FINDER. However, instead of using any constraint solving meth- ods, we prefer to use a decision procedure for the sat- isfiability (SAT) of propositional formulas: *Partially supported by the National Science Founda- tion under Grants CCR-9202838 and CCR-9357851. 162 Automated Reasoning While the SAT problem is a special case of constraint satisfaction problems, many constraint satisfaction problems can be easily and efficiently converted into an instance of the SAT problem. The SAT problem is a core of a large family of computationally in- tractable NP-complete problems and has been iden- tified as central to a variety of areas in computing theory and engineering. There has been great interet in designing efficient algorithms to solve the SAT problem. Various satis- fiability testing methods are available, such as back- tracking, resolution and its variations - the Davis- Putnam algorithm is one of the known methods. Some local search algorithms have been developed to solve large size instances of the SAT problem (Gu 1993). Since we intended that the user of OTTER can eas- ily use special methods to handle problems of finite domain, we of course must have a procedure which converts first order formulas into propositional clauses. We found that automatically converting first-order formulas into propositional formulas is not a trivial task. One of the 33 Research Problems proposed in (Wos 1988) by W OS asks what criteria can be used effectively choose between predicate and function no- tation for representing the problem under study. For instance, “the product of a and b equals c” can be writ- ten as P(cz, b, c) or prod(a, b) = c. However, no refer- ences are given in (Wos 1988) for the conditions which ensure that the initial formulas are satisfiable iff the converted formulas are. The existence of quantifiers in the formulas makes the problem more complicated. For example, suppose one of the axioms for a group of order 7 is axiom 2 * i(z) = e, where a: is a variable over a domain S of seven elements, say S = { 1,2, . . . . 7). We may obtain 7 instances of this axiom by replacing z by a value from 1 to 7. The resulting clauses are ground (i.e., variable-free) but they are not proposi- tional clauses. We have to replace functions like * and i by predicate symbols. We may introduce a predicate Pi such that Pi(z, y) is true whenever i(z) = y. To get rid of i(z) in that axiom, we may assume i(z) = u and use Pi(cc, u) 3 (a: * u = e) as a new axiom. Now From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. the question is: Since the two axioms are not logically equivalent, what additional information is needed to make them equivalent ? This questions must be an- swered if we want to correctly convert a set of formulas into a set of propositional clauses. We are also inter- ested in the efficiency of the conversion, in the sense that the converted clauses have shorter and less dupli- cated clauses. These questions will be answered in this paper. Traditional constraint solving methods do not need to convert general formulas into propositional clauses. For instance, FINDER (Stanley 1992) uses generate- and-test approach to test constraints represented by clauses. While the design philosophy of FINDER and ModGen are very different, FINDER has a great im- pact on the design of ModGen. Because of the different design philosophies, ModGen offers some advantages: e ModGen accepts arbitrary formulas (including quan- tifiers) while FINDER accepts only clauses. ModGen can be used to generate propositional clauses for other programs and it is very easy to change SAT decision procedures in ModGen. Experimental results show that ModGen outper- forms FINDER for almost all the examples tried. This paper is organized as follows: At first, we give an overview of ModGen and show by examples how ModGen is used. Next, we describe how to correctly and efficiently convert general formulas into proposi- tional clauses; we discuss how to handle function sym- bols and quantifiers. Finally, we present some experi- mental results of ModGen. Overview of ModGen ModGen mainly consists of two modules, a proposi- tional clause generator and the program SAT0 (SAt- isfiability Testing Optimized) (Zhang 1993) which is an efficient implementation of the Davis-Putnam algo- rithm (Davis & Putnam 1960). The overall structure of ModGen is shown in Figure 1. ModGen takes first order formulas either in arbitrary form or in clausal form as input, and generates models of input formu- las. All variables in input formulas should be of finite domain. Also, ranges of all functions in input formulas should be finite. The propositional clause generator generates propo- sitional clauses in clausal form from input formulas. If input formulas are not in clausal form, ModGen trans- forms them in clausal form, and then generates propo- sitional clauses. The generated propositional clauses are fed to SATO, which determines the satisfiability of the clauses. If the clauses are satisfiable, SAT0 generates their Herbrand models, that is, which propositional variables are set to true. Since there is a one-to-one mapping between a propositional variable and a func- tion instance, from the Herbrand models generated by first order formulas/ clauses models Figure 1: Overview of ModGen SATO, ModGen can print out solutions in terms of function values. The input to ModGen consists of three parts: (a) sorts of finite elements, (b) functions (including pred- icates); and (c) ( multisort) first order formulas. Mod- Gen decides whether there exist any (or how many) models for the input formulas. In the beginning of this project, we decided to use the syntax of OTTER (McCune 1990) for input formu- las and clauses. This is because OTTER is the best known resolution-based theorem prover and is very popular in the community of au- tomated theorem proving; we wish that ModGen become a complementary tool to OTTER for finite domain problems and many OT- TER'S input files can be directly input to ModGen without any modification. For the above reasons, some code of OTTER has been used in implementing ModGen. Especially, the entire module for parsing input formulas has been used, so the syntax of ModGen is the same as that of OTTER. We illustrate the use of ModGen by two simple ex- amples. The Queen Problem The 8-queen problem is to find placements of 8 queens over a 8 x 8 chess board so that no two queens attack each other. sortcboard, 8). % the number of queens is 8 func(p(board, board), bool). % p(i, j> = true iff a queen is placed at (i, j>. list(usable). % a list of clauses % (a) No two queens are on the same column. -p(x, z> I -p(y, z> I (x = y>. % (b) INo two queens are on the same row. -p(z, x> I -p(z, y> I (x = y> . % (c) No two queens are on the same diagonal. -p(x,y) I -p(u,v> 1 $ABS(x-u) = $ABS(y-v) I (x=u>. end-of-list. formula-list(usable). % a list of formulas % (d) Each column must have a queen. (all x exists y p(x, y>>. end-of-list. Note that the built-in function $ABS(X) returns the absolute value of z. It takes less than 0.3 second on an IBM RS6000 for ModGen to decide that there are 92 solutions to the above input. If the user likes to Automated Reasoning test the 15-queen problem, the only change to the in- put file is to replace 8 by 15. It takes 2.6 hours for ModGen to decide that there are 2,279,184 solutions for the case of 15. This result cannot compare to that of Sosic and Gu whose program can decide 3,000,OOO queens in one minute (Sosic & Gu 1991). However, it is known that there exist sol utions to any case but the exact numbers of solutions for large queen p roblems are .still unknown. ModGen may be used to answer such unknown questions while Sosic and Gu ‘s problem cannot. The queen problem can be also specified in terms of a function Q such that q(i) = j iff p(i, j). Below is an input file to ModGen: assign(MODEL, 1). % search only one model sort(row, 8). % the number of queens is 8 func(q(row), row, bijective). % q being bijective implies that no two queens % in the same row or the same column and % there exists a queen for each column. list(usable). % No two queens are on the same diagonal. -(q(u) = q(v) + X) I -($ABSh - VI = X) I (X = 0) end-of-list. The second input file is much simpler than the first one - this shows the flexibility of ModGen for specify- ing problems. The following is the result of executing ModGen with the above input. Model #l: row I 01234567 ----+----------------- Q 1 31625740 The Non-Obviousness Problem The second example shows how easy to use ModGen, that is, ModGen can use some of OTTER'S input file without any change. The example is called the “non- obviousness” problem and has appeared in many issues of Newsletter of Association on Automated Reasoning (Pelletier & Rudnicki 1986). The input file of OTTER (~3.0.0) is as follows: set(aut0). listcusable). -p(a,b) . -q&d). p(x,y) I q(x,yL q(x,y) I -q(y,xL p(x,z> I -p(x,y) I -p(y,z>. q(x,z) I -q(x,y) I -q(y,zL end-of-list. The same file can be used by ModGen: The com- mand set (auto), which automatically turns on a set of inference rules of OTTER, is skipped by ModGen. ModGen assumes by default that p and q are binary predicates over S = {a, b, c , d}. While it takes 3.8 seconds for OTTER to show that the input clauses are unsatisfiable, it takes only 0.04 second on the same machine for ModGen; our result is the best among the results reported soning. in the Newsletters of Automated Rea- Propositional Clause Generation In this section, we present a procedure which can correctly and efficiently convert general formulas into propositional clauses for functions of finite domains. The procedure consists of the following steps: 1. Transform general formulas into clauses. 2. Eliminate function symbols in each clause by intro- ducing new predicates and variables. 3. Instantiate variables in each clause by values and evaluate the truth value of built-in functions and predicates. 4. Return each instantiated clause in an abstract form. Methods for transforming general formulas into clauses can be found in many textbooks on logic pro- gramming. An abstract form of a clause is a list of integers such that the absolute value of each integer is the index of a propositional variable and the sign of the integer is the sign of the literal. In the following, we discuss only steps 2 and 3. Eliminating function symbols We will use functions with only one argument for no- tational convenience; functions with more than one ar- gument can be treated similarly. As mentioned in the introduction, for each function f, we introduce a pred- icate Pf such that f(z) = y iff Pf (II:, y). We can elimi- nate each term f(t) in a clause formula by substituting a new variable u for f(t), assuming f(t) = u. Thus, the transformation rule is as follows. (P) Uf(t)) I M -wt> 4 I Jw I Wf (t) + 4 where M is a disjunction of literals, L( f (t)) is a literal containing the term f(t) and f is not a predicate. The soundness and completeness of the above rule is ensured by the totalness of f: Theorem 1 Suppose f(z) = y ifl Pf(z, y) and f is total. For any clause L(f(t)) 1 M and any set S of clauses, Sl = S U {L(f(t)) I M} is satisfiable if and only if S2 = S U {-Pj(t,z) I L(z) I M[f(t) t 21) is sutisjiuble. Proof: If Sr is satisfiable, because L(f (t)) I M implies --wt, 4 I w I Mf (t) c x], S2 must be satisfiable. If S1 is unsatisfiable, by Herbrand’s theorem, there exists a unsatisfiable set Gr of ground instances of S1. For any Herbrand interpretation H on Gi, there much exist a ground clause in Gr which is false in H. If this ground clause is not an instance of L(f (t)) I M, then this ground clause must be an instance of S’s, so H will falsify S2. 164 Automated Rkkoning If this ground clause is an instance of L(f(t)) 1 M, then it can be written as aL(f(t)) 1 aM for some sub- stitution 0. Because f is total, there must exist a value a such that f(at) = a. Consider the instance (*) +f(& 4 I 44 I aW(t) - 4 of -Pj(t, 2) 1 L(z) I M[f(t) + 21. Because Pj(at, a) iff f( LT~) = a, 1Pf (at, a) is false under H. The rest literals of (*) are also false under H because aL(f(t)) I aM is false under H and f(at) = a. Hence H will falsify S2, too. In other words, every interpretation will falsify Sz, so Sz must be unsatisfiable. 0. While the totalness of functions is a sufficient condi- tion for the above theorem, we were unable to weaken this condition further. In (Wos 1988), it is said that an equation like prod(prod( z, y) , z) = prod( 2, prod( y, z)) could be replaced by two clauses when using predicate notation: -P(x, Y, u) I -P(Y, z, 4 I -P(% z, 4 I P(% w, vu), -qx> Y, 4 I -P(Y, v-4 I --p(vv) I ~(V,~). By the above theorem, if prod is total, then only one clause is sufficient. However, when prod is partial, we do not know if the two clauses are sufficient to replace Prod(Pro+ Y), 4 = pro+, prod(y, 4). To ensure that f(z) = y iff Pf (2, y), some formulas about Pf should be added: 1. Totalness: Vdy . Pf(z,y). 2. Image Uniqueness: VZVYlVY2 - Pj(“, Yl) A yf(2, Y2) 3 (Yl = Y2). In ModGen, the transformation rule (p) is repeat- edly applied to the general clauses until no functions are left, with the exception that when function sym- bols appear with equalities, the application of the rule becomes selective. Dealing with equalities When functions are used in equalities, we use special techniques to reduce the number of ground clauses gen- erated from general clauses. There are two cases: (1) equalities between a function and a variable/constant, and (2) equalities between functions. For the first case, say f(z) = y, we directly trans- form this equation into a literal, without introducing a new variable, that is, Pf(z, y) instead of u = y I lPf(z, u); the latter is obtained by the transforma- tion rule (p) and would result in too many ground clauses, because it introduces a new variable. The fol- lowing lemmas ensures that the former transformation is sound. Lemma 2 Assuming the totalness and image unique- ness properties off, Pf(x,y) and u = y I lPf(x,u) are logically equivalent. Proof: Note that the instances of u = y I lPj(x, u) (af- ter removing evaluable literals) are of form 1Pf (ai, uk) and the instances of Pj(x, y) are of form Pf(ui,uj). The ground clauses obtained from the totalness prop- erty of a function, that is, assuming the range of f(x) is {al, . . . . a,), are: Pf(“, al) I --- I p&b an) (1) for all x. Using resolution, for any value ui and uj , we can deduce Pj (ai, uj ) from instances of u = uj lPf(u;,u) and (1). On the other hand, we can also deduce lPf(ui, U~,I from Pf(ui, uj) and the ground clause generated from the image-uniqueness property. Hence, Pf (x, y) and u = y I Pj (x, u) are logically equivalent under the pres- ence of the totalness and image-uniqueness properties off. 0 For the second case, say f(x) = g(y), we have two choices, to remove f(z) first or to remove g(y) first, and depending on the removal sequence, the resulting clause will be different. If we remove f(x) first, then the resulting clause will be lPf(x, u) I P,(y, u). On the other hand, if we remove g(y) first, then the resulting clause will be Ps(y, v) I lPf(x, v). When a function is total, by the theorem in the previous subsection, it is sufficient to generate either of the two clauses. Dealing with S kolem functions ModGen takes first order formulas with quantifiers as input and then transforms these formulas into clauses; skolem functions may be introduced during this pro- cess. Skolem functions can be treated as ordinary functions which have the totalness and the image- uniqueness properties. Skolem constants are also treated as ordinary func- tions, that is, 0-arity functions. The difference is that the image-uniqueness property can not be enforced. Although treating skolem functions as ordinary func- tions is sufficient, for efficiency, we treat some skolem functions specially. If a skolem function has all the universally quantified variables as its arguments and does not appear in other clauses, then we can elimi- nate the skolem function as follows: Suppose f(x) is a skolem function appearing in clause C(f(x)). We replace f(x) by a new variable y and C( f(x)) is equiv- alent to 3y . C(y). If the domain of y is {al, . . . . a,}, then 3y . C(y) is equivalent to C(ul) I . . . I C(u,). If a skolem function appears in more than one clauses, then we can not eliminate it this way, because 3y(P(y) A Q(y)) is not equivalent to (3yP(y)) A (3&(y)) in gen- eral. For the same reason, we can eliminate skolem constants if a clause containing skolem constants is a ground clause and skolem constants do not appear in other clauses. Example 3 Consider the formulaVy3xf(x) = y. The clausal form of this formula is f(S(y)) = y, where S(y) is a skolem function. Assume that the sort of vari- ables x and y contains n elements. Since the skolem function S has all universally quantified variables as its arguments, we can eliminate the skolem function as Automated Reasoning 165 Queen of No. of FINDER ModGen order models set No. of clauses runtlme(sec) for each values of variables in C do VI, . . . . wn 5 10 0.20 170 0.07 6 36 0.25 302 0.17 for each evaluable literal Z in a clause C do 7 40 0.42 490 0.31 if 1 is evaluated to false, a 92 0.75 744 9 352 1.95 1074 0.61 1.34 then delete Z from C. 10 724 6.15 1490 3.46 else exit // No propositional clause from C 11 12 14200 2680 131.73 26.10 2002 2620 11.65 52.03 endfor 13 73712 725.78 3354 267.97 // C consists of literals with unevaluable predicates. 14 365596 4212.52 4214 1500.27 15 2279184 26604.08 5210 9323.61 generate a ground clause by instantiating each zli endfor Figure 2: Evaluation of literals and propositional clause generation follows. f(w) = Y I *** I f(G) = Y (2) By instantiating (2), n ground clauses will be gen- erated. On the contrary, if we did not eliminate the skolem function first, then we would instantiate Pf (u, Y) I lPS(Y> ) u and n2 ground clauses would be generated. 0 Instant iat ing general clauses The next step is to generate propositional clauses in case that all evaluable literals are evaluated to false while instantiating all variables in a clause. Evalu- atable literals are those consisting of only variables and builtin functions/predicates like =(equality). If one of the evaluable literals in a clause is evaluated to true, then no propositional clause will be generated from the clause because the entire clause is eventually true. On the other hand, if one of evaluable literals in a clause is evaluated to false, then the literal will be deleted from the clause because this literal is known to be false, thereby having no effect on the evaluation of the clause. The procedure for generating propositional clauses from a clause, in which function instances are removed, is in Figure 2. Example 4 The clause f(z) < f(y) I x 2 y becomes, by substituting u for f(z) and w for f(y), lPf(X, 4 I lPf(Y> 4 I u < v I x L Y (3) where Pj(x, u) is true iff f(x) = u and Pf(x, w) is true iff f(x) = V. The next step is to instantiate all the variables in the formula 3. Assume for one instance that u = 2, w = 1,x = 1 and y = 2. Then a ground clause (-‘Pf(l, 1) I lPf(O,2)) will b e g enerated because both u < x and z 2 y are evaluated to false. Assume another instance that u = 1, w = 2,x = 1 and y = 2. Then no ground clause will be generated because u < x is evaluated to true. cl In general, it is possible that identical ground clauses are generated more than once. ModGen avoids du- plication of ground clauses only for symmetric cases. 166 Automated Reasoning Table 1: Experiment with Queen problems NOELIMINATION ELIMINATION QG5 of No. of N 0. 0 f runtlme No. of runtlme order models clauses (set) clauses (set) 5 1 2211 0.14 1461 0.10 6 0 4552 0.31 3040 0.17 7 3 8401 0.47 5657 0.31 8 1 14301 0.81 9693 0.51 9 0 22879 1.29 15589 0.89 10 0 54846 4.09 43846 2.62 11 5 80279 10.01 64307 5.41 12 0 113683 25.37 91219 11.26 13 0 156573 562.84 125815 234.71 Table 2: Experiment with Quasigroup 5 problems When predicates to be generated are invariant to the exchange of two variables, predicates are said to be symmetric with respect to the two variables. The fol- lowing example illustrates the elimination of redundant clauses by the symmetry checking. Example 5 Consider PJ (x, y) I Pf (x, z). Assume that x = 1,y = 1 and z = 2. Then Pf(l, 1) I Pi(1,2) will be generated. Assume also that x = 1, y = 2 and z = 1. Then Pf(1,2) I Pf(l,l) will be generated. Clearly, the two ground clauses are identical. If we exchange y for z in the above clause, the clause becomes P~(x,z) I Pf(x, y) which is identical to the original clause. Then, it is sufficient to generate ground clauses from Pf (x, y) 1 Pj (x, Z) only for y 5 z since all ground clauses generated for y > z are redundant. 0 It is also possible to generate fewer ground clauses by applying some of the unit literal deletion and pure literal deletion. However, this kind of checkings can be done by the propositional decision procedure. Experimental We tested ModGen with the queen problem, quasi- group problems, and several puzzles. The experiment is done on a IBM RS6000/530. All times are taken as the best of three runs. The result of the experiment with the queen prob- lem is shown in Table 1, which also includes the re- sult of FINDER for performance comparison. Mod- Gen runs as more than twice faster than FINDER for queen problems of order > 10. The experimental results with some quasigroup problems (Bennett 1989; Stanley, Fujita, & Stickel 1993) are listed in Tables 2 and 3. The QG5 problem is to investigate the existence of Latin squares GQ6 INDIRECT I DIRECT I of No. of 0. 0 f run time I No. of run time order models clauses set clauses set 5 I 0 I 48121 4.19 1 2711 0.13 Table 3: Experiment with Quasigroup 6 problem problem 1 models 1 No. of clauses runtime set Agatha 1 34 0.02 N&obvious I 1 0 162 0.04 Jobs 16 404 0.12 Steamroller 0 2250 0.21 Table 4: Experiment with puzzle problems eferences Bennett, F. 1989 Quasigroup Identities and Mendel- sohn Designs, Canadian Journal of Mathematics 41: 341-368. Gu, J. 1993 Local search for satisfiability (SAT) prob- lem, IEEE Trans. on Systems, Man, and Cybernet- ics 23(4): 1108-1129. Davis, M; Putnam, H 1960 A computing procedure for quantification theory, J. of ACM 7: 201-215. . satisfying the identity (((y * x) * y) * y) = x (viewing the square as a multiplication table). This problem in- cludes two skolem functions which can be eliminated as explained in the previous section. The data in the column under ELIMINATION in Table 2 are the re- sult of eliminating skolem functions and the data un- der NOELIMINATION are the result of treating the skolem function as ordinary functions. Eliminating skolem functions not only generates smaller number of ground clauses but also accelerates the search. The performance difference comes from the fact that Mod- Gen generates one less order of ground clauses for for- mulas having skolem symbols. McCune, W. W 1990 Otter 2.0 users’ guide, Mathe- matics and Computer Science Division, Argonne Na- tional Laboratory, Argonne, Illinois. Pelletier, F. J; Rudnicki, P 1986 Non-Obviousness, Automated Reasoning Newsletter 6: 4-5. Selman, B.; Levesque, H.; Mitchell, D. 1992 A new method for solving hard satisfiability problems, In Proceedings of A AAI’92: 440-446. Slaney, J. 1992 FINDER, Finite Domain Enumera- tor: Version 2.0 Notes and Guide, Technical report TR-ARP-l/92, Automated Reasoning Project, Aus- tralian National University. Slaney, J; Fujita, M; and Stickel, M Automated rea- soning and exhaustive search: Quasigroup existence problems To appear in Computers and Mathematics with Applications. The experimental results with another quasigroup problem, QG6 (Stanley, Fujita, & Stickel 1993), are is listed in Table 3. This problem is to investigate the existence of Latin squares satisfying the identity ((x * y) * y) = (x * (51: * y)), which is an equality between function instances ans is specially treated in ModGen. The data in the column under INDIRECT in Table 3 are the result of employing the transformation of f(x) = y to u = y I lPf(z, u). The data under DI- RECT in Table 3 are the result of employing the trans- formation of f(x) = y to Pf (x:, y). As shown in Table 3, the performance difference is amazingly large. We could not experiment beyond order 7 for INDIRECT because of the excessive computing time. This per- formance difference is manifested by the observation that the INDIRECT strategy generates one more or- der of ground clauses for each literal having equality with function instances. We also experimented with some puzzle prob- lems such as Non-obviousness, Schubert’s Steamroller (Stickel 1986), J o b s and Agatha; the results are listed in Table 4. Shubert’s Steamroller has the conclusion negated so that it is unsatisfiable. This experiment shows that ModGen can solve puzzle problems very fast. Sosic, R.; Gu, J. 1991 3,000,OOO queens in less than one minute, SIGART Bulletin, 2(2): 22-24 Stickel, M. 1986 Shubert’s steamroller problem: for- mulations and solutions, J. of Automated reasoning 2: 89-101. Wos, L. 1988 Automated reasoning: 33 Basic research problems, Prentice Hall, New Jersey. Zhang, H. 1993 SATO: A decision procedure for propositional logic. Association for Automated Rea- soning Newsletter, 22: l-3. Automated Reasoning 167 | 1994 | 5 |
1,677 | Making the Most of What : using Models and ata to Improve Learning rediction Accuracy Julio Ortega Computer Science Dept., Vanderbilt University P.O. Box 1679, Station B Nashville, TN 37235 julio@vuse.vanderbilt .edu Abstract Prediction and classification in areas such as engineer- ing, medicine, and applied expert systems often relies on two sources of knowledge: actual data and a model of the domain. Recent efforts in machine learning (Ourston 1991) (T owell, Shavlik, & Noordewier 1990) have developed techniques that take advantage of both sources, but the methods are often tied to particular types of models and induction techniques. We propose two general techniques that allow induction methods, C4.5(Quinlan 1993) in our case, to take advantage of an available model( Ortega 1994). Our first technique exploits the implicit information in the model, which is used as a feature generator for induction. In particular, “model” simulation on input data computes many intermediate and output values which can serve to extend the features that describe the data. For example, in models expressed as proposi- tional theories, we generate extended features from the proofs of the intermediate concepts in the theory. As the number of extended features proliferates quickly, we use feature selection techniques borrowed from the statistical recognition literature (Kittler 1985) to re- duce the number of features considered during induc- tion. The original data is re-expressed in terms of the selected features, and induction (i.e. C4.5) is run over this set of data. Our second technique is motivated by the observa- tion that the reliability of both the available model and the available data may vary widely from one domain (or situation) to another. Our approach consists of evaluating the effectiveness of the model as a predic- tor using the available data. The data set available for training is divided in two categories: data on which the model is accurate, and data on which the model is inaccurate. This divided data set is used to a build a “Model Reliability” predictor (using our default in- ductive method, i.e. C4.5) that provides a mechanism for deciding in which situations the model should be chosen for the prediction of future instances. Another predictor, the “Data” predictor is built using induction on the available data. This predictor is used on future instances where the “Model Reliability” predictor in- dicates that the model is unreliable. We have conducted experiments using some databases (recognizing DNA promoter sequences, soy- bean and audiology diseases) which are often used in the Machine Learning community as a benchmark. The results show that the combined use of our tech- niques compare favorably to existing approaches, both in terms of efficiency and accuracy. However, unlike other techniques for combining inductive and deduc- tive learning, the techniques we are developing are quite general and can be adapted to apply in non- propositional domains. We are also implementing our techniques in a domain where the model is of a math- ematical nature (prediction of diabetes glucose levels), and a domain where the model is of a qualitative na- ture (Reaction Control System of the Space Shuttle). References Kittler, T. 1985. Feature selection and extraction. In Young, T. Y., and Fu, K. S., eds., Handbook of Pattern Recognition and Image Processing. Orlando, FL: Academic Press. 59-83. Ortega, J. 1994. Making the most of what you’ve got: using models and data to improve learning rate and prediction accuracy. Technical Report TR-94-01, Computer Science Dept., Vanderbilt University. Ourston, D. 1991. Using Explanation-Based and Em- pirical Methods in Theory Revision. Ph.D. Disserta- tion, University of Texas, Austin, TX. Quinlan, J. R. 1993. C4.5: Programs for Machine Learning. San Mateo, CA: Morgan Kaufmann. Towell, G. G.; Shavlik, J. W.; and Noordewier, M. 0. 1990. Refinement of approximate domain theories by knowledge-based neural networks. In Proceedings of the Eighth National Conference on Artificial Intelli- gence, 861-866. Acknowledgments This research is supported by NASA Ames grant NAG 2-834 to D.H. Fisher. Student Abstracts 1483 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 50 |
1,678 | ased Sensor Diag e itore Joi51 MILGRAM Electricit De France, DER-IMA-TIEM 1, avenue du General De Gaulle 92 14 1 Clamart Cedex FRANCE Joel.Milgram @ der.edf.fr Abstract A complex industrial plant, such as a nuclear power plant, is monitored thanks to a number of sensors. The instrumentation may be itself a complex system liable to failures. We propose a model-based sensor diagnosis system which relies on the topological description of the plant and on a set of component models. This model implicitly conceals relations involving only sensor data. Such relations must always be verified if components behave normally; thus, the detection task consists of verifying these relations. So, this work is a first step in extending the scope of model-based diagnosis, since we question here the information stemming from the plant and normally considered as safe. As further studies, we wish to monitor this detection system itself; i.e., whenever the instrumentation is supposed to behave correctly, non- verified constraints point out to errors in the plant model. Questioning the model-based diagnosis A model-based diagnosis (Reiter 1987) relies on structural and behavioural knowledge and on observations. Observations in a plant stem from sensors. Since the instrumentation is liable to failures, sensor data are questionable. On the other hand, component models in a thermohydraulic circuit are very crude and the topological database describing the plant must be updated after each human intervention on the plant. So, when a model-based reasoning system provides a result, three assumptions must be taken into account: there is no sensor failure, component models are accurate enough, and the topological database rigorously describes the plant. Sensor failure in a thermohydraulic circuit Fluid behaviour is described by a set of equations of different kinds stemming from the plant model. As some of the variables are measured by sensors, we seek to exhibit, when they exist, algebraic relationships between them by eliminating the variables which are not measured. Such constraints should be verified at each step if every component behaves properly. Constraint violation is equivalent to a malfunction and is seen as a sensor failure. 1476 Student Abstracts Constraints can be found in two steps. First, a qualitative model of constraint existence is set up by means of structural analysis. Secondly, models are formally handled as according to the structural analysis results in order to establish the constraints on sensor data. The set of equations is turned into a structural matrix (Iwasaki & Simon 1986) in which each variable v is characterized with respect to each equation E by only two pieces of information: whether v is involved in E and whether E can be solved with respect to v. Constraints are found by triangulation of a part of this matrix. Further research direction Whereas the operator may check the installation thanks to the instrumentation, the present system aims at providing a diagnosis on the instrumentation itself, rather than on the installation. We wish to check the sensors with their own values. Sensor data, thus validated, may be used in other monitoring systems. Sensor diagnosis may be seen as a part of the diagnosis of a monitoring system. On the other hand, this sensor diagnosis system may itself be faulty, and should also be monitored. This system is based on four sources of knowledge and data, namely: the topological database describing the installation (TDB), the models library (ML), the research and generation algorithm (A), and sensors data. If no sensor is assumed to be faulty, then constraints violation is seen as a set of malfuctions of (TDB), (ML), or even (A). Conclusion The system proposed here relies on structural analysis and generates constraints on sensor data. Presently, for each circuit, a monitoring program is automatically generated from the model. This application uses resources which must themselves be monitored. When the sensors behave normally, we wish to diagnose the topological data base or the component model; this is still under study. References Reiter, R. 1987. A theory of diagnosis from first principles. Artificial Intelligence, 3257-95. Iwasaki, Y., and Simon, H. A. 1986. Causality in device behavior. Artificial Intelligence, 29:3-32. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 51 |
1,679 | Theoretical and Experimental Studies of Temporal Constraint Satisfaction Problem Debasis Mitra Center for Advanced Computer Studies University of Southwestern Louisiana, P.O. Box 44330 Lafayette, Louisiana 70504-4330 dm@cacs.usl.edu Reasoning with time is embedded in many appli- cation domains than we are often aware of. For ex- ample, understanding a parallel program involves how each unit of the program is temporally related to the other unit through dependency. There is a growing awareness about the importance of understanding time in any dynamic or evolving situation. Within last twenty years different dimensions of reasoning have been identified, such as, qualitative reasoning versus quantitative reasoning, point-based representation ver- sus interval-based representation, propositional expres- sion versus first order expression. My work concen- trates on interval-based qualitative propositional rea- soning. The representation scheme and a polynomial approximate algorithm were proposed by James Allen. The problem of detecting global consistency has been subsequently proved to be NP-complete. Practical rea- soning systems have been developed based on Allen’s S-consistency algorithm. This algorithm checks for consistency over constraints between each subset of 3 temporal entities of the full set of temporal asser- tions in the system (rather than checking for complete consistency between all constraints, which is called global-consistency). There has been very little system- atic study on either the S-consistency problem, or the global-consistency problem. We have hypothesized that the hardness of the prob- lem, measured by the average-case time-complexity of S-consistency algorithm, is a well-behaved function of the initially generated constraints, parameterized with two distributional coefficients (average, and second mo- ment) of (1) initially constrained arcs (with a con- straint network representation) for each node (tempo- ral entities), and (2) the degree of constraints on each initially constrained arc. We are doing rigorous statis- tical analyses to find a predictable behavior of the time- complexity with respect to those structural parameters of the input problem. Our work is in line with the cur- rent experimental research on NP-complete problems. But a richer problem structure in TCSP demands a more rigorous data analyses technique than have been attempted so far. We have developed a statistical re- gression model for predicting time-complexity of the algorithm. The model can be used for the purpose of theoretical explanation of empirical results, thus pro- viding with a better insight into the problem of tem- poral consistency. We have also identified easy-hard zones of the problem[l]. I have also developed a heuristic-based global- consistency algorithm to find all consistent temporal scenarios. Ladkin et al has recently shown that the problem of detecting global-consistency is not as hard, on an average, as is suggested by its property of being NP-complete. Our algorithm has been implemented. Current experiments with the implementation is pro- ducing promising results from the point of view of ef- ficiency. One of our results shows that, on randomly generated network, the growth rate of the number of temporally consistent models is not as explosive as in- tuition suggests. The algorithm has some importance from application points of view, specially in temporal data base’. However, apart from having its applied significance, we hope to do some fundamental experi- mental studies on global-consistency problem with this algorithm in future. This result, along with the sta- tistical studies of 3-consistency algorithm, is likely to produce a better understanding of the temporal con- straint satisfaction problem. Hopefully, this study will also lead to a better insight in relating NP-complete problems and P-class problems. Such a study involv- ing approximate algorithms for temporal reasoning are also part of the project. eferenees [l] Debasis Mitra and Rasiah Loganantharaj. Some experimental works with 3-consistent temporal con- straint propagation algorithm. In IJCAI-93 Work- shop on Spatial and Temporal Reasoning, 1993. ‘Our implementation is in C++. We hope to extend it to a practical reasoning system in future. Student Abstracts 1477 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 52 |
1,680 | A Theory of Reading* Kenneth Moorman and Ashwin Ram Georgia Institute of Technology College of Computing Atlanta, GA 30332-0280 {kennethm,ashwin}@cc.gatech.edu Introduction Reading has been studied for decades, yet no theories exist which completely explain it. In particular, a type of knowl- edge intensive reading, creative reading, has been practically ignored. Creative reading is the reading of texts which con- tain novel concepts. Nearly all reading will be creative to some degree; thus, any theory which overlooks this will be incomplete. By combining results from psychology, artificial intelligence, and education, we have produced a functional theory of the complete reading process, aimed at explaining creative reading. Reading supertasks In order to produce a functional theory of reading, we need to identify the tasks which the process must perform in or- der to produce the desired behavior. Related tasks are then grouped into supertasks. The supertasks presented below are the result of functional analyses of our own reading pro- cesses, backed up by extensive prior research in the areas of psycholinguistics (e.g., van Dijk & Kintsch 1983), read- ing comprehension (e.g., Black & Seifert 1981), story un- derstanding (e.g., Rumelhart 1977), memory (e.g., Schank 1982), and metacognition (e.g., Flavell 1976). Metacontrol integrates the other supertasks and includes focus control, which manages the depth of reading; time management; and suspension of disbelief, which enables a reader to accept a text which violates her/his world view. Sentence processing is responsible for low-level understand- ing, and includes tasks such as pronoun reference, syntac- tic parsing, and punctuation analysis. The story structure understanding supertask handles story structure details, in- cluding character and setting identification, plot descrip- tion, and genre identification. The tasks making up the scenario understander are the event parser, which identi- fies agents, actions, states, objects, and locations; the agent modeler, which maintains models of the agents; and the de- vice modeler, which forms models of objects. The explana- tion and reasoning supertask performs high-level reasoning and learning through the tasks of creative understanding, which attempts to understand novel concepts; interest man- *This work was supported by a Fannie and John Hertz Foun- dation fellowship and by the Georgia Institute of Technology. agement; belief management, responsible for managing the beliefs of the characters and the reader; explanation, which builds inferences; and metareasoning, which reflects on the reader’s own actions. Finally, the memory management supertask handles memory storage and retrieval. Conclusions Our theory is implemented in ISAAC, a system which cre- atively reads science fiction stories. ISAAC deals with real stories and currently possesses the knowledge and processes to successfully understand Men Are DifSerent (Bloch 1963), which contains novel concepts (sentient robots, the death of Mankind, space travel, etc.). Future work is focused on the addition of stories, as well as exploring issues in evaluation of both reading and creative performance. Reading is a complex cognitive ability; through under- standing the process, we gain a window into understanding general cognition. By making extensive use of the knowl- edge which exists within a story and by relying on a close interaction between the various reading supertasks, our the- ory is capable of modeling the reading process in a way which allows creative reading issues to be dealt with, a research goal not reached with earlier theories and models. References Black, J. B., and Seifert, C. M. 198 1. The psychological study of story understanding. Technical Report 18, Yale. Bloch, A. 1963. Men Are Different. In Asimov, I., and Conklin, G., eds., 50 Short Science Fiction Tales. New York: MacMillan Publishing Co. Flavell, J. H. 1976. Metacognitive aspects of problem solving. In Resnick, L., ed., The Nature of Intelligence. Hillsdale, NJ: Lawrence Erlbaum Associates. Rumelhart, D. E. 1977. Understanding and summarizing brief stories. In Berge, D. L., and Samuels, J., eds., Basic processes in reading and comprehension. Hillsdale, NJ: Lawrence Erlbaum Associates. Schank, R. 1982. Dynamic Memory: A Theory of Learn- ing in Computers and People. New York: Cambridge University Press. van Dijk, T. A., and Kintsch, W. 1983. Strategies of Discourse Comprehension. New York: Academic Press. 1478 Student Abstracts From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 53 |
1,681 | A Hybrid Parallel IDA* Search * Shubha S. Nerur Computer Science and Engineering University of Texas at Arlington Box 19015, Arlington, TX 76019 nerur@cse.uta.edu ABSTRACT Heuristic search is a fundamental problem-solving method in artificial intelligence. The main limitation of search is its computational complexity which can be overcome by parallel implementation of the algo- rithms. Distributed tree search and Parallel window search are two of the approaches to parallelizing search algorithms. We are developing an algorithm called HyPS (Hy- brid Parallel Search ) which is a combination of dis- tributed tree search (RKR87) and parallel window search (PK91). In the HyPS, the set of processors is divided into clusters. Each cluster searches the same space, but uses a unique cost threshold. Within each cluster, processors are given unique portions of the search space to expand. Each cluster, adopts the rule of parallel windows, but distributed tree search is per- formed within a cluster. First, the initial state is ex- panded generating distinct subtrees. The number of distinct subtrees generated is equal to the number of processors in a cluster. Each processor in a cluster receives a subtree on which IDA* search is performed. The first cluster is given the heuristic estimate to reach the goal. All remaining clusters are given incremen- tally larger thresholds. The algorithm finds a first so- lution or an optimal solution. Many of the proces- sors will be idle when searching for an optimal solu- tion. Load balancing within a cluster will overcome the idling of processors within a cluster. HyPS is imple- mented on Connection Machine 5. The parallel algo- rithm is tested for different cluster sizes to find the first solution and the optimal solution. We are interested in finding which cluster size yields the best solution. Test to Find First Sol. First Sol. with operator ordering Optimal Sol. Clusters Speedup Efficiency 1 19.07 0.30 2 22.02 0.34 4 45.69 0.71 1 14.65 0.23 2 27.53 0.43 4 108.03 1.69 1 7.9 0.12 2 6.7 0.10 4 2.2 0.03 Optimal Sol. with 1 9.36 0.14 Test to Find Clusters Speedup Efficiency Optimal Sol. with 1 57.70 0.90 Load balancing 2 106.82 1.67 & operator ordering 4 36.71 0.57 The domain of testing is the Fifteen Puzzle problem and the robot path planning problem. The average speedup and efficiency for the Fifteen Puzzle Problem instances are shown in the first table. Also the av- erage speedup and efficiency for the Robot Planning Problem instances are shown in the second table. The initial testing shows marked improvement over serial and parallel algorithms. References Curt Powley and Richard E Korf. Single-agent par- allel window search. IEEE Transactions on Put-tern Analysis and Machine Intelligence, 13(5), 1991. V N Rao, V Kumar, and K Ramesh. A parallel imple- mentation of Iterative-Deepening-A*. In Proceedings of AAAI, pages 178-182, 1987. *Supported by the National Science Foundation grant IRI-9308308 and by grant TRA93029N from the National Center for Supercomputing Applications. Student Abstracts 1479 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 54 |
1,682 | Time-situated reasoning within tight deadlines and realistic space and computation bounds Madhura Nirkhe Dept. of EE and Dept. of CS University of Maryland, College Park, MD 20742 madhura@cs.umd.edu advisor: Donald Perlis (perlis@cs.umd.edu) collaborator: Sarit Kraus (sarit@bimacs.cs.biu.ac.il) We develop an effective representational and inferen- tial framework for fully deadline-coupled, time-situated problem solving. Our effort is to model an agent in a tight and rigid deadline situation, in need of suc- cessfully formulating and executing a deadline-feasible plan of action as the world around the agent contin- ues to change. We highlight the severe time-pressure under which the agent must operate with a paradig- matic problem scenario : Nell & Dudley and the rail- road tracks. Nell is tied to the railroad tracks as a train approaches. Dudley, our agent, must formulate a plan to save her and carry it out before the oncoming train reaches her. He must deliberate (plan) in order to decide this, yet as he does so, the train draws nearer to Nell. While meta-planning is the usual proposal for rea- soning about the reasoning process, few formalisms ac- knowledge that it takes time, and none to date ac- count for all the time spent in the reasoning within the same framework. We cite here some key related works: (Dean & Boddy 1988) formulate an algorith- mic approach to time-dependent planning problems by introducing “anytime algorithms” which capture the notion that utility is a monotonic function of delibera- tion time. (Pollack & Ringuette 1990) explore the rela- tion between agent design and environmental factors. (Rosenschein & Kaelbling 1989) provide a situated au- tomata theory highlighting the role of logic, complexity and information in situated agents. (Russell & Wefald 1991) offer an optimal design for a limited rational agent using utility-based search. Our fully deadline- coupled planner has an important qualification that these efforts fail to meet: in addition to determining the current time, estimating the expected execution time of partially completed plans and being able to discard alternatives that are deadline-infeasible, it also has a built-in way of accounting for all the time spent as a deadline approaches. The underlying framework is that of Step-logics (Elgot-Drapkin & Perlis 1990) (now renamed active logics) which is a mechanism for reasoning situated in time. We have demonstrated the generality of the for- mal methods employed by our formalism by solving some real-time versions of canonical temporal projec- tion problems such as the Yale Shooting Problem. While an agent under severe time-pressure may spend substantial amount of the available time in reasoning toward and about a plan of action, in a realistic set- ting, the same agent must also measure up to two other crucial resource limitations as well, namely space and computation bounds. We address these concerns and offer improvements by introducing a limited short term memory combined with a primitive relevance mech- anism and a limited capacity inference engine. We propose heuristics to maximize the agent’s chances of meeting the deadline in this enhanced framework with additional space and computation constraints. We provide a modal semantics for active logics which serves as a link between active logics and existing logic approaches that deal with time. Logical omniscience, and in particular inferential closure is a computational impossibility for an agent in the real-world. We have constructed a variation on active-logics for which there is a sound and complete modal semantics. It overcomes the key obstacle of closure under consequence, and re- stricts closure under valid consequence. It illustrates important comparisons between active logic work and previous modal approaches to knowledge and belief. References Dean, T., and Boddy, M. 1988. An analysis of time- dependent planning. In Proceedings, AAAI-88,49-54. Elgot-Drapkin, J., and Perlis, D. 1990. Reasoning situated in time I: Basic concepts. Journal of Experi- mental and Theoretical Artificial Intelligence 2( 1):75- 98. Pollack, M. E., and Ringuette, M. 1990. Introducing the tileworld: Experimentally evaluating agent archi- tectures. In Proceedings, AAAI-90, 183-189. Rosenschein, S., and Kaelbling, L. 1989. Integrat- ing planning and reactive control. In Proceedings of NASA Telerobotics conference. Pasadena, CA. Russell, S., and Wefald, E. 1991. Do the right thing. The MIT press, Cambridge, Mass. 1480 Student Abstracts From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 55 |
1,683 | Integrating Induct io & Instruction: Connectisnist Advice king David C. Noelle and Garrison W. Cottrell Department of Computer Science and Engineering University of California, San Diego La Jolla, CA 92093-0114 dnoelle@cs.ucsd.edu and gary@cs.ucsd.edu Humans improve their performance by means of a variety of learning strategies, including both gradual statistical induction from experience and rapid incor- poration of advice. In many learning environments, these strategies may interact in complementary ways. The focus of this work is on cognitively plausible models of multistrategy learning involving the integra- tion of inductive generalization and learning “by being told”. Such models might be developed by starting with an architecture for which advice taking is rela- tively easy, such as one based upon a sentential knowl- edge representation, and subsequently adding some form of inductive learning mechanism. Alternatively, such models might be grounded in a statistical learn- ing framework appropriately extended to operational- ize instruction. This latter approach is taken here. Specifically, connectionist back-propagation networks (Rumelhart, McClelland, & the PDP Research Group 1986) are made to instantaneously modify their behav- ior in response to quasi-linguistic advice. Many of the previous approaches to the instruction of connectionist networks have involved the encoding of symbolic rules as initial connection weights which may be later refined by inductive learning (Giles & Omlin 1993) (Tresp, Hollatz, & Ahmad 1993). A ma- jor drawback of this approach is that advice may only be given before inductive training begins. This is an unreasonable constraint for a cognitive model of in- structed learning. Instead, a connectionist network is needed which may have its behavior altered by a stream of encoded instructions without a delay period for lengthy retraining. The approach which is examined here focuses on en- coding the receipt of instruction as motion in a net- work’s activation space. In short, advice is presented to such an instructable network as a temporal sequence of instruction tokens, where each token is encoded as an input activation pattern. The network is trained to appropriately modulate its behavior based on in- put of such advice sequences. The correct interpre- tation and operationalization of input instruction se- quences is learned inductively, but, once this initial learning is complete, instruction following proceeds at the speed of activation propagation. This focus on ac- tivation space dynamics allows instructional learning and standard connectionist inductive learning to func- tion in tandem. This strategy has been successfully applied to a sim- ple discrete mapping task and to the learning of nat- ural number arithmetic. In this latter domain, the connectionist adder of Cottrell and Tsung (Cottrell & Tsung 1993)) which is capable of systematically op- erating on arbitrarily large natural numbers, was aug- mented to receive instruction in various methods of ad- dition and subtraction. The resulting network tackles arithmetic problems by examining one column of dig- its at a time and sequentially performing actions such as writing a resultant digit for the column, announcing a carry or borrow, and shifting attention to the next digit column. The network’s behavior is determined by the most recently presented sequence of instruction to- kens. Future experiments will extend these multistrat- egy learners to include auto-associative memories con- taining articulated attractors in activation space which will facilitate systematic generalization to novel advice sequences. These later experiments will abandon arith- metic and will focus instead on simple planning tasks in a “blocks world” environment. References Cottrell, G. W., and Tsung, F.-S. 1993. Learning simple arithmetic procedures. Connection Science 5( 1):37-58. Giles, C. L., and Omlin, C. W. 1993. Rule refinement with recurrent neural networks. In 1993 IEEE In- ternational Conference on Neural Networks, 801-806. San Francisco: IEEE Neural Networks Council. Rumelhart, D. E.; McClelland, J. L.; and the PDP Research Group. 1986. Purulled Distributed Process- ing: Explorations in the Microstructure of Cognition, volume 1. Cambridge: The MIT Press. Tresp, V.; Hollatz, J.; and Ahmad, S. 1993. Network structuring and training using rule-based knowledge. In Hanson, S. J.; Cowan, J. D.; and Giles, C. L., eds., Advances in Neural Information Processing Systems 5. San Mateo: Morgan Kaufmann. Student Abstracts 1481 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 56 |
1,684 | A Comparison of Reinforcement Learning Methods for Automatic Guided Vehicle Scheduling DoKyeong Ok* Department of Computer Science Oregon State University Corvallis, OR 97331 okd@research.cs.orst .edu Automatic Guided Vehicles or AGVs are increas- ingly being used in manufacturing plants for trans- portation tasks. Optimal scheduling of AGVs is a dif- ficult problem. A learning AGV is very attractive in a manufacturing plant since it is hard to manually opti- mize the scheduling algorithm to each new situation. In this paper we compare four reinforcement learn- ing methods for scheduling AGVs. Q-learning[Watkins and Dayan 921 and R-learning[Schwartz 931 do not use action models. Q-learning optimizes the discounted total reward, while R-learning optimizes the average undiscounted reward per step. ARTDP[Barto et al. to appear] is a discounted method that uses action models. H-learning[Tadepalli and Ok 941 is an undis- counted version of ARTDP based on an algorithm of Jalali and Ferguson[Jalali and Ferguson 891. In our domain(see Figure l), there are two queues generating jobs, an AGV, a moving obstacle and two lanes. Queue 1 generates jobs for lane 2 half the time and Queue 2 always generates lane 1 jobs. The task of AGV is to move jobs from the queues to their destina- tion lanes while avoiding collisions with the obstacle, which randomly moves up and down. There are a total of 540 states. At any time an AGV may do nothing, load, unload, or move up, down, left or right. The goal is to maximize the average reward per step. An experiment compared Q-learning, R-learning, ARTDP and H-learning in our AGV domain. The re- ward is -5 when the AGV collides with the obstacle, +5 when it unloads a job to lane 1, and +l when it unloads a job to lane 2. Figure 1 shows the medians of average reward per step over 30 trials evaluated sepa- rately after turning off learning at various stages. To enable exploration, 50% of the time a randomly chosen action was excuted during learning. The parameters of ARTDP, Q-learning, and R-learning were tuned to this domain by trial and error. ARTDP with discount fac- tor y=O.9 and Q-learning could not converge to the optimal policy even after 2 million steps. Even though R-learning and ARTDP with high y converged to the *This research was supported by the National Science Foundation under grant number IRI:9111231. I thank my advisor Prasad Tadepalli for his help and guidance. 1482 Student Abstracts @ Moving Obtal* lo;; Q $$ A6V 0.03 0 0 akmm b.806 1Aerod 2ea.m Figure 1: An AGV domain(left); :Lrage reward per step for the four learning methods(right) optimal policy, they converged slower than H-learning. The results show clearly that H-learning converges to the optimal policy fastest without any parameter tun- ing, while the other three methods are very sensitive to the parameters. The future research will explore extensions to H- learning that scale for larger state spaces. References Barto, A. G., Bradtke, S. J., and Singh, S. P. To ap- pear. Learning to Act using Real-Time Dynamic Pro- gramming. ArtificiaZ Intellignece. Jalali, A. and Ferguson, M. 1989. Computation- ally Efficient Adaptive Control Algorithms for Markov Chains. In IEEE proceedings of the 28th Conference on Decision and Control, Tampa, FL. Schwartz, A. 1993. A Reinforcement Learning Method for Maximizing Undiscounted Rewards. In proceedings of the Tenth International Machine Learning Confer- ence, 298305. San Mateo, CA.:Morgan Kaufmann. Tadepalli, P. and Ok, D. 1994. H-learning: A Rein- forcement Learning Method to Optimize Undiscounted Average Reward, Technical Report, 94-30-l. Dept. of Computer Science, Oregon State Univ. Watkins, C. J. C. H. 1989. Learning from Delayed Rewards. Ph.D. Thesis, Cambridge univ., Cambridge, England. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 57 |
1,685 | Learning Quality-Enhancing Control Knowledge M. Alicia Phrez * School of Computer Science Carnegie Mellon University Pittsburgh PA 15213-3891 aperez@cs.cmu.edu Generating production-quality plans is an essential element in transforming planners from research tools into real-world applications. However most research on planning so far has concentrated on methods for constructing sound and complete planners that find a satisficing solution, and on how to find such solu- tion in an efficient way. Similarly most of the work to date on automated control-knowledge acquisition has been aimed at improving the eficiency of plan- ning; this work has been termed “speed-up learning”. Our work focuses on how control knowledge may guide a planner towards better plans, and how such control knowledge can be learned. “Better” may be defined in a domain-dependent way and vary over time. (Perez & Carbonell 1993) contains a detailed taxonomy of plan quality metrics. We have concentrated on metrics re- lated to plan execution cost, expressed as an evaluation function additive on the cost of the individual opera- tors. These functions are linear and do not capture the existence of tradeoffs between different quality factors. Our goal is to have a system that improves over ex- perience the quality of the plans it generates by ac- quiring in a fully automated fashion control knowledge to guide the search. Figure 1 shows the architecture of the current system, fully implemented on top of the PRODIGY nonlinear planner (Carbonell et al. 1992). Problems Control Knowledge Domain Knowledge -operators -inference rules Objective function (domain dependent) a pi&l for better plans Control Knowledge for faster planning Plans Figure 1: Architecture of a system to learn control knowl- edge to improve plan quality (Perez & Carbonell 1994). *Thanks to Jaime Carbonell for his suggestions and support in this work. This research is sponsored by the Wright Laboratory, Aeronautical Systems Center, Air Force Materiel Command, USAF, and the Advanced Research Projects Agency (ARPA) under grant number F336 15-93-l- 1330. Views and conclusions cpnt ained in this document are those of the authors and should not be interpreted as necessarily representing official policies or endorsements, either expressed or implied, of Wright Laboratory or the United States Government. The author holds a scholarship from the Ministerio de Educacibn y Ciencia of Spain. 1484 Student Abstracts The learning algorithm is given a domain theory (op- erators and inference rules) and a domain-dependent objective function that describes the quality of the plans. It is also given problems to solve in that do- main. The algorithm analyzes the problem-solving episodes by comparing the search trace for the plan- ner solution given the current control knowledge, and another search trace corresponding to a better solu- tion (better according to the evaluation function). The latter search trace is obtained by letting the problem solver search further until a better solution is found, or by asking a human expert for a better solution and then producing a search trace that leads to that so- lution. The decision points where control knowledge failed to guide the planner to the better plan are used as learning opportunities. From the comparison of the two traces the algorithm eccpdains why one solution is better than the other using the evaluation function, and its output is search control knowledge that leads future problem solving towards better quality plans. Two points are worth mentioning: o Learning is driven by the existence of a better solu- tion and a failure of the current control knowledge to produce it. o There is a change of representation from the knowl- edge about quality encoded on the objective function into knowledge that the planner may use at problem solving time, as the plan and search tree are only partially available when a decision has to be made. We do not claim that this control knowledge will neces- sarily guide the planner to find optimal solutions, but that the quality of the plans will incrementally improve with experience, as the planner sees new interesting problems in the domain. We have obtained good preliminary results using randomly-generated problems in a process planning domain. We plan to explore different domains and types of evaluation functions. References CarboneII, J. G., and The PRODIGY Research Group. 1992. PRODIGY4.0: The manual and tutorial. TR CMU- CS-92-150, Carnegie Mellon University. Perez, M. A., and CarboneII, J. G. 1993. Automated acquisition of control knowledge to improve the quality of plans. TR CMU-CS-93-142, Carnegie Mellon University. Perez, M. A., and CarboneII, J. G. 1994. Control knowl- edge to improve plan quality. Proceedings AIPS 94. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 58 |
1,686 | Database Learning for Software Agents Mike Perkowitz Oren Etzioni Department of Computer Science and Engineering, FR-35 University of Washington, Seattle, WA 98195 {map, etzioni}Qcs.washington.edu With the amount of information available rapidly outstripping the ability of individuals to use it, we wish to explore how a software agent can learn a description of an information resource (such as a database on the internet) in order turn it into a well-understood tool at the agent’s disposal. An agent who could do this would have access to all the information it could find without having to cache the internet. As the agent makes queries to an information re- source, it will generalize from those queries and gener- ate hypotheses about the structure and content of the database. We therefore formulate this problem as a learning problem in which the input is (1) the agent’s model - its representation of the world; and (2) a se- ries of queries to and responses from a database. The output is a mapping from fields in the information re- source to predicates in the model. Our approach to this learning problem relies on over- lap between the agent’s model and the information in the database. The agent will use its own knowledge to form hypotheses about the structure of the records. We have developed the correspondence heuristic, which states that a correspondence of tokens between the agent’s world model and the information resource in- dicates a correspondence between types. The agent matches the values of the fields in the database against facts in its model. The relationships that hold among these facts in the model are assumed to correspond to relationships in the database. Suppose that the agent makes a query to staffdir, the UW personnel directory, and gets back “Oren Etzioni 206”. The agent would have facts in its model like (lastname person37 Etzioni) and (office person37 206). From this query and this knowledge, the agent could conclude that the second field of the output is lastname and the third field is office. Our work has many similarities to structure- mapping work (Falkenhainer, Forbus, & Gentner 1986). Both approaches rely on discovering corre- spondences between separate domains. Structure- mapping, however, seeks correspondence between un- derlying structure, while the correspondence heuristic relates tokens in order to make inferences about the structure. The correspondence heuristic is an inductive bias which can be formalized as a determination: V(G Y)Pw A T(Y) A (W = w4> - S(Y) = WY)1 T is a type predicate such as “on the UW faculty”. S is a syntactic predicate like “the first field in the output of staffdir x”. M is a semantic predicate (i.e. from the agent’s model) such as “the first name of x”. This formalization clearly indicates three areas for work. Learning T could be handled by standard in- ductive learning algorithms. We assume a syntactic model of ordered fields to account for S. Future work may pursue other kinds of syntax, such as keyword- based syntax. The focus of our work is learning the appropriate M predicate. In particular, we have been exploring the problem of Predicate mismatch, which occurs when instances of one type in the database are instances of a different type in the model, or when relations in the database do not correspond to primitive relations in the model. For example, imagine that the agent gets back “Oren Etzioni FR-35” from a query. FR-35 is actually the mail stop of Etzioni’s department and so there is no fact to link the person Etzioni to the string FR-35 directly. Instead, the agent must realize that the entry in the database corresponds to a chain of predicates in its model linking Etzioni to Computer Science and Computer Science to FR-35. We have devised a way of doing this using a method reminiscent of spread- ing activation, in which a link between two tokens is found by exploring outward from the tokens until an intersection is found. Given simplifying assumptions about the syntax, our implemented algorithm has learned staff dir as well as 1s and finger (UNIX commands with tabular out- put can be treated as query/response databases). In the future, we will extend this to be able to handle in- formation resources found on the World Wide Web by programs that traverse the web automatically. References Falkenhainer, B., Forbus, K., and Gentner, D. 1986. The structure-mapping engine. In Proc. 5th Nut. Conf. on A.I. Student Abstracts 1485 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 59 |
1,687 | Small is Beautiful: A Brute-Force Approach to Learning First-Order Formulas Steven Minton and Ian Underwood Recom Technologies NASA Ames Research Center Mail Stop 269-2 Moffett Field, CA 94035 {minton,ian)@ptolemy.arc.nasa.gov Abstract We describe a method for learning formulas in first- order logic using a brute-force, smallest-first search. The method is exceedingly simple. It generates all ir- reducible well-formed formulas up to a fixed size and tests them against a set of examples. Although the method has some obvious limitations due to its com- putational complexity, it performs surprisingly well on some tasks. This paper describes experiments with two applications of the method in the MULTI-TAC sys- tem, a program synthesizer for constraint satisfaction problems. In the first application, axioms are learned, and in the second application, search control rules are learned. We describe these experiments, and consider why searching the space of small formulas makes sense in our applications. Introduction Most machine learning systems prefer smaller, simpler hypotheses to larger, more complex ones. This bias is a form of Occam’s Razor. While Occam’s razor has obvi- ous aesthetic appeal, some researchers have attempted to justify Occam’s razor on more principled grounds by showing that it produces more accurate hypothe- ses; for instance, Blumer et al. (1987) show formally that one version of Occam’s razor produces hypothesis that are likely to be predictive of future observations. However, in some applications, the utility of the learned information depends on more than just predic- tion accuracy. Utility considerations often provide us with an additional reason for applying Occam’s Razor, a point which has received scant attention. In our ap- plication, which involves automated problem solving, utility considerations place strong requirements on the learning process. In particular, the learned theories must, consist of small sets of simple first-order formu- las. Complex formulas, or large numbers of formulas, can significantly degrade system performance. Yet another reason for preferring simpler hypothe- ses is that they can be relatively straightforward to find, particularly if we equate “simplest” with “small- est”. In our system, the learning component systemat- ically generates well-formed formulas, in order of size, beginning with the smallest,. It tests each formula 168 Automated Reasoning against a set of training examples, attempting to find formulas that are adequate for the needs of the per- formance component. This brute force, smallest-first (BFSF) search often produces theories that are more efficient and more comprehensive than those entered by hand. In this paper we describe two applications of BFSF inductive learning in the MULTI-TAC system. In one application, the system learns axioms that are then used by a theorem prover to reason about generic con- straint satisfaction problems (CSPS), such as graph col- oring and bin packing. In the second application, the system learns search control rules to guide a constraint satisfaction engine. We were initially surprised that a brute force approach worked so well for our applica- tions. In retrospect, we can identify several reasons why searching the space of small formulas is appropri- ate in our domains. Au Overview of the Multi-TAC system MULTI-TAC (Multi-Tactic Analytic Compiler) is de- signed for a scenario where a combinatorial search problem must be solved routinely, as in a scheduling application where each week manufacturing tasks are assigned to workers. The system takes as input a spec- ification of the generic problem and a set, of problem instances. The objective is to synthesize an efficient program for the instance population. In practice, our goal is to do as well as competent programmers, as opposed to algorithms experts. Attaining this level of performance on a wide variety of problems would very useful; many relatively simple applications are not au- tomated because programmers are unavailable. The system starts with a set of domain-independent heuristics. When it encounters a new domain, it cre- ates problem-specific approximations of these heuris- tics, and then searches for the combination that per- forms best on the instance population. It returns as output a Lisp program that incorporates this combi- nation of heuristics. In order to present a problem to MULTI-TAC it must be formalized as an integer CSP, that is, as a set of constraints over a set, of integer variables. A solution From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. (declare-parameter ‘K 2) (declare-type-size ‘edge ‘7) (declare-type-size ‘vertex 5) (declare-relation-data ‘((endpoint edge0 vertex0) (endpoint edge0 vertexl) (endpoint edge1 vertex0) (endpoint edge1 vertex3). . .)) Figure 1: An instance of MMM with K = 2. A solution E’ = (edge2 edge5) is indicated in boldface. The instance specification is on the right. exists when all the variables are assigned a value such the constraints on each variable are satisfied. For example, consider the NP-complete problem, “Minimum Maximal Matching” (MMM), described in (Garey & Johnson 1979). An instance of MMM con- sists of a graph G = (V, E) and an integer K 5 1 E I. The problem is to determine whether there is a subset E’ C E with 1 E’ I< K such that no two edges in E’ share a common endpoint and every edge in E - E’ shares a common endpoint with some edge in E’. See Figure 1 for an example. To formulate MMM as a CSP, we represent each edge in the graph with a variable. If an edge is chosen to be in E’, it is assigned the value 1, otherwise it is assigned the value 0. The constraints can be stated as follows: 1. If edgea is assigned 1, then for every edgej that shares a common endpoint with edgei, edgej must be assigned 0. 2. If edgea is assigned 0, then there must exist, an edgej such that edgei and edgej share a common endpoint, and edgej is assigned 1. 3. The cardinality of the set, of edges assigned 1 must, be less than or equal to K. A problem specification describes the types (e.g., vertex and edge) and relations (e.g., endpoint) and specifies the constraints in a typed predicate logic. An instance specification (Figure 1) instantiates the types and relations referred to in the problem specification. Our constraint language is relatively expressive, as it allows for full first-order quantification and the forma- tion of sets and bags. Below we show how the first constraint above is specified, for some edge Edgei: (or (not (assigned Edgei 1)) (V Vrtz : (endpoint Edgei Vrtz) (V Edgej : (endpoint Edgej Vrtz) (or (equal Edgej Edgei) (assigned Edgej 0)))) The notation (Vx: (endpoint x y). . .) should be read as “forall x such that (endpoint x y)...” . The constraint language includes two types of re- lations, problem-specific user-defined relations such as endpoint, and built-in system-defined relations, such as assigned, equal and less-than. (There are no functions; instead, we use two-place relations.) The assigned relation has special significance since it rep- resents the state during the search process. In MMM, for example, the search proceeds by assigning each edge a value. In a solution state, every edge must, be as- signed a value such that the constraints are satisfied. Enumerating Formulas We now describe how the MULTI-TAC systematically generates hypotheses of increasing size. A formula is defined to be of size s if it contains s atomic formu- las. The system first generates formulas of size 1, then formulas up to size 2, and so on, until it, exceeds a pre-determined bound on either the computation time or the number of formulas. The generation process is based on a recursive grammar’ for the language: wfl= (V var: atomic wfl 1 (3 var : atomic w-g) 1 (and wfl . . . wff) 1 (or pug... wfl 1 (not atomic) I atomic cstomic = (predicate term . . . term) term = var I constant Formulas of size s > 1 are generated by existentially or universally quantifying formulas of size s - 1, or con- joining or disjoining sets of formulas whose size sums to s. In MULTI-TAC a recursive procedure, GENERATE- FORMULAS accomplishes this. GENERATE-FORMULAS takes a size s and a set “free variables”, and generates all formulas of size s defined over one or more of the free variables. Atomic formulas are generated using the user- defined types and relations (from the problem speci- fication) and the system-defined relations. Each argu- ment either is a variable or is a constant mentioned in the problem specification (i.e., arbitrary integers are not used). The MMM specification, for example, men- tions the constants 1 and 0, and the relation endpoint. Our implementation uses several simple techniques to improve the efficiency of the generation process. The most significant of these is that only “irreducible” formulas are generated. MULTI-TAC uses a simplifier to check each (sub)formula returned by GENERATE- FORMULAS; any formula which can be reduced to a smaller equivalent formula is discarded since the smaller formula will have been generated as well. ‘The grammar shown here is simplified, since it does not include set/bag generators. Automated Reasoning 169 After the candidate formulas have been generated, MULTI-TAC employs training examples to identify which formulas are useful. In the following sections we describe two applications, and for each we describe how the useful formulas are identified. Inducing axioms MULTI-TAC includes a resolution theorem-prover that can be used during program synthesis for several dif- ferent reasoning tasks. For example, the prover can be used to verify that a given value will necessarily violate a constraint, or that the antecedent of a search control rule will be satisfied in a given situation. In order to use the theorem prover, we require ax- ioms that describe the problem domain. Some axioms can be derived from the problem specification. For ex- ample, the problem description explicitly specifies the argument types for each relation. So, for MMM, an axiom stating that (endpoint x y) implies (edge x) can be created directly from the problem specification. However, other information may be left implicit in the instances. For example, in MMM (or any graph) it is necessarily true that for every edge there is at least one vertex that is its endpoint, but this is not stated in the problem specification. We need these additional axioms for the theorem prover to operate effectively. In addition, for the theo- rem prover to operate efficiently, it helps significantly if there are only a few small axioms. Having too many axioms, or very complex axioms, may greatly impair a resolution theorem prover’s performance because the branching factor will be higher. These axioms have to come from somewhere. One possibility is to require the user to enter them along with the problem specification. However, experience shows that axioms entered by users tend to be incom- plete, unnecessarily complicated, and just plain incor- rect. One contributing factor is that people are gen- erally not facile with predicate calculus. (In fact, the authors have noticed that we ourselves make many mis- takes.) But even if users are asked to enter the axioms in English they tend to neglect, relevant information. For example, for the MMM problem, one might forget to mention that every edge has an endpoint since it is so obvious. (It, may also seem obvious that every edge actually has two unique endpoints, but in fact this is not, true, since some edges may be connected to the same vertex at both ends. This illustrates the difficulty of writing axioms.) Alternatively, we have found that a suitable set, of axioms can often be found using BFSF induction. Our training examples are problem instances randomly se- lected from the instance distribution. (The instance distribution only provides positive examples, so we do not, use negative examples.) An iterative approach is used to produce axioms. On the nth iteration, the sys- tem generates formulas of size n and tests them against the training examples, retaining only those formulas that are consistent with all of the examples. Then the system filters this set, further, eliminating formulas that can be proved using smaller formulas as axioms (i.e., those found on the previous iterations). The re- maining formulas are reduced to an independent set by trying to prove each formula, using the other formu- las as axioms. This set is minimal, in the sense that each axiom in the set is not provable in terms of the others. (This is time-consuming, but necessary, since redundant formulas degrade the theorem prover’s per- formance.) The system then proceeds with the next iteration, until a resource bound is exceeded. Of course, there is always a chance that the sys- tem may induce incorrect axioms. We can either ask the user for assistance in eliminating incorrect axioms or accept the entire set and take the chance that our proofs will be incorrect in some cases. Here we consider only the former approach. After each iteration, the user is asked to approve the pro- posed axioms. If the user chooses not to accept an axiom, he can provide an example that is inconsistent with the proposed axiom. The example is then added to the training set. For instance, the system may pro- pose that “there are at least two edges in every graph”. The user can then enter a graph containing a single edge as a counterexample. Often a single counterex- ample will rule out a whole class of potential axioms; we have found that a few counterexamples often suffice to rule out all incorrect axioms. Table 1 summarizes a set of experiments with several combinatorial problems described in (Garey & John- son 1979): BIN PACKING, DOMINATING SET, GRAPH Q-COLORABILITY, NOT ALL EQUAL S-SAT, PARTITION- INTO-TRIANGLES and MMM. To make the experiment more challenging, the task was to produce axioms for distributions consisting only of solvable instances. Ax- ioms characterizing only solvable instances can be used to quickly screen out unsolvable instances, and in ad- dition are useful for many other tasks.2 For purposes of comparison, we asked two human volunteers to do the same task. (Both were familiar with predicate cal- culus, and one was a MULTI-TAC project member who had experience with the theorem prover.) For each problem, all formulas up to size 4 were gen- erated. To test the formulas, fifteen training examples were generated. As explained above, the user (one of the authors) could enter additional examples by hand, and in our experiments between 2 and 4 additional examples were entered per problem in response to in- correct axioms. Columns 2,3 and 4 show the number of formulas of each size that were generated. The last column shows the number of axioms finally retained. 2These axioms are essentially a superset of the axioms describing arbitrary instances (solvable or not). For exam- ple, for Graph 3-Colorability, the axiom set would in- clude the axioms describing graphs in general, but it might also include the axiom “No vertex has an edge to itself”, since this is true of solvable instances. 170 Automated Reasoning Table 1: Axiom Learning, Experimental Results One striking aspect of these experiments was how few training instances were required. In fact, the set of formulas generally stabilized after the third example - relatively few formulas were eliminated by subsequent examples (except for the user-provided counterexam- ples). This is somewhat surprising, since a PAC analy- sis reveals that for 1000 hypotheses, approximately 200 examples are required just to be .95 confident that the error is less than .05. Of course, this is a worst-case analysis, and it appears that the worst case assump- tions are violated in at least two ways. First, many of the formulas are equivalent (or almost equivalent j, since there are many ways to state the same fact. Sec- ond, most of the formulas appear to be either true, false, almost always true or almost always false. Thus, after just a few examples, the formulas that are left are true or almost always-true. We conjecture that this will occur for many problems. An analogous situation has been identified in the CSP literature - for some well- known problems, almost all instances are easy to solve because they are either over-constrained or under- constrained (Cheeseman, Kanefsky, & Taylor 1991; Mitchell, Selman, & Levesque 1992). If we compare the learned axioms to those produced by our human subjects, the results are as expected. Of- ten the humans neglected to state relevant axioms or stated them incorrectly. The machine-generated axiom sets were more complete, and in some cases, the ax- ioms were stated more concisely. (In fact, the machine did a better job than the authors for MMM.) On the other hand, for one problem, NOT ALL EQUAL %AT, the system generated many redundant axioms because it could not prove they were redundant within the time limit. Finally, the humans also identified a couple of axioms of size 5 and 6 that the system obviously did not generate. (However, these axioms appeared to be useless for the system’s purposes.) As we have argued, one advantage of the BFSF method is that it- - produces small sets of small ax- ioms. To illustrate the benefits, we tried reversing the smallest-first bias, producing MMM axioms of size four before looking for smaller axioms. This did indeed re- sult in a poorer set of axioms, including: (V El : (edge El) (3 ~92 : (edge J!+) (jtV;Jyp+;F V) en oin 2 This states that “for every edge El, there is an edge E2 that shares an endpoint with El. Although this ap- pears to be false, it is in fact true, since El and Ez can refer to the same edge. Thus, it is actually an obscure way to state the axiom, “every edge has an endpoint”. The problem with this, aside from obscurity, is that it is much less efficient for resolution theorem-proving; larger axioms translate into more (and larger) clauses, and thus increase the prover’s branching factor. Inducing Search Control Rules In MULTI-TAC, search control rules are used to con- trol the choices made during the constraint satisfaction process, such as variable and value-ordering choices. For example, we can implement the generic variable- ordering heuristic “prefer the most-constrained vari- able” by using a rule which, at each choice point, se- lects the variable with the fewest possible remaining values. Unfortunately, using this generic rule can be costly since it requires that the system maintain the possible values for each variable during the search. Minton (1993a) has described an analytic approach for automatically generating control rules. This method operationalizes generic variable and value- ordering heuristics by incorporating information from the problem specification. For MMM this process pro- duced 52 candidate control rules, including the those shown below. (Recall that in MMM the CSP search pro- ceeds by assigning each edge either 0 or 1.) e Prefer an edge cent edges). with the most neighbors (i.e., adja- Prefer an edge with been assigned values. Prefer an edge that assigned the value 1. the most neighbors that have has a neighbor that has been These rules were produced by operationalizing and approximating the generic “most constrained variable first” heuristic. The rules vary in their application cost and their effectiveness in reducing search. For exam- ple, the first rule is relatively inexpensive, since the ordering can be precomputed and the edges sorted ac- cordingly before the CSP search process begins. (The compiler has been specially crafted to make efficient use of such rules.) The third rule is more powerful but more costly to apply since the ordering cannot be pre- computed. MULTI-TAC allows such rules to be used in combination. The system’s utility evaluation module carries out a beam search for the best combination of rules; different combinations are evaluated by running them on representative problem instances. Although the analytic learning method has per- formed well, producing control rules that are compa- rable or better than hand-coded ones (Minton 1993b; 1993a), there is a significant drawback. For each generic heuristic, the system’s designers must write a meta-level theory that can be operationalized to produce control rules. This involves a sophisticated “theory-engineering” process where the designers guess Automated Reasoning 171 I Minimum Maximal Matching I 92 .lO II 38 I .‘73 I 535 I 22 II Table 2: Search Control Learning, Experimental Results what operationalizations will produce useful rules, without knowing exactly what problems the system will eventually be tried on. An alternative approach is to use BFSF induction for generating control rules. (Actually, as we will see, it makes sense to use both learning methods for robust- ness!) Minton (1990) and Etzioni & Minton (1992) have argued that smaller control rules tend to be more efficient and more general. We will not review these ar- guments here, but we will show empirically that BFSF induction produces good control rules. We begin by considering how candidate control rules approximating the “most-constrained variable” heuris- tic can be learned. In MULTI-TAC, variable ordering preference rules3 take the form “(Prefer V) if (P 21)” where (P V) is an arbitrary formula containing v. The BFSF method generates all candidate variable-ordering rules up to size s, and tests them using examples that illustrate the most-constrained heuristic. To find ex- amples we run our CSP problem solver (without any ordering heuristics) on randomly selected problem in- stances and periodically stop the solver at variable se- lection choice points. Each example consists of a pair of variables and a state, such that one variable is a most-constrained variable in that state and the other variable is not. A variable is “most-constrained” if no other variable has fewer possible values. We test each rule on each example by seeing if the antecedent holds for the most-constrained variable and does not hold for the other variable. In this case we say the rule was correct on the example. Since we do not expect our rules to be one-hundred percent correct, we simply retain all rules which are correct more often than they are incorrect. The utility evaluation module then finds the best combination of these rules. MULTI-TAC can learn other types of control rules similarly, such as rules that prefer the “least constrain- ing value”. The main requirement is an inexpensive way of generating examples. Unfortunately, for some generic heuristics, we have not yet found an inexpen- sive way of producing examples. For instance, we would like to induce rules that recognize problem sym- 3There is also an alternative syntax for preference rules that allows individual candidates to be numerically scored. We also generate rules of this form, but since the syntax involves the set generator construct which we avoided dis- cussing in the last section, we will not describe it here. 172 Automated Reasoning metries (Minton 1993a) but we do not know an inex- pensive way of generating examples of symmetries. We experimentally evaluated the inductive method by comparing to the analytic method on the 6 prob- lems introduced earlier. This is a significant test for the inductive method because in previous experiments (Minton 1993b; 1993a) the analytic method produced very good results - in some cases, MULTI-TAC'S pro- grams were faster than those of human programmers. To compare the inductive and analytic approaches on each problem, both methods were used to pro- duce most-constrained-first variable-ordering rules and least-constraining-first value-ordering rules. The BFSF method generated rules up to a size limit of 4. Thirty examples were used in the BFSF test phase. In our experiments, the rules produced by the induc- tive approach resulted in superior programs on four of the six problems. To evaluate the programs, we used one hundred randomly-generated instances as in (Minton 199313). Th e columns labeled “Solved” in Ta- ble 2 show the primary performance indicator: how many of the 100 test instances were solved within a pre- set time limit. The columns labeled “Time” show the fraction of the total available CPU time actually used. (This is relevant primarily for GRAPH %COLORABILITY and PARTITION-INTO-TRIANGLES where both methods solved most of the instances). The remaining two columns show the total number of rules generated dur- ing BFSF search and the number of rules retained. The inductive approach proved superior on four problems, but its performance was particularly good on BIN PACKING and DOMINATING SET, wheresubstan- tially more instances were solved. There was also one problem where the inductive approach was substan- tially inferior, MMM. We analyzed why the inductive approach performed poorly on MMM, and found that the “good” rules (those learned by the analytic ap- proach) were generated, but they did not do well in the test phase. We believe the problem arises because our examples are produced during un-informed search, which in some respects does not mirror the situations that occur when control rules are used. Finally, we note that, as in our axiom learning exper- iments, very few examples were necessary for our ex- periments. As can be seen from the last two columns, it was relatively rare for a rule to be retained. Discussion In the preceding sections we outlined a relatively sim- plistic, brute force approach for generating axioms and search control knowledge in MULTI-TAC. Initially, we were surprised that the approach worked so well. In retrospect, we can identify several important factors that contribute to its success. variety of other tasks besides automated software syn- thesis. In particular, BFSF induction might prove use- ful in other design tasks where a user creates a problem specification and the design task is broken down into small subcomponents. Limitations and Future work First, computers are very good at brute force search. They can quickly examine large numbers of candidate formulas. But even so, brute force would be out of the question without a strong bias for small formulas. Thus, a second contributing factor is the “smallest- first” bias. This bias is clearly appropriate for our ap- plications. Both the theorem prover and the search control module are much more likely to be effective if the learned formulas (the axioms and search control rules) are concise. A third reason for the success is that certain charac- teristics of our problem domains help keep the number of small candidate formulas manageable. Most impor- tantly, each problem specification generally includes only a few user-defined predicates. This is similar to having only a few “features” per domain. Similarly, the problem specification generally only mentions a few constants. (Recall that the generator uses only those constants mentioned in the problem specification, es- sentially a form of language bias.) The most obvious limitation of our approach is that the number of generated formulas grows exponentially as the size bound is increased.4 In our experiments, it typically took under a minute for a Sparc2 to generate all formulas of size 4. Generating formulas of size 5 can usually be accomplished in several minutes. For the axiom-learning application, the number of size 5 formulas ranges from 3450 for MMM to almost 34000 for DOMINATING SET. In practice, however, generat- ing the formulas is not the bottleneck. In order to test whether a formula is consistent with an example, MULTI-TAC converts each formula to an Lisp procedure which is then compiled. The most time-consuming as- pect of the induction process is running the Common- Lisp compiler on these procedures.5 For 5000 formulas, this takes more than an hour. Once the formulas have been compiled, testing the examples is relatively quick. These justifications are still insufficient to explain our results, however. The situation reminds us of the story of the drunk who was looking for his keys by the lamppost. (The drunk looks for his keys by the light, even though he thinks he may have dropped them somewhere else.) While we know that small formulas are preferable for our applications and furthermore, that we can easily search the space of small formu- las, do we really have any confidence that our target formulas (either axioms or control rules) will actually BE small? Clearly there is no guarantee. But we note that the language has been designed so that users can easily and concisely specify the constraints on a large variety of combinatorial problems. Furthermore, when the user formulates a given problem domain, he will tend to define relations that will make the constraints simple to specify. Therefore, because we believe that the problem constraints will usually be concisely spec- ified, we also have some confidence that the axioms and search control rules will be concisely specifiable as well. This is hard to formalize or quantify, but we believe that it is a significant factor. Thus, the most profitable improvement would be to reduce the number of formulas generated. Currently, GENERATE-FORMULAS often produces “nonsensical” subformulas that are unsatisfiable. In principal these could be identified by a theorem-prover if it had the appropriate domain axioms. We are currently investi- gating a much more practical approach that uses exam- ples to identify subformulas that are probably unsat- isfiable. Instead of generating all formulas and testing them on the examples, we interleave the generation and test processes. Any subformula that is false on all examples is eliminated during the generation phase. Another improvement involves the invention of new predicates to reformulate the constraints. As we ex- plained previously, the success of our approach de- pends on whether the target concepts can be expressed concisely, given the constraint language and the user- defined predicates. In some cases, a concise represen- tation may require the invention of new predicates. How can we invent appropriate predicates? One way is to look for transformations that rewrite the prob- lem constraints in a more concise form. For exam- ple, the MMM problem constraints could be rewritten more concisely given a “neighbor” predicate, such that Finally, we have already remarked upon the fact that very few training examples were required for our ap- plications. On a related note, we should mention that the issue of noise is not an important consideration in our applications. The theorem-proving application is noise-free, and the search control application does not involve noise in the traditional sense. 4Assume the domain has p predicates and k constants, where r is the maximum arity of any predicate. Then, since a formula of size s has at most s atomic formulas, there are at most sr distinct variables in any formula. Consequently, if Q is the number of literals that could be generated, then a 5 2p(k + ST)? Since a formula of size s may include no more than s quantifiers and connectives (of which there are 4), the number of possible formulas is O(48as). Interestingly, the factors we have identified as impor- 5We also note that eliminating redundant axioms is time tant to the success of our approach should hold for a consuming, since the theorem prover is used. Automated Reasoning 173 (neighbor edger edgea) if edger and edges share a those mentioned in the problem specification, a type of common endpoint. Currently, MULTI-TAC is capable a language bias. We pointed out that our approach will of inventing new predicates (through finite-differencing be successful only if the target concepts can be repre- and related techniques), but these are used only to sented concisely. Since presumably the language allows rewrite the problem constraints for efficiency purposes. the problem constraints to be represented concisely, we We plan to investigate whether the invented predicates conjectured that the language is also sufficient to allow can improve the induction process as well. the target concepts to be represented concisely. Related Work Most the the empirical work on first-order learning has been in the context of inductive logic program- ming (ILP), a paradigm which is quite different from ours (Muggleton 1992). In ILP the target language is usually restricted to horn clauses, while we allow full first-order formulas. On the other hand, ILP methods can be used to learn recursive programs, while we are interested only in simple formulas. Furthermore, ILP methods are generally concerned with optimizing ac- curacy in an environment that is typically noisy. In contrast, our applications have led us to focus primar- ily on efficiency. Finally, perhaps the most significant difference is that ILP systems usually operate by gen- eralizing or specializing hypotheses. In our approach, the hypothesis space is explicitly enumerated. All in all, there has been surprising little applied work using brute force enumeration of formulas, per- haps because the approach seems so simplistic. Weiss et a1.(1990) d escribe an algorithm that looks for the best logical expression of a fixed length or less that covers a sample population, but they search the space heuristically. Systematic enumeration techniques have received a bit more attention from researchers inter- ested in more restricted languages. Riddle, Segal and Etzioni (1994) report good results with an exhaustive, depth-bounded algorithm for learning decision trees, and Schlimmer (1993) describes an exhaustive, but ef- ficient, method for learning determinations. Methodologically, we were influenced by Holte’s (1993) study showing that one-level decision trees per- form well on many commonly used datasets. Holte ad- vocates exploring algorithms that have small hypoth- esis spaces, a methodology he refers to as “simplicity- first”. If a simple algorithm works, then one can ana- lyze why it worked, otherwise the hypothesis space can be expanded to rectify specific deficiencies. We view our work as an instance of this methodology. Conclusion We have shown that brute force induction is surpris- ingly useful for learning axioms and control rules in MULTI-TAC. Our approach relies on a bias in favor of small formulas. One reason that this bias is appropri- ate is that small formulas tend to have much higher utility in our applications, a point rarely discussed in the induction literature. The success of our approach also depends on cer- tain aspects of the domain. In particular, we limit the predicates and terms in our generalization language to We expect that our approach will prove useful for many of the problems that MULTI-TAC encounters. It also seems plausible that the approach will work for other types of design problems, and thus may be a promising avenue for further research. eferences Blumer, A.; Ehrenfeucht, A.; Haussler, D.; and War- muth, M. K. 1987. Occam’s razor. Information Pro- cessing Letters 24:377-380. Cheeseman, P.; Kanefsky, B.; and Taylor, W. 1991. Where the really hard problems are. In IJCAI-91. Etzioni, O., and Minton, S. 1992. Why EBL produces overly-specific knowledge: A critique of the prodigy approaches. In Proc. Ninth International Machine Learning Conference. Garey, M., and Johnson, D. 1979. Computers and Intractability: A Guide to the Theory of NP- Completeness. W.H. Freeman and Co. Holte, R. 1993. Very simple classification rules per- form well on most commonly used datasets. Machine Learning l( 11):63-90. Minton, S. 1990. Quantitative results concerning the utility of explanation-based learning. Artificial Intel- ligence 42. Minton, S. 1993a. An analytic learning system for specializing heuristics. In Proc. IJCA I-93. Minton, S. 1993b. Integrating heuristics for constraint satisfaction problems: A case study. In Proc. AAAI. Mitchell, D.; Selman, B.; and Levesque, H. 1992. Hard and easy distributions of SAT problems. In Proc. AAAI-92. Muggleton, S. 1992. Inductive Logic Progamming. Academic Press. Riddle, P.; Segal, R.; and Etzioni, 0. 1994. Repre- sentation design and brute-force induction in a Boeing manufacturing domain. Applied Artificial Intelligence 8: 125-147. Schlimmer, J. 1993. Efficiently inducing determina- tions: A complete and systematic search algorithm that uses optimal pruning. In Proc. Tenth Interna- tional Machine Learning Conference. Weiss, S.; Galen, R.; and Tadepalli, P. 1990. Maximis- ing the predictive value of production rules. Artificial Intelligence 45. 174 Automated Reasoning | 1994 | 6 |
1,688 | Building Emotional C aracters for Interactive Drama W. Scott Reilly Computer Science Department, Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA 15213-3891 scott.reilly@cs.cmu.edu Goals and Methodology The Oz project is developing tools to create inter- active, dramatic stories (Bates 1992).l An important aspect of this work is to develop technology for creat- ing the characters for these stories. We feel it’s critical that these characters appear emotional; just as char- acters in novels and movies that are unemotional are called “flat” and aren’t very believable, we expect the same applies to computer controlled drama as well. We’re developing an agent architecture, Tok (Bates, Loyall, & Reilly 1992), and an emotion subsystem, Em (Reilly & Bates 1992), that will allow artists to build emotional characters for their particular interac- tive stories. This goal places a number of constraints on the architecture. First, the architecture must be usable. That is, it must not be overly complicated to develop emotional characters, especially simple ones. Second, the architecture must be fZezible enough to create idiosyncratic characters. We’re willing to pass up psychological reality for the usablility and flexibility needed to create believable, artistic characters. Emotions in Em are generated by a flexible set of generation rules. We make emotion generation usable by providing a default set of rules based on the cogni- tive emotion system of (Ortony, Clore, & Collins 1988). For example, Em will generate joy whenever an impor- tant goal of the character succeeds. Using similar rules, Em generates: distress, fear, hope, like, dislike, pride, shame, admiration, reproach, anger, gratitude, grati- fication, remorse, satisfaction, disappointment, relief, and fears-confirmed. Also planned are: happy-for, pity, gloating, resentment, and frustration. The emotions, once generated, are mapped into Be- havioral Features (BFs) which, in turn, affect other Tok processes. For example, anger will often result in an aggressive BF being generated. This BF then af- fects other Tok subsystems. The BFs allow for a bit of individualism in the characters. So, not all characters must act aggressively when angry. It is just as simple to create a character who acts withdrawn when angry ‘This work is supp orted in part by Fujitsu Laboratories, Ltd. or aggressively when frightened. We’re exploring how to model the effects of emo- tions (via BFs) on the rest of Tok. Emotions currently affect goal processing by creating new goals, altering plan choices, rearranging goal priorities, and affecting the style of actions (e.g., stomping instead of walking). These effects are presently hand-coded, but we plan to create a useful set of behavioral features that will map automatically into these kinds of effects. Results The best way to test such a system is to build agents. One Tok/Em agent is Lyotard the cat (Bates, Loyall, & Reilly 1992). Lyotard was the first demonstration that Em and Tok can be used to create reasonably believable, albeit somewhat simple, agents. A second set of agents are the Woggles: three ellipsoidal crea- tures who live in a real-time graphical world (Loyal1 & Bates 1993). Informal evidence from hundreds of users indicates that the Woggles are believable, engag- ing characters. We’re also developing a gunman and a cashier for use in a hold-up story. References Bates, .I.; Loyal& A. B.; and Reilly, W. S. 1992. In- tegrating reactivity, goals, and emotion in a broad agent. In Proceedings of the Fourteenth Annual Con- ference of the Cognitive Science Society. Bates, J. 1992. Virtual reality, art, and entertain- ment. PRESENCE: Teleoperators and Virtual Envi- ronments l( 1):133-138. Loyall, A. B., and Bates, J. 1993. Real-time con- trol of animated broad agents. In Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society. Ortony, A.; Clore, G.; and Collins, A. 1988. The Cog- nitive Structure of Emotions. Cambridge University Press. Reilly, W. S., and Bates, J. 1992. Building emotional agents. Technical Report CMU-CS-92-143, School of Computer Science, Carnegie Mellon University, Pitts- burgh, PA. Student Abstracts 1487 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 60 |
1,689 | ON THE COMPUTATION OF POINT OF VIEW Warren Sack MIT Media Laboratory, 20 Ames St., E15-487, Cambridge, MA 02139 email: wsack@media.mit.edu phone: 617/253-9497 fm: 6 17/258-6264 Abstract Previous work in AI story understanding has largely been used to build tools which can summarize stories and categorize them according to the events they describe (e.g., the technologies developed for the Message Understanding Conferences). These sorts of technologies are built around the assumptions that (1) events reported as facts in news stories should be “understood” as facts; (2) the style of a story, i.e., the way in which a story is told, is not of interest; and, (3) the source of a story should not influence its analysis. These assumptions are obviously unrealistic. Everyone knows that one should not believe everything in the news. But, by making these simplifying assumptions most existing story understanding systems function as gullible “readers.” l The focus of my current research is to build a less gullible story understander by encoding in it a means to recognize point of view. The techniques that I am developing will be useful, not only for information retrieval tasks which demand a search for credible stories, but also in future entertainment technologies which will be capable of fiiding and then assembling together into a unified presentation a set of texts or video clips to tell a story fiom an ensemble of points of view. It is often possible, upon reading the fust sentence or two of a news story, to determine the storyteller’s point of view. For example, consider the following lead sentences from two different news reports about two different events: 1. Clandestine, 30 Mar 89 (Radio Venceremos) -- A report from San Miguel Department states that FMLN antiaircraft units ambushed a Salvadoran Air Force helicopter in Arenales canton at 1700 GMT on 29 March, as it was traveling from Usulutan to San Miguel department. Our unit’s effective antiaircraft fire hit ‘and damaged the helicopter. [MUC3-00961 2. San Salvador, 9 Jan 90 (DPA) -- The Salvadoran Army today prevented the occupation of cities in the eastern part of El Salvador, waging strong clashes between midnight and dawn, according to reports by military sources. [MUC3- 00061 One does not need to know about Salvadoran news agencies nor much about the past civil war in El Salvador to notice clues which give away the storytellers’ points of view: In story 1 the author notes the actions of the FMLN’s antiaircraft units and then refers to the antiaircraft units as “ours.” Clearly the use of the possessive shows that the fast story is told fi-om the point of view of the FMLN. In story 2 the point of view is less clear, but can be identified nonetheless. First of all, “military sources” 1 There are some early exceptions (e.g., Abelson and Carroll, 1966) and this neglect has not been complete in closely related areas (in dialog and argument understanding,, e.g., Allen and Perrault 1980, Birnbaum Flowers and McGuire 1980, Alvarado 1990; intelligent tutoring systems, e.g., Farrell and Bloch 1988; and, in the field of language generation, e.g., Hovy 1988). 1488 Student Abstracts are said to be the main source of the story. Secondly, and more subtly, it was said that the Army “prevented the occupation of cities” instead of, for example, “prevented the liberation.” Together, these two clues mark story 2 as one told from the Salvadoran Army’s point of view. SpinDoctor is a system which identifies a news story’s point of view using mechanisms which are built on the following observation: News products with significantly different points of view habitually cast the same news actors in different roles (e.g., the American press will cast Hussein as the villain, whereas the Iraqi press will cast Hussein as the hero). The current system has a database of fairy-tale-like roles described by linguist George Lakoff as those employed by American journalists to describe actions and actors in the Gulf War (Lakoff .199 1). Under orders from President Bush, U.S. and allied troops moved into defensive positions, ready to shoot if attacked but otherwise content to let President Saddam Hussein’s conquered warriors slink [my emphasis] home, leaving their tanks and artillery behind them. (p. 1, San Jose Mercury News, February 28, 1991) SpinDoctor’s analysis process is as follows: (1) it parses the news story; (2) notes which sorts of roles are evoked by various words and phrases (e.g., that “slink home” connotes a serpentine or animal-like activity by comparing the verb phrase to the part of the role definition of serpent which describes typical and unique actions for a serpent); (3) uses a set of heuristics to determine which actors are assigned to which sorts of roles (e.g., that the conquered warriors are being compared, metaphorically, to a snake, via the verb “slink”); (4) resolves various relations of anaphora (e.g., the fact that “President Saddam Hussein’s conquered warriors” is a reference to the Iraqi Army) by chaining together actor-role assignments (e.g., if role(a1) = rl, role(a2) = rl, then al might be equal to a2); and, (5) outputs the name of one or more news sources (as the recognized point of view) which use actor-role assignments consistent with the actor-role assignments identified. Most contemporary story understanding systems are built for data extraction and text categorization tasks and so are designed to answer the standard questions of news reporting: Who? What? When? Where? Why? How? In contrast SpinDoctor has been designed to help explore the issues of news filtering and editing, namely, Whose point of view, whose interests, are represented in the news? SpinDoctor is now being scaled up to analyze the corpus of news stories used in the MSJC3 competition. References Lakoff, G. 1991. Metaphor and War: The Metaphor System Used to Justify the War in the Gulf. Journal of Urban and Cultural Studies 2(l): 59-72. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 61 |
1,690 | Diagnosing Multiple Interacting Defects with Combination Descriptions Nancy E. Reed Computer Science Department, University of Minnesota 4192 EE/CS Bldg., 200 Union St. S.E., Minneapolis, MN 55455 reed@cs.umn.edu Cases with multiple defects can be difficult to di- agnose because the defects can interact, meaning that the observable cues are not a sum of the cues for the component defects. Diagnostic methods that use cue- to-defect relationships fail when interactions between defects change the observable cues. The primary alter- native, model-based methods, are limited to domains with accurate and complete models, along with initial- ization data. Using these traditional methods, when defects interact and models aren’t available, each possi- ble defect combination must be included in the knowl- edge base. This results in an explosion of possible alter- natives, greatly increased knowledge acquisition effort, slower processing, and increased maintenance effort. This research develops a computational diagnostic model that can diagnose multiple defects, even when cues are altered or missing, by using descriptions of cue combinations. We develop a description and classifica- tion of the ways cues change when defects interact. Each type of cue may combine in a different way, so each type has a separate description. The combination methods use the expectations of component defects to diagnose multiple interacting defects, instead of requir- ing a description of each possible defect combination. In a medical domain (diagnosis of congenital heart defects), we found that cues combine with one an- other in a small number of ways: all cues may appear (union), the values of the cues may be added (quanti- tatively or qualitatively), or dominant cues may mask other cues present. Cues of each type combine in one of these basic ways, or use a combination of a few of the basic ways, depending on characteristics of the cues, case, or domain. The cues are different than expected because the de- fects interact. Two murmurs are expected, a loud sys- tolic ejection murmur in the pulmonary area for ASD, and a moderate systolic ejection murmur in the aortic area for AS. Only one murmur is observed. Loud mur- murs mask softer ones occurring at the same time, so the absence of the (softer) expected murmur for AS is explained. The observed murmur supports ASD alone or ASD+AS. The observed heart sound S2 is normal, while both defect expectations are abnormal. ASD produces a wide, fixed split S2 while AS produces a narrow, variably split S2. The wide and narrow widths combine additively to explain a normal width, while the variable and fixed expectations combine additively to a variable split, which is a normal S2. Neither ASD nor AS is supported alone, but ASD+AS is supported by the normal S2 cue. If we had used cue-to-defect relationships and matching on this case, we would have explained only the observed murmur (with one of the component de- fects), leaving three missing abnormal expectations un- explained. The diagnostic model is tested by constructing a pro- gram with a knowledge base in pediatric cardiology (Fallot) and testing it on cases of single and multiple defects from hospital files. Fallot uses a combination of recognition-based reasoning (Thompson et al. 1983) and the cue combination descriptions. This program correctly diagnoses cases with multiple interacting de- fects for which conventional methods fail. References Figure 1 shows two types of cues, murmurs and heart sounds, for an example case. The case has two defects, atria1 septal defect (ASD) and aortic stenosis (AS). W. B. Thompson, P. E. Johnson, and J. B. Moen. 1983. Recognition-based diagnostic reasoning. In Pro- ceedings of the Eighth International Joint Conference on Artificial Intebligence, pages 236-238. observm interaction Key ASD - loud pulmonary systolic ejection murmur dominant c?!? AS _ _ _ -> matching expectation - - > support ,-> additive - ASD - observed cue cancel AS - - -> Figure 1: Explanation for murmur and heart sound cues for a case 1486 Student Abstracts a-> ASD+AS From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 62 |
1,691 | Multi-agent Learning in Non-cooperative Domains Mahendra Sekaran and Sandip Sen Department of Mathematical & Computer Sciences University of Tulsa 600 South College Avenue, Tulsa OK 74104-3189 mahend@euler.mcs.utulsa.edu Motivation Previous work in coordination (Bond & Gasser 1988) on multi-agent systems are specific either to cooper- ative or non-coperative problem domains. Previous work in learning in multi-agent systems have consid- ered agents operating to solve a cooperative task with explicit information sharing and negotiations (Wei 1993, Tan 1993). In a companion paper (Sen, Sekaran, & Hale 1994) we describe a general purpose system which describes a cooperative domain in which two agents work together on a joint task without explicit sharing of knowledge or information. The focus of this poster is to extend this approach to a non-cooperative domain, where the agents have conflicting goals. The strength of this work lies in the fact that there is no explicit knowledge exchange between the agents and no dependencies on agent relationships. Problem description The problem we consider is the “Block pushing” prob- lem in which two autonomous agents with different ca- pabilities and no knowledge of the domain are to push a block from a initial position to individual goal po- sitions in Euclidean space. At each step, each agent applies a force and angle and the block is transferred to the next state by a combination of the actions. A trial ends when the block reaches either one of the goal positions or when it is out of the playing field. Each agent through repeated trials learns a optimal policy to reach (as close as possible) its goal position. The feedback received after each action is an exponentially decreasing function of the current distance of the block from the optimal path to their respective goals. Based on the received feedback the agents update their indi- vidual policies using a well-known reinforcement learn- ing scheme , the Q-learning algorithm (Watkins 1989). Convergence of policy matrices (there is no significant update in the individual policies over a set of trials) is used as the stopping criteria for experiments. Experiments and Results We found that when the force range for one agent is greater than the other agent, it is able to overpower the other agent and drag the block to its goal. The number of trials to convergence increases as the force range for the weaker agent is increased (because it offers more resistance). When the two agents possess equal ca- pabilities, neither of them are able to push the block to their goal and they manage to push the block to a position in between the goals. As the strength of the weaker agent increases the final block position moves away from the goal of the stronger agent. This phe- nomenon is accentuated when the number of discrete options available to the weaker agent is increased. This is because the stronger agent coverges to a sub-optimal policy and can be avoided by choosing a probabilistic action scheme instead of a deterministic one (though policy convergence will be much slower). We show that agents can use reinforcement learn- ing schemes to achieve their goal even when working against a non-benevolent agent without requiring a model of the latter. Currently, we are investigating re- source sharing between multiple agents using the same approach. References A. H. Bond and L. Gasser. Readings in Distributed Artificial Intelligence. Morgan Kaufmann Publishers, San Mateo, CA, 1988. C. Watkins. Learning from Delayed Rewards. PhD thesis, King’s College, Cambridge University, 1989. G. We%. Learning to coordinate actions in multi- agent systems. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 311-316, August 1993. M. Tan. Multi-agent reinforcement learning: Inde- pendent vs. cooperative agents. In Proceedings of the Tenth International conference on Machine Learning, pages 330-337, June 1993. S. Sen, M. Sekaran and J. Hale. Learning to co- ordinate without sharing information. In Proceedings of the twelfth national conference on Artijicial Intel- ligence, August 1994 Student Abstracts 1489 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 63 |
1,692 | Coalition format ion met hods in multi-agent environments * Onn Shechory Department of Mathematics and Computer Science Bar Ban University Ramat Gan, 52900 Israel shechory@bimacs.cs.biu.ac.il Tel: +972-3-5318863 Fax: +972-3-5353325 Autonomous agents are designed to reach goals that were pre-defined by their operators. An important way to execute tasks and to maximize utility is to share resources and to cooperate on task execution by cre- ating coalitions of agents. If the agents are individ- ually rational, such coalitions will take place if, and only if, each member of a coalition gains more if it joins the coalition than it could gain previously. There are several ways of creating such coalitions and divid- ing the joint payoff among the members. Variation in these methods is due to different environments, dif- ferent settings in a specific environment, and different approaches to a specific environment with specific set- tings (Zlotkin & Rosenschein 1993). In this research we develop methods for coalition- formation and utility distribution in various environ- ments, we discuss their advantages and suggest occa- sions when each is most suitable (Shechory & Kraus 1993). The algorithms are developed with reference to different approaches. Some approaches are based on theoretical concepts from game theory (Shapley & Shubik 1973). Other approaches are based upon ne- gotiation (Kraus & Wilkenfeld 1991), and the use of methods and concepts from distributed AI. The algo- rithms require communication and computation oper- ations. These operations are either distributed among the agents or performed all by one agent. There are algorithms that can be halted in the middle of pro- cesses but still give reasonable results, i.e., any-time algorithms (Dean & Boddy 1988), while others, if were stopped before they end will give no results. We use a new concept of polynomial Kernel- stability based on the original Kernel-stability (Davis & Maschler 1965), to develop a Coalition Negotiation polynomial Algorithm (CNA), on which we focus. The CNA consists of steps in which coalitions are formed, where each step is constructed as follows: 1. Each coalition ranks the other coalitions according to the expected utility from forming a joint coalition. *The author is indebted to Sarit Kraus for her support and for her helpful advice. The material in this research is based upon work supported in part by the NSF under Grant No. IRI-9123460. 1490 Student Abstracts 2. Each coalition designs proposals to be offered to other coalitions, transmits the proposals and waits for response. 3. Each coalition that receives proposals accepts or re- jects them according to an evaluation done with re- spect to the polynomial-kernel-stability of the offer. The CNA leads to distribution of calculations and com- munications and to a vast reduction of the calcula- tional complexity, although it partially employs com- putational methods that were developed for the ex- ponential problem, e.g., the Stearns transfer scheme (Stearns 1968). It is an anytime algorithm: if halted after any negotiation step, it provides the agents with a set of formed polynomial K-stable coalitions. The advantages of our algorithm are that the average ex- pected utility of the agents is an increasing function of the time and effort spent by the agents performing the CNA steps, and is always better than when coopera- tion is avoided. References Davis, M., and Maschler, M. 1965. The kernel of a cooperative game. Naval research Logistics Quarterly 12:223-259. Dean, T., and Boddy, M. 1988. An analysis of time- dependent planning. In Proceedings, AAAI88, 49-54. Kraus, S., and Wilkenfeld, J. 1991. Negotiations over time in a multi agent environment: Preliminary report. In Proc. of IJCAI-91, 56-61. Shapley, L. S., and Shubik, M. 1973. Game The- ory in economics. Santa Monica, California: Rand Corporation. Shechory, O., and Kraus, S. 1993. Coalition formation among autonomous agents: Strategies and complex- ity. In Proc. of MAAMAW-93. Stearns, R. E. 1968. Convergent transfer schemes for n-person games. Transactions of the American Mathematical Society 134:449-459. Zlotkin, G., and Rosenschein, J. 1993. One,two,many: Coalitions in multi-agent systems. In Proc. of MAAMA W-93. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 64 |
1,693 | Integrating Specialized Procedures in Proof Systems Vishal Sikka Computer Science Department St anford University Stanford, CA - 94305 vishal@cs.stanford.edu Introduction We present the outline of a simple but powerful scheme for describing procedures that can be used by an au- tomatic theorem prover. Our approach is to describe specialized procedures to a theorem prover by adding procedure description axioms to its set of facts, instead of building in these procedures by using attachments. Our work can be viewed as an extension of the hybrid reasoning techniques based on attachments (Myers9 1). In this abstract we briefly describe our approach and state some of its advantages. In (Sikka94), we present this work in detail and formally show how the full expressibility of attachment-like approaches can be achieved in a simple logic-theoretic way. The work described here is part of the author’s Ph.D. thesis re- search in collaboration with Prof. Michael Genesereth. A Simple Integration Scheme We treat a programming environment as a 3-tuple 3 : (P,VJq, of p rocedures (P), data structures (D), and an evaluation function 8 : P x V* + 27. We integrate procedures from such an environment into a first order deductive calculus. Here we briefly describe its syntax and semantics. The language Ln/l is a con- struction from a standard first order language L, a set PN of procedure names (of P in s), and an n-ary func- tion symbol apply. We can use LM to describe procedures in a program- ming environment and their relationship to functions and relations. For example, the sentence VX.VY. Pqx, Y> = aPPlY(+, x, Y) relates the procedure + to the function plus. Every expression containing the function symbol apply has the following semantics: flPPlY(P, h, t2, * * *, t7Ja = q+, n, T2, * * *, TX> where p’ = 4, and ti’ = ri for every i, 1 5 i 5 n. Every other expression in -CM has standard first or- der semantics. We add to the deductive machinery an inference rule that allows us to replace a ground term containing the function symbol apply with the result of applying the associated procedure on the cor- responding argument terms. This framework allows us to prove the following result. It is formally described and proved in (Sikka94). Theorem 1 For every set of attachments, there is a set of sentences in LM that entail the same deductions. Summary There are four principal advantages to using this ap- proach for integration: 1. Attachments are principally substitutional in na- ture. Our scheme can be used to describe and use specialized procedures that perform more complex types of reasoning. Attachment-based approaches are limited in the kinds of conditions that can be imposed on the invo- cation of procedures. With our scheme the language of representation, i.e. LM itself can be used to pre- scribe any conditions on the use of the attached pro- cedures. Sentences with the function symbol apply can be used to reason about the attached procedures. Since sentences containing the function symbol apply are ordinary sentences, composition axioms for attached procedures can be described and reasoned with or- dinarily. Describing attached procedures to a theorem prover is much easier, from an implementational viewpoint, than building in the attachment for every function and relation symbol that has an associated proce- dure. References Myers, K.L. 1991, Universal Attachments: A Log- ical Framework for Hybrid Reasoning, Ph.D. The- sis, Dept. of Computer Science, Stanford University, 1991. Sikka, V.I., and Genesereth, M.R. 1994. Integrat- ing Specialized Procedures in Proof Systems. Logic Group Technical Report LOGIC-94-3, Dept. of Com- puter Science, Stanford University. Also to appear in the Workshop on Metatheoretic Extensibility of Auto- mated Reasoning Systems, CADS12, Nancy, France. Student Abstracts 1491 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 65 |
1,694 | Towards Situated Explanation Raja Sooriamurthi and David Leake Computer Science Department Indiana University, Bloomington, IN 47405 (raja,leake}Qcs.indiana.edu In AI research on explanation, the mechanisms used to construct explanations have traditionally been neu- tral to the environment in which the explanations are sought. Our view is that the explanation process can- not be isolated from the situation in which it occurs. Without considering the intended use for an explana- tion, the explanation construction process cannot be properly focussed; without considering the situation the process cannot act effectively to gather corroborating information. The emphasis of this research is to view explanation as a means to an end and in this work the end is the successful functioning of the system request- ing explanation. We develop a model of explanation as a situated, utility-based, hierarchical, goal-driven pro- cess. Explanation is viewed as a memory process of adapt- ing prior explanations of similar problems to fit the current situation. By using case-based reasoning we in- corporate prior experience during the explanation pro- cess and also generate an initial set of hypotheses in a relatively inexpensive way. The system under devel- opment consists of a planner, acting in a simple sim- ulated world, integrated with a case-based explainer. The over-arching goal of the explanation system is to aid the formulation and execution of plans. The occur- rence of a planning or execution failure triggers expla- nation. Given the goals of the planner the explanation system has to decide when to explain, what to explain and how to explain in a dynamic environment. Re- lated to earlier work on goal-directed diagnosis (Rymon 1993), a major issue being addressed in this research is how contextual changes influence the ongoing explana- tion process. As an example of the issues to address consider the following scenario implemented in our system. The planner is trying to achieve the goal of catching a plane and generates two possible plans: driving to the air- port or taking a taxi. Choosing the option of driving, the plan steps are executed in a simulated world and it is detected that the car does not start. In trying to determine why the car will not start our model of the ensuing explanation process involves: e Situated reasoning. The explanation process re- sponds to two types of situational changes: 1. Changes in the external environment: For exam- 1492 Student Abstracts 2 ple, due to time constraints the explanation effort could be curtailed and the system might choose the alternative plan of taking a taxi. But if the system becomes aware of a delay in the flight it opportunistically uses the extra available time for continuing with the explanation effort. Changes in the system goals: The system will be able to produce explanations for three explanation purposes (Leake 1992): anomaly resolution, recov- ery and prevention. Changes in these explanation goals might produce explanations at levels of detail ranging from “something is wrong with the engine” to “drained-battery”. Knowledge planning. An important facet of situ- ated explanation is that all the information necessary to formulate an explanation might not be initially available to the system. The explainer has to deter- mine what type of additional information is needed and how to procure it by planning to acquire knowl- edge (Hunter 1990). Prior cases help to package such knowledge planning actions that guide the informa- tion search. Utility-based and hierarchical reasoning. The utilities of the alternatives the explainer considers change with changes in the external environment. Our model of explanation allows the system to switch its focus to those alternatives that look most worth- while in the current situation. The utilities of the alternatives also help to adjust the depth of the ex- plainer’s exploratory efforts. Case-based reasoning forms an effective mechanism to determine and up- date the situational utility of the alternative expla- nations. References Hunter, L. 1990. Planning to learn. In 12th Annual Conference of the Cognitive Science Society, Cam- bridge, Massachusetts, 261-268. Lawrence Erlbaum Associates, Inc., Hillsdale, New Jersey. Leake, D. B. 1992. Evaluating Explanations: A con- tent theory. Lawrence Erlbaum Associates, Inc., Hills- dale, New Jersey. Rymon, R. 1993. Diagnostic Reasoning and Planning in Exploratory- Corrective Domains. Ph.D. Disserta- tion, University of Pennsylvania. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 66 |
1,695 | Reflective Reasoning and Learning Eleni Stroulia * College of Computing Georgia Institute of Technology Atlanta, GA 30332-0280 eleni@cc.gatech.edu The capability of learning is a prerequisite for auton- omy. Autonomous intelligent agents, who solve problems in a realistic environment need to learn in order to extend the classes of problems they can solve, to improve their performance on these problems, and to improve the quality of the solutions they produce. One way in which an intelligent agent may effectively use its experiences to learn, is by reflection upon its own problem-solving process. To do that, the agent needs to have an explicit meta-model of its own reasoning and knowledge. This work takes a functional stance towards reflective learning. This stance gives rise to a specific computational model which is based on three major hy- potheses: (i) agents can be viewed as abstract devices, (ii) their reasoning can be understood in terms of structure- behavior-function (SBF) models, and (iii) learning can be viewed as a self-redesign task in which the agent uses its understanding of its own reasoning to improve its subse- quent performance. Modeling Reasoning in terms of SBF Models Intelligent agents accomplish their problem-solving tasks through the internal information-processing behaviors of their func- tional architecture. The SBF model describes the agent’s reasoning as a non-deterministic sequence of information transformations, through which the output information of the agent’s task is produced from its input. Each information transformation corresponds to some subtask of the agent. The SBF model explicitly specifies the interactions among subtasks in terms of information and control flow. For each subtask, the model also specifies the role it plays to the accomplishment of the overall task in terms of the information it consumes, the information it produces, and a set of “correctness relations” between its input and output. Further, the SBF model specifies the representational and organizational assumptions on which the agent’s world knowledge is based, and they ways in which this knowledge is used by the agent to select among its reasoning methods and accomplish its tasks. Reflection If an agent has such a model of its own rea- soning, it can use it to 1. monitor its own behavior. The SBF model of the prob- lem solver provides a language for the agent to interpret its own reasoning steps in terms of its current goals and to generate expectations regarding their outcomes. *This research was conducted under the advice of Dr. Ashok Goel. It has been supported by the NSF (grant IRI-92-10925), the ONR (contract NOOO14-92-J-1234), the Advanced Projects Research Agency, and an IBM graduate fellowship. assign blame when it fails. The SBF model of the problem solver along with the record of its reasoning on the failed problem-solving episode, enables the agent to localize the cause of its failure to some element of its task structure. redesign itself appropriately. The semantics of the SBF language enable the the agent to modify itself in a way that maintains the overall consistency of its reasoning. This reflection process enables problem solvers, to some extent, to redesign themselves and adapt their problem- solving behavior to meet new requirements. Therefore, it is especially useful when the agent’s tasks are complex and when the requirements imposed by the the environment upon the agent regarding its processing and the quality of the solutions it produces can change. If, on the other hand, the environment is stable and the task structure is close to optimal, it may be less cost efficient. Discussion AUTOGNOSTIC (Stroulia and Goel 1993) is a system that implements and evaluates this theory of reflec- tive reasoning and learning. Given the SBF model of a problem solver, AUTOGNOSTIC monitors its reasoning, and when it fails, assigns blame to some of its elements and redesigns it appropriately. AUTOGNOSTIC presently operates in two widely different task domains: on top of ROUTER, in the domain of navigational planning, and on top of KRI- TIK~, in the domain of engineering design. Both ROUTER and KRITIK~ are autonomous multistrategy systems devel- oped independently of AUTOGNOSTIC, and since they solve widely different tasks in widely different domains, the suc- cess of AUT~GNOSTIC’S reflection process suggests that its SBF models of problem solving and reflection process are quite general. AUTOGNOSTIC is capable of identifying and correcting errors 1. in the representation scheme of the world knowledge, 2. in the organization of the world knowledge, 3. in the content of the world knowledge itself, 4. in the assumptions on the applicability and utility of different reasoning methods, and 5. the role of a subtask in the overall reasoning process. References [Stroulia and Goel 19931 Stroulia, E; and Goel, A. 1993. Functional Representation and Reasoning for. Reflective Systems. AppliedArtificial Intelligence: An International Journal Forthcoming. Student Abstracts 1493 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 67 |
1,696 | Case-Based Reasoning for Weather Prediction C. Vasudevan AUV Group, Department of Ocean Engineering, Florida Atlantic University, 500, NW 20th St., Boca Raton, FL 33431. email: vasu@transquest.oe.fau.edu Abstract Computer-based forecasting of weather was first exper- imented in 1950 at Princeton University. Since then, there have been newer and more accurate methods to predict the incoming climate. One common practice of weather prediction is by using the general circula- tion models which are based on the laws of physics (J.M.Moran & M.D.Morgan 1986). These models are highly complex and computational intensive limiting their use for only short range predictions and that too needing supercomputers. The accuracy of fore- casting deteriorates rapidly for periods longer than 48 hours and it often becomes minimal beyond 10 days due to imperfections in the models. The analog tech- nique of weather forecasting is another approach which searches for periods in the past when the current condi- tions were similar and use the past spatial patterns as analogs (J.T.Houghton, G.J.Jenkins, & J.J.Ephraums 1990). Long term trends and recurring events guide the decisions. This is more relevant for long range pre- dictions as well as in single station predictions. The araudog method is relatively simple compared to the complex processes of development, validation, use, and maintenance of numerical models. The analog technique closely resembles the princi- ples of case-based reasoning (CBR) (Kolodner 1993; Hammond 1989). The CBR scheme attempts to iden- tify a solution by searching a historical database of solutions. Rather than performing statistical compu- tations on past records, CBR attempts to retrieve one or a few best matching cases from its casebase and modifies them to fit the current scenario. The CBR approach often results in a faster synthesis of solutions compared to rule-based reasoning or reasoning from first principles. This paper discusses the relevance of CBR in weather forecasting and outlines an indexing and eval- uation scheme for prediction. The major issue is the task of identifying a set of indices to retrieve match- ing past case records and interpret them in the current context. For weather cases, the indices are typically the observations of relevant atmospheric parameters such as cloud amount, cloud altitude, cloud water con- 1494 Student Abstracts tent, wind direction and speed, sea and land surface temperatures, location and density of heat islands, at- mospheric pressulre, and water vapor content. In ad- dition to matching individual records, the variational patterns of these factors are also to be considered in assessing the situation. There are a number of rules of thumb derived from past experience that should be reflected in the case indices. Some examples are: Falling air pressure may indicate the approach of a stormy weather. A wind shift from northwest to west to southwest is usually accompanied by warm air ad- vection. Building the casebase for weather prediction benefits from the archives already maintained by vari- ous meteorological agencies. The ‘repair’ or adaptation of matching case(s) is based on the immediate past in- formation and the interpretation of mismatches in the observed data with the past case data. The case-based reasoning scheme naturally suits weather prediction based on historical records. Al- though recurrence of climatic patterns may not be al- ways dependable, this approach provides a simpler and faster method to predict the future weather conditions than the complex numerical models. Moreover, this scheme establishes a baseline for a detailed and more accurate scheme based on the physics of the system. This project is in a preliminary stage and a detailed knowledge engineering of weather patterns and predic- tion skills is needed to build the case library. References Hammond, K. 1989. Case-Based Planning: Viewing Planning as a Memo y Task. Academic Press. J.M.Moran, and M.D.Morgan. 1986. Meteorology. Macmillan Publishing Company. J.T.Houghton; G.J.Jenkins; and J.J.Ephraums. 1990. Climate Change: The IPCC Assessment. Cambridge University Press. Kolodner, J. 1993. Case- based Reasoning. Morgan- Kaufmann. From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 68 |
1,697 | Agent Modeling Methods Using Limited Jo& M. Vidal and Edmund W. Durfee * Artificial Intelligence Laboratory, University of Michigan. 1101 Beal Avenue, Ann Arbor, Michigan 48109-2110 jmvidal@umich.edu To decide what to do in a multiagent world, an agent should model what others might simultaneously be de- ciding to do, but that in turn requires modeling what those others might think that others are deciding to do, and so on. The Recursive Modeling Method (RMM) [I] provides representations and algorithms for devel- oping these nested models of beliefs and using them to make rational choices of action. However, because these nested models can involve many branches and recurse deeply, making decisions in time-constrained multiagent worlds requires methods for inexpensive ap- proximation and for metareasoning to balance decision quality with decisionmaking cost. RMM represents an interaction as a payoff matrix that specifies an agent’s payoffs for different combina- tions of agents’ actions. To predict others’ actions, an agent will similarly model how it believes they see the interaction as matrices specifying their payoffs. The agent can model how the others see others as another layer of payoff matrices, and so on. When uncertain of how others will model the interaction, an agent asso- ciates probabilities with alternative models. We thus define a situation as a 4-tuple which includes the ma- trix (M) that corresponds to the agent’s expected pay- offs in this interaction, a probability density function (f) over the possible strategies that it should play, an estimate of the number of nested levels (a) of belief to which it has expanded this situation, and the set of situations that it thinks the other agents are in: s = (W f, d, {(P, T)I >: P = 1, ?- E w E s (1) The set of all situations is denoted as S. p is the probability with which the agent believes that some other agent is in the situation r. The recursive definition of a situation makes it pos- sible for loops to exist. That is, an agent might be in a situation s and believe, with some probability, that all the other agents are in the same situation s, and so on recursively. If the probability associated with these models is one, this can be interpreted as “all agents have common knowledge that they are in situation s.” Such situations could lead RMM into infinitely deep recursion but, fortunately, game’ theory can provide *Supported, in part, by NSF grant IRI-9158473. alternative algorithms for identifying solutions in com- mon knowledge situations. In fact, in some cases these algorithms can be substantially more efficient than rea- soning about nested beliefs as RMM does. Thus, even when common knowledge does not exist, it might be more cost effective for an agent to assume that it does and converge on an approximate solution quickly, than to compute an exact solution using RMM. In time-constrained cases where RMM should be em- ployed, meta-reasoning can be used to selectively ex- pand the recursive nesting of situations. We borrow some of Russell’s notation [2] for limited rationality in turn-taking games (examining future game states), and apply it to RMM (examining more deeply-nested beliefs in the current state). The time cost to examine a situation s is denoted by TC(s). Limiting ourselves to only two agents, we denote our top-level strategy as (Y and our counterpart’s as p. The payoff we, as an agent, expect is P(o,p). If a situation s is not the top- level one, then we define our strategy, after expanding s and propagating a strategy back up the tree, as a,. Similarly, our counterpart’s is ps. When we do not have time to fully expand a situation, we use the situ- ation’s function f to predict what strategy it is likely to return. In these cases, the associated strategies are ,Y &!s and fls. We can now define the value of a situation V(s) in terms of it’s utility U(s) = P(cys,ps), and do the same for its expected value E gain in expanding a situation is 1 V(s)). Our expected (s). V(s) = U(s) - TC(s) = P(&, ps) - TC(3) (2) E(V(s)) = E(U(s)) - TC(s) = P(&, f$) - TC(s) (3) G(s) = I’(&,, js) - I+, p5) - c - W(s) (4) We have designed an algorithm that uses these con- cepts to determine which parts, if any, of the RMM hierarchy could be gainfully expanded. We are work- ing on its implementation and improving its ability to learn expected strategies. [l] P. J.Gmytrasiewicz, E.H.Durfee, and D.K.Wehe. A decision theoretic approach to coordinating multi- agent interactions. IJCA I, 1991. [2] S.RusselI and E.Wefald. Do The Right Thing. The MIT Press, Cambridge, Massachusetts, 1991. Student Abstracts 1495 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 69 |
1,698 | Avoiding Tests for Subsum Anavai Ramesh Neil V. Murray Inst. for Programming and Logics - CSI Dept. University at Albany - SUNY, Albany, NY 12222 rameshag/nvm @cs.albany.edu Abstract Useful equivalence-preserving operations based on unfi- links are described. These operations eliminate a poten- tially large number of subsumed paths in a negation nor- mal form formula. Those anti-links that directly indicate the presence of subsumed paths are characterized. These operations are useful for prime implicant/implicate algo- rithms because most of the computational effort in com- puting the prime implicants and prime implicates of a pro- positional formula is spent on subsumption checks. The problem of removing all subsumed paths in an NNF for- mula is shown to be NP-hard, even though such formulas may be small relative to the size of their path sets. The general problem of determining whether a pair of sub- sumed paths is associated with an arbitrary anti-link is shown to be NP-complete. Further reductions of sub- sumption checks are shown to be available when strictly put-e full blocks are present. The effectiveness of opera- tions based on anti-links and strictly pure full blocks is examined with respect to some benchmark examples from the literature. Introduction The consequences of a ground formula, expressed as minimal implied clauses, are useful in certain approaches to non-monotonic reasoning [5,11,13], where all consequences of a formula set (e.g., the support set for a proposed commonsense conclusion) are required. Minimal conjunctions that imply a formula are useful in situations where satisfying models are desired, as in error analysis during hardware verification. Such minimal implied clauses are the formula’s prime implicates, and the minimal conjunctions that imply it are its prime impli- cants. Many algorithms have been proposed to compute the prime implicates of propositional boolean formula. Most algorithms [ 1,2,3,4,14] assume that the input is either in conjunctive normal form (CNF) or in disjunctive normal form (DNF). Other algorithms [lo] require the input to be a conjunction of DNF formulas. In [12] a set of techniques is proposed for finding the prime impli- cates of formulas in negation normal form (NNF). Those ’ This research was supported in part by National Science Foundation Grant CCR-9101208. techniques are based on dissolution, an inference rule introduced in [8], and on ah algorithm called PI. The techniques described here are polynomial for classes of formulas for which any CNF/DNF-based technique must be exponential. The PI algorithm is described in [12]; there, PI is used to enumerate all the prime implicates of a f&l dis- solvent, an NNF formula that has no conjunctive links (defined later). PI repeatedly does subsumption checks to keep intermediate results as small as possible. However these checks are expensive. Most result in failure, and they have to be done on sets which can be exponentially large. The time required for these operations can be reduced by using a more compact representation of the intermediate results [l J, but avoiding as many such checks as possible is the focus of this paper. We show that the full dissolvent can be restructured before applying PI such that many non-prime implicates are removed without doing subsumption checks at all. We define disjunctive and conjunctive anti-links’ in NNF formulas, and we identify operations to remove such anti-links and their associated subsumed paths. This leaves fewer subsumption checks for the PI algorithm. In the next section we describe our path semantics viewpoint and our graphical representation of formulas in classical logic. In Section 3 we introduce anti-links and develop useful equivalence-preserving operations based on them. In Section 4, complexity issues are discussed and some NP-completeness results are proven. Section 5 introduces further techniques based on strictly pure sub- formulas. The effectiveness of our techniques on certain benchmark formulas described by Ngair [IO] is explored. Proof are omitted for lack of space. ’ Anti-links and some associated operators were first pro- posed by Beckert and N&nle - personal communication. The first motivation for studying anti-links arose in con- nection with regular clausal tableau calculi (Letz, p. 114 [6]). The anti-link rule as it will be defined later can be viewed as an implementation of the regularity condition in [6] for the propositional non-clausal case (Letz considered the first-order clausal case). There, refinements of general inference rules are considered, whereas the anti-link rule allows implementation as a preprocessing step. Automated Reasoning 175 From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. Foundations: Facts on Formulas in Negation Normal Form We assume the reader to be familiar with the notions of atom, literal, and formula from classical logic. We consider only formulas in negation normal form (NNF): The only connectives used are conjunction and disjunction, and all negations are at the atomic level. In this section, we review a number of technical terms and definitions taken from [9]. They are required for the development of the anti-link operations defined in Section 3, and they make the paper somewhat sclf- contained even for readers not familiar with dissolution. Semantic Graphs A semantic graph G is a triple (iV,CD) of nodes, c-arcs, and d-arcs, respectively, where a node is a literal occurrence, a c-arc is a conjunction of two semantic graphs, and a d-arc is a disjunction of two semantic graphs. Any of N,C,D may be empty. If N is empty, G is either true (empty conjunction) or fake (empty disjunc- tion). Each semantic graph used in the construction of a semantic graph is called an expZicit subgraph, and each proper explicit subgraph is contained in exactly one arc. We will typically use G to refer to both the graph and to the corresponding node set when the meaning is evident from context. We use the notation (X,Y), for the c-arc from X to Y and similarly use (X,Y)d for a d-arc; the subscript may be omitted when no confusion is possible. Arbitrary sub- formulas are denoted by upper case italic letters; plain upper case letters are used for single nodes. Figure below the (( 4?A) V D V E) A i7A V (BAC)), formula is displayed graphically: iz 2 V D V E A B x v A C Figure 1. Note that c-arcs and d-arcs are indicated by the usual symbols for conjunction and disjunction. Essentially, the only difference between a semantic graph and a formula in NNF is the point of view, and we will use either term depending upon the desired emphasis. For a more detailed exposition, see [9]. If A and B are nodes in a graph, and if a = (X,Y& is an arc (a= c or a = d) with A in X and B in Y, we say that a is the arc connecting A and B, and that A and B are a-connected. In Figure 1, C is c-conzected to each of B, A, C, D, and E and is d-connected to A. Let G be a semantic graph. A partial c-path through G is a set of nodes such that any two are c- connected, and a c-path through G is a partial c-path that is not properly contained in any partial c-qath. -The s- paths of the graph in Figure 1 above_are: (C, A, A), (C, A, B, Cl, ID, A), (D, B, CL E, AL E I% Cl. We similarly define d-path using d-arcs instead of c-arcs. The following lemma is obvious. Lemma 1. Let G be a semantic graph. Then an interpretation I satisfies (falsifies) G iff I satisfies (falsifies) every literal on some c-path (d-path) through G. If we consider conjunction and disjunction as nary connectives, then we informally define a furl block to be subset of the arguments of one connective, i.e., of one explicit subformula. Let H be a full block; H is a conjunction or a dis- junction of fundamental subgraphs of some explicit sub- graph M. If the final arc (main connective) of M is a con- junction, then we define the c-extension of H to be M and the d-extension of H to be H itself. The situation is reversed if the final arc (main connective) of M is a d-arc. We will use the notation CE(H) and DE(H) for the_c- an$ d-extensions, respe.$ively, of H. In Figure 1, CE(A) = A a.ndDE(x)=;i:vA. C Path Dissolution A c-link is defined to be a complementary pair of c-connected nodes; d-connected complementary nodes form a d-link. Unless stated otherwise, we use the term link to refer to a c-link. Path dissolution is in general applicable to collections of links; here we restrict atten- tion to single links& Suppose then that we have literal occurrences A and A residing in conjoined subgraphs X and ,Y, respectively. Consider, for example, the link {A, A) in Figure 1. Then the entire graph G = (X A Y) is the smallest full block containing the, link, where x= +vEandY = XV:: C' The c-path complement of an arbitrary subgraph H with respect to X, written CC(H, X), is defined to be the sub- graph of X consisting of all literals in X that lie on paths that do not contain nodes from H, the c-path extension of H with respect to X, written CPE(H, X), is the subgraph containing all literals in X that lie on paths that pass through I-I. (In the development of anti-link operations, we will require the dual operations of CC and CPE. We use DC for the d-path complement and DPE for the d- path extension operators. Their definitions and properties are straightforward by duality.) It is intuitively clear that the paths through (X A Y) that do not con&in the link are those through OWL x) A CC(A, r)) plus thOSe through (WA, W A CP&WN Plus thOSe through (CC(A, X) A CC(A, Y)). The reader is referred to [9] for the formal definitions of CC and of CPE. 176 Automated Reasoning Let H = (A, x) be a link, and let M = (X, Y)c be the smallest full block containing H. We define DV(H, M), the dissolvent of H in M, as follows: X CC@, x) cc& Y) V CPE;;i, Y) Theorem 1. Let H link in a semantic graph 6, and let M be the smallest full block containing H. Then M and DV(H, M) are equivalent. We may therefore select an arbitrary link H in G and replace the smallest full block containing H by its dissolvent, producing (in the ground case) an equivalent graph that has strictly fewer c-paths than the old one. This proves Theorem 2. At the ground level, path dissolution is a strongly complete rule of inference. Fully Dissolved Formulas If we dissolve in semantic graph G until it is link- less, the resulting graph is called the fur2 dissolvent of 6; we denote it by m)(G). The set of c-paths in FD(G) is unique: It is exactly the set of satisfiable c-paths in G. In the discussion that follows, we will often refer to subsumption of d- and c-paths rather than of disjuncts and conjuncts. We denote by Z(p) the literal set of path p. In this way, no change in the standard definition of sub- sumption is necessary. We also assume the reader to be familiar with the standard definitions of prime implicate and prime implicant. The theorem below is from [12]. Theorem 3. In any non-empty formula in which no c-path (d-path) contains a link, every implicate (impli- cant) of the formula is subsumed by some d-path (c-path) in the formula. In [ 121, the prime implicates of G are computed by first obtaining FD(G); then, knowing that all implicates are present in the d-paths of m>(G), the PI algorithm computes v(m)(G)), where v&3 = {P I ( P is a d-path through 3) A (P f true ) A (V d-paths Q through 3, Z(Q) $ Z(P)) } . Used in this way, PI extracts all unsubsumed (non- tautological) d-paths from an NNF formula without c- links. In general, PI computes ~(3) for an arbitrary NNF formula 3. Subsumed Paths and Anti-Links Let M=(X,Yjd be a d-arc in a semantic graph G and let Ax and AY be occurrences of the literal A in X and in Y respectively. Then we call (Ax,Ar) a disjunc- tive anti-link. Note that M is the smallest full block con- taining the anti-link. If M=(X,Y), is a c-arc in a seman- tic graph G and if Ax and AY are nodes in X and in Y respectively, then we call (A,,AY) a conjunctive anti- link. Theorem 4. Let G be a semantic graph in which d-path p is subsumed by a distinct non-tautological d-path p’ in 6. Then G contains either a disjunctive anti-link or a conjunctive anti-link. Unfortunately, the presence of anti-links does not imply the presence-of subsumed paths, and hence the verse of the above theorem is not true. con- Redundant Anti-links We now identify those disjunctive anti-links which do imply the presence of subsumed paths. We say a dis- junctive anti-link (Ax,Ar) with respect to the graph G is redundant if either CE(A,) # A or CE(Ay) # A. Let (A,,A,) be a disjunctive anti-link in graph 6, where M = (X,Y), is the smallest. ful!l block containing the anti-link. We define 39&&G to be the set of all d-paths of M which pass through both CE(Ax) - (Ax) and AY or through both CE(AY) - (AY) and Ax. In general, one or both of the literals in a redundant anti-link (Lx, Ly ) is an argument of a conjunction, and apLx.LY.G f 0. Theorem 5. Let {Ax ,Ay) be a redundant disjunc- tive anti-link in semantic graph G. Then each d-path in 39&&G is properly subsumed by a d-path in G that contains the anti-link. An Anti-Link Operator The identification of redundant disjunctive anti- links can be done easily by checking to see if either CE(Ax) z Ax or CE(AY) f Ay. After identifying a redun- dant anti-link, it is possible to remove it using the dis- junctive anti-link dissolvent (DADV) operator; in the pro- cess, all d-paths in a&,x,AY,G are eliminated, and the two occurrences of the anti-link literal are collapsed into one. Let (Ax,Au) be a disjunctive anti-link and let M = (X, YJd be the smallest. full block containing the anti-link. Then DADV( (Ax, AY) , M) = WAxrn ” WAY3 A WCE(Ax), X) ” DPE(A,,Y) A DPE(Ax,X) ” CC&J) . Consider the formula G of the form (X, yld, where A”C A G= A V A l B E”C We have DC(Ax, X) = B and DC(AY, Y) = (E V C), so the upper conjunct in DADV is (B V E V C). For the middle conjunct, CE(Ax) = AX, DC(CE(Ax), x) = B, and DPE(Ay, Y) = A,; this conjunct is (B V A). Finally in the lower conjunct, DPE(A,, X) = (A V C) and CC(Ay, Y) = 0 (false), so this reduces to (A V C).The Automated Reasoning 177 result is: B v EVC DAW(Ax, AYL M) = BCA ACC We point out. that although DADV produces a CNF formula in this simple example, in general it does not. Theorem 6 below states that DADV({ Ax, Ay ) ,G) is logi- cally equivalent to G and does not contain those d-paths in ~~Ax.Ar.G- Theorem 6. Let M = (X V Y) be the smallest full block containing (Ax,Ay}, a disjunctive anti-link in semantic graph G. Then DADV((Ax, Ay), M) is equivalent to M and differs in d-paths from M as follows: Those d-paths in Z)~‘A~,A~,M are not present, and any d- path of M containing the anti-link is replaced by a path with the same literal set having only one occurrence of the anti-link literal. By identifying a redundant anti-link H = {A,,Ay) and the smallest full block M containing it, and then replacing M by DADV(H, M), at least one subsumed d- path is removed. This proves Theorem 7. Finitely many applications of the DADV operation on redundant anti-links will result in a graph without redundant disjunctive anti-links, and termi- nation of this process is independent of the choice of anti-link at each step. Simplifications The following simplified versions of DADV result in formulas that are syntactically smaller than those that result from the.general definition. 1. If CE(Ax) = Ax (and CE(Ax) #X), then DC(CE(Ax), X) = DC(Ax , X). Therefore by (pos- sibly non atomic) factoring on DC(Ax, X) and observing that (DC(Ay, Y) A DPE(Ay, Y)) = Y, DADV( { Ax, AY) , M) becomes DC(Ax,X) v Y DPE(Aly,X) (: CC(Ay,Y) 2. If CE(Ax) = X, then DC(CE(Ax), X) = 0 (true). Hence DPE(Ax, X) = Ax and DC(Ax, X) = X -(Ax). DADV((Ax,Ay }, M) becomes X- (Ax) V DWW-7 Ax c WAY, Y) 3. If both Case 1 and Case 2 apply, then CE(A& = X = Ax, and the above formula simplifies to Ax V CC(Ay, Y). Note that in all the above versions of DADV, the roles of X and Y can be interchanged. 178 Automated Reasoning Conjunctive Anti-Links There are conjunctive Santi-links that always indi- cate the presence of d-paths that are subsumed by others, and they are easy to detect. Wowever, the conditions to be met are much more restrictive than those for redundant disjunctive anti-links. Consider a conjunctive anti-link {Ax, Azr), where the smallest full block M containing the anti-link is (Ax /\ Y). Every d-path in Y which passes through AY will be subsumed by the d-path consisting of the single literal Ax. Hence we can replace Y by WAY, Y)* plexity Considerations The problem of eliminating all subsumed paths in a graph in an efficient manner does not seem feasible. Let G be a semantic graph, and let p be any path in G. The graph G’ is called a d-minimal equivalent of G if it satisfies the following conditions. 1. G is logically equivalent to G’. 2. If p’ and q’ are two distinct d-paths in G’, then p’ does not subsume q’ and vice versa. 3. If p’ is a d-path in G’, then there is a d-path p in G such that, I(p) = Z(p’). 4. If p is a minimal d-path in G, then there is a d-path p’ in G’ such that r(p’) L Z(p). Note that Property 1 is implied by Properties 3 and 4, and that G’ need not be unique. However, the d-paths of 6’ will always include all essential (and possibly some inessential) prime implicates of G. The c-minimal equivalent of a graph is defined in the obvious dual way. Computing d-minimal equivalent graphs efficiently would be helpful for finding prime implicates. In a d- minimal equivalent graph of a full dissolvent, subsump- tion checks can be completely eliminated by Property 2 above. Hence to find the prime implicates of G, we can find a d-minimal equivalent G’ of the full dissolvent FD(G), and then simply enumerate the d-paths of G’. A d-minimal equivalent of a given graph G can be trivially obtained by first enumerating all the d-paths of the given graph G and then eliminating all the subsumed d-paths. The above algorithm is exponential in the size of G, because G’ is being constructed in CNF. However an NNF d-minimal equivalent G’ of G may be small com- pared to a CNF d-minimal equivalent. Even so, the prob- lem is NP-hard (proof follows) and hence is not likely to have an efficient algorithm. Theorem 8. The following problem (Elimination of subsumed paths) is NP-haid. Given a graph G, find a d-minimal equivalent graph G’. We have seen that the general problem of comput- ing d-minimal graphs is N&hard. Nevertheless, redun- dant disjunctive anti-links are easily recognized, and eliminating their corresponding subsumed d-paths can be done without direct subsumption checks. On the other hand, recognizable subsumed d-paths due to conjunctive anti-links are not likely to be as plentiful due to the strong restriction defining such useful anti-links. It is also difficult to find out if an arbitrary conjunctive anti- link results in subsumed d-paths. In fact, this problem is NP-complete. Theorem 9. The following problem is Np- complete. INSTANCE: Given a conjunctive anti-link (Ax, Ay} in graph G. QUESTION: Are there two d-paths px and py in G, such that px passes through Ax and py passes through AY and either px subsumes py or vice versa. Ngair [lo] has investigated examples that prove difficult for many proposed prime implicate/implicant algorithms. In this section, we show that PI + anti-links is effective for some of these examples. For other examples from [lo], applying anti-link techniques appears not to produce as significant an improvement. We also develop another technique based on strictly pure full blocks, and which results in a dramatic improvement for these latter examples. Examples Using Anti-Links In [lo] Ngair proposes a class of formulas for which reliance on an intermediate CNF form can result in an exponential increase in size and hence would be intractable for CNF-based algorithms. Dissolution + PI also does poorly for these examples: Although the full dissolvent can be computed quickly, a large number of subsumption checks must be performed by PI. It turns out, however, that the subsumed implicates correspond to useful and easily recognizable anti-links of both the dis- junctive and conjunctive kind. We show that if these anti-links links are removed after dissolution is per- formed, dissolution +PI can find all the implicates in polynomial time. We represent this class of formulas as (3i ) , i 2 1. Shown below is the formula 3~: ((~3~w~.~ji2N-1)VAl)~((A4~‘..~ji2N)VA2) A ((AI A AZ) V - l 0 v (Ati-r A Ah)) Observe that 3~ has 3.N liter&, and 2.N c-links; dissolution can remove these links by performing 2-N dis- solution steps we get a full disolvent. Using N+3 factoring operations [9] (a special case of anti-link operation) and 3 anti-link operations the full dissolvent reduces to (At A AZ); the prime implicates are just (A1 } and (AZ}. Hence dissolution + removal of anti-links + PI can handle the above class of problems in polynomial time. Perhaps the most important point is that no subsumption checks whatsoever are required. Strictly Pure Full Blocks Recall that a full block is essentially an explicit subgraph; it is a subset of the arguments of a conjunction or disjunction, and, via commutations and reassociations, can in fact be made explicit. We say a full block M in graph G is pure if there are no c-links or d-links that con- sist of exactly one node from M. (This is just the obvious generalization of pure literal used in the literature on CNF-based automated deduction.) If, in addition, there are no conjunctive or disjunctive anti-links that consist of exactly one node from M, we say that M is strictZy pure. (Simply put, M shares no variables with the rest of 6.) When factored, some of the examples from [lo] contain surprisingly many strictly pure full blocks. Note that both factoring and recognizing strictly full blocks are polynomial operations. Intuitively, such full blocks can be replaced by single new variables, and the implicates of the resulting graph bear a strong relationship to those of the original. Theorem 10. Let M be a satisfiable strictly pure full block in satisfiable semantic graph G, and let X be a new variable not occurring in G. We denote by Gx the graph obtained by the substitution of X for M in G. Let D=D- V 0~ be a non-tautological disjunction of literals from G, where DGM consists of literals not in M, and DM consists of literals that are. We define the dis- junction Dx to be D- V (DM / X) = DGLM V X (the result of replacing in D every literal of DM by the new variable X and collapsing the multiple occurrences of X). Then 1) If D does not contain literals from , then D k a prime implicate of G H D is a prime implicate of Gx 2) If D contains literals from M then D is a prime impli- cate of G a Dx is a prime implicate of Gx and DM is a prime implicate of GM. ore examples In [lo] Kean provides the class of examples referred to as I(,. They have m(n+l) input CNF clauses and (m+l)“+mn prime implicates. This set of clauses can be factored to get a more compact representation in NNF as shown below. Since the number of prime implicates is exponential, so is the number of subsumption checks required. The number of subsumption checks for the IPIA [ 1 ] and GEN-PI [lo] are shown in Table 1. Since then also have no anti-links, For each i the literals { Si 1 * * l Si,) form a full block Mi, and all literals in it are strictly pure. Let K’, be the graph obtained by replacing each full block Mi by a new variable Xi. By the corollary of Theorem 10, we can get the prime implicates of Kmn from the prime implicates of I-c’,. Since each of the subgraphs Mi has no c-links, the prime implicates of Mi are present as d-paths by Theorem 3. By the contrapositive of Theorem 4, neither are sub- Automated Reasoning 179 eferences Table 1. sumption checks required to find these prime implicates. Thus the number of subsumption checks to be done is exactly that required for computing the prime implicates of K’,, and this is significantly less than that needed for K Note that the number of prime implicates of K’, is on!$y 2”+n. For the problems in Table 1, we applied the above technique in combination with anti-link operations. For Klmn, the full dissolvent depends only on n and can be defined recursively. (We omit the graph due to space limitations.) The number of subsumption checks required in this case is also shown in Table 1. There is clearly a significant reduction in the number of subsumption checks required by our techniques. Note that for the prob- lem K,, the number of subsumption checks depends only on n and not on m. Our techniques are not limited to NNF formulas. They can sometimes be used by other algorithms like IPIA and GEN-PI which are not based on NNF formulas. For example K’, turns out to be in CNF and hence both IPIA and GEN-PI can handle these formulas, thereby reducing the number of subsumption checks needed. However normal forms like CNF provide very little scope for applyjng thes_e techniques directly. For example the literals { Si 1 - l l Si m) in the unfactored form of K, n do not form a full block. Hence one cannot apply Theorem 10. They do form a full block after factoring. This pro- vides stronger evidence that by avoiding less general nor- mal forms like CNF/DNF, one can improve the perfor- mance of prime implicate algorithms. ’ Conclusions and Future Work Anti-links admit useful equivalence-preserving operations that remove subsumed paths without any direct checks for subsumption. This is significant for prime implicate computations, since such computations tend to be dominated by subsumption checks. Although prime implicate/implicant problems are intractable in general, our techniques perform exponen- tially better than others on certain examples. In addition, we are able to improve performance greatly on the inherently exponential examples of [lo]. Some experimental results on a dissolution- and PI-based prime implicate system are reported in [12]. The system will be extended to include anti-link operations, so as to test their effectiveness in practice. 2 Data obtained from [1O].3 Inferred from [l]. 180 Automated Reasoning 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. de Kleer, J. An improved incremental algorithm for computing prime implicants. Proceedings of AAAI-92, 780-785. Jackson, P., and Pais, J. Computing prime impli- cants. Proceedings of the CUE-IO, Kaiserslau- tern, Germany, July, 1990. In WV., Springer- Verlag, Vol. 449, 543-557. Jackson, P. Computing prime implicants incremen- tally. Proceedings of CADE-11, Saratoga Springs, NY, June, 1992. In WVAI, Springer-Verlag, Vol. 607,253-267. Kean, A., and Tsiknis, G. An incremental method for generating prime implicants/iiplicates. Journal of Symbolic Computation 9 (1990), 185-206. Kean, A., and Tsiknis, 6. Assumption based rea- soning and clause management systems. Computa- tional Intelligence 8,l (Nov. 1992),1-24. Letz, R. First-order calculi and proof procedures for automated deduction. Ph.D. thesis, TH Darmstadt, June 1993. Murray, N.V., and Rosenthal, E. Inference with path resolution and semantic graphs. JAW 34,2 (April 1987), 225-254. Murray, N.V., and Rosenthal, E. Path dissolution: A strongly complete rule of inference. Proceedings of AAAI-87, Seattle, WA, July, 1987, 161-166. Murray, N.V., and Rosenthal, E. Dissolution: Mak- ing paths vanish. JACK 40,3 (July 1993), 504- 535. Ngair,T. A new algorithm for incremental prime implicate generation. Proceedings of IJCAI-93, Chambery, France, August, 1993. Przymusinski, T.C. An algorithm to compute cir- cumscription. Artificial Intelligence 38 (1989), 49- 73. Ramesh, A., and Murray, N.V. Non-clausal deduc- tive techniques for computing prime implicants and prime implicates. Proceedings of LPAR-93, St. Petersburg, RussiaJuly, 1993. In WVAI, Springer- Verlag, Vol. 698, 277-288. Reiter, R. and de Kleer, J. Foundations of assumption-based truth maintenance systems: prel- iminary report Proceedings of m-87, Seattle, WA, July, 1987, 183-lF8. Slagle, J.R., Chang, C.L., and Lee, R.C.T. A new algorithm for generating prime implicants. IEEE Transactions on Computers, C-19(4) (1970), 304- 310. Sttzemecki, T. Polynomial-time algorithms for generation of prime implicants. Journal of Com- plexity 8 (1992), 37-63. | 1994 | 7 |
1,699 | When the Best Move Isn’t Optimal: Q-learning with Exploration George H. John* Computer Science Department St anford University Stanford, CA 94305 gjohn@cs.Stanford.EDU The most popular delayed reinforcement learning technique, Q-learning (Watkins 1989)) estimates the future reward expected from executing each action in every state. If these estimates are correct, then an agent can use them to select the action with maximal expected future reward in each state, and thus perform optimally. Watkins has proved that Q-learning pro- duces an optimal policy (the function mapping states to actions) and that these estimates converge to the correct values given the optimal policy. However, often the agent does not follow the op- timal policy faithfully - the agent must also explore the world, taking suboptimal actions in order to learn more about its environment. The “optimal” policy produced by Q-learning is no longer optimal if its pre- scriptions are only followed occasionally. In many sit- uations (e.g., dynamic environments), the agent never stops exploring. In such domains Q-learning converges to policies which are suboptimal in the sense that there exists a different policy which would achieve higher re- ward when combined with exploration. A bit of notation: &(z, a) is the expected future re- ward received after taking action a in state x. V(x) is the expected future reward received after starting in state x. 0 and v are used to denote the approxi- mations kept by the algorithm. Each time the agent takes an action a moving it from state x to state y and generating a reward T, Q-learning updates the approx- imations according to the following rules: 9(x, 4 + P(r + 7%)) + (1 - fM(X~ 4 P(x) t maxa&^(z,u) (1) where p is the learning rate parameter and y is the discount rate parameter. We propose replacing the ? update equation by P(x) + ~~(~)~(w-4 * (2) a That is, update p(x) with the expected, not the muxi- mul, future reward, taking into account the exploration *This material is based upon work supported un- der a National Science Foundation Graduate Research Fellowship. Q: reward = 3.35 9: reward = 3.44 Figure 1: Policies and average reward produced by Q and G-learning. “S” is the starting state and “G” indicates goal states which give a reward of 9 units. The algorithms were run for lo6 steps. Here random wcdk exploration was used, where 30% of the time the agent took a random action instead of the policy-recommended action. y = .9, p = .5. policy when calculating the expected reward. We call this new algorithm a-learning. When the agent always takes the best action, Equations 1 and 2 are equivalent. For some exploration strategies P(u), the probability of taking action a, might be estimated using sample statistics if it is not possible to calculate in closed form. In our experiments this did not degrade performance. Figure 1 shows an example motivating our approach. The agent begins in the middle of the world and must choose whether to approach the wall of goals on the left, or the single goal on the right. Q-learning is indif- ferent as to which action should be performed, because with no exploration either action is optimal - a goal is only two steps away in either direction. G prefers to move left towards the wall of goals because it knows that the agent will explore, and because of this it is better to move left since a goal is still close if explo- ration causes it to move UJ or down. By thus taking exploration into account, & achieves higher reward. The results in Figure 1 are typical of our exper- iments. G-1 earning always generates policies giving greater average reward, but the improvement over Q- learning depends on the domain and the amount of exploration. References Watkins, C. J. C. H. 1989. Learning from Delayed Re- wards. Ph.D. Dissertation, Cambridge University. Psy- chology Department. 1464 Student Abstracts From: AAAI-94 Proceedings. Copyright © 1994, AAAI (www.aaai.org). All rights reserved. | 1994 | 70 |
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