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Policy gradient method : A further improvement is proximal policy optimization (PPO), which avoids even computing F ( θ ) and F ( θ ) − 1 via a first-order approximation using clipped probability ratios. Specifically, instead of maximizing the surrogate advantage max θ L ( θ , θ t ) = E s , a ∼ π θ t [ π θ ( a | s ) ... |
Policy gradient method : Reinforcement learning Deep reinforcement learning Actor-critic method |
Policy gradient method : Sutton, Richard S.; Barto, Andrew G. (2018). Reinforcement learning: an introduction. Adaptive computation and machine learning series (2 ed.). Cambridge, Massachusetts: The MIT Press. ISBN 978-0-262-03924-6. Bertsekas, Dimitri P. (2019). Reinforcement learning and optimal control (2 ed.). Belm... |
Policy gradient method : Weng, Lilian (2018-04-08). "Policy Gradient Algorithms". lilianweng.github.io. Retrieved 2025-01-25. "Vanilla Policy Gradient — Spinning Up documentation". spinningup.openai.com. Retrieved 2025-01-25. |
Proximal policy optimization : Proximal policy optimization (PPO) is a reinforcement learning (RL) algorithm for training an intelligent agent. Specifically, it is a policy gradient method, often used for deep RL when the policy network is very large. The predecessor to PPO, Trust Region Policy Optimization (TRPO), was... |
Proximal policy optimization : TRPO, the predecessor of PPO, is an on-policy algorithm. It can be used for environments with either discrete or continuous action spaces. The pseudocode is as follows: Input: initial policy parameters θ 0 , initial value function parameters ϕ 0 Hyperparameters: KL-divergence limit δ ,... |
Proximal policy optimization : The pseudocode is as follows: Input: initial policy parameters θ 0 , initial value function parameters ϕ 0 for k = 0 , 1 , 2 , … do Collect set of trajectories D k = _=\left\\right\ by running policy π k = π ( θ k ) =\pi \left(\theta _\right) in the environment. Compute rewards-to-go ... |
Proximal policy optimization : Reinforcement learning Temporal difference learning Game theory |
Proximal policy optimization : Announcement of Proximal Policy Optimization by OpenAI GitHub repo |
Q-learning : Q-learning is a reinforcement learning algorithm that trains an agent to assign values to its possible actions based on its current state, without requiring a model of the environment (model-free). It can handle problems with stochastic transitions and rewards without requiring adaptations. For example, in... |
Q-learning : Reinforcement learning involves an agent, a set of states S , and a set A of actions per state. By performing an action a ∈ A , the agent transitions from state to state. Executing an action in a specific state provides the agent with a reward (a numerical score). The goal of the agent is to maximize it... |
Q-learning : After Δ t steps into the future the agent will decide some next step. The weight for this step is calculated as γ Δ t , where γ (the discount factor) is a number between 0 and 1 ( 0 ≤ γ ≤ 1 ). Assuming γ < 1 , it has the effect of valuing rewards received earlier higher than those received later (refl... |
Q-learning : Q-learning at its simplest stores data in tables. This approach falters with increasing numbers of states/actions since the likelihood of the agent visiting a particular state and performing a particular action is increasingly small. |
Q-learning : Q-learning was introduced by Chris Watkins in 1989. A convergence proof was presented by Watkins and Peter Dayan in 1992. Watkins was addressing “Learning from delayed rewards”, the title of his PhD thesis. Eight years earlier in 1981 the same problem, under the name of “Delayed reinforcement learning”, wa... |
Q-learning : The standard Q-learning algorithm (using a Q table) applies only to discrete action and state spaces. Discretization of these values leads to inefficient learning, largely due to the curse of dimensionality. However, there are adaptations of Q-learning that attempt to solve this problem such as Wire-fitte... |
Q-learning : Reinforcement learning Temporal difference learning SARSA Iterated prisoner's dilemma Game theory |
Q-learning : Watkins, C.J.C.H. (1989). Learning from Delayed Rewards. PhD thesis, Cambridge University, Cambridge, England. Strehl, Li, Wiewiora, Langford, Littman (2006). PAC model-free reinforcement learning Reinforcement Learning: An Introduction by Richard Sutton and Andrew S. Barto, an online textbook. See "6.5 Q-... |
Reinforcement learning from human feedback : In machine learning, reinforcement learning from human feedback (RLHF) is a technique to align an intelligent agent with human preferences. It involves training a reward model to represent preferences, which can then be used to train other models through reinforcement learni... |
Reinforcement learning from human feedback : Optimizing a model based on human feedback is desirable when a task is difficult to specify yet easy to judge. For example, one may want to train a model to generate safe text that is both helpful and harmless (such as lacking bias, toxicity, or otherwise harmful content). A... |
Reinforcement learning from human feedback : Human feedback is commonly collected by prompting humans to rank instances of the agent's behavior. These rankings can then be used to score outputs, for example, using the Elo rating system, which is an algorithm for calculating the relative skill levels of players in a gam... |
Reinforcement learning from human feedback : RLHF has been applied to various domains of natural language processing (NLP), such as conversational agents, text summarization, and natural language understanding. Ordinary reinforcement learning, in which agents learn from their actions based on a predefined "reward funct... |
Reinforcement learning from human feedback : In RLHF, two different models are trained: a reward model and a reinforcement learning (RL) policy. The reward model learns to determine what behavior is desirable based on human feedback, while the policy is guided by the reward model to determine the agent's actions. Both ... |
Reinforcement learning from human feedback : RLHF suffers from challenges with collecting human feedback, learning a reward model, and optimizing the policy. Compared to data collection for techniques like unsupervised or self-supervised learning, collecting data for RLHF is less scalable and more expensive. Its qualit... |
Reinforcement learning from human feedback : "Learning RLHF (PPO) with codes (Huggingface TRL) | Yiyang Feng". yiyangfeng.me. Retrieved 2025-01-26. "The N Implementation Details of RLHF with PPO". huggingface.co. 2025-01-19. Retrieved 2025-01-26. "Proximal Policy Optimization — Spinning Up documentation". spinningup.op... |
Sequential decision making : Sequential decision making is a concept in control theory and operations research, which involves making a series of decisions over time to optimize an objective function, such as maximizing cumulative rewards or minimizing costs. In this framework, each decision influences subsequent choic... |
TD-Gammon : TD-Gammon is a computer backgammon program developed in 1992 by Gerald Tesauro at IBM's Thomas J. Watson Research Center. Its name comes from the fact that it is an artificial neural net trained by a form of temporal-difference learning, specifically TD-Lambda. The final version of TD-Gammon (2.1) was train... |
TD-Gammon : During play, TD-Gammon examines on each turn all possible legal moves and all their possible responses (two-ply lookahead), feeds each resulting board position into its evaluation function, and chooses the move that leads to the board position that got the highest score. In this respect, TD-Gammon is no dif... |
TD-Gammon : Unlike previous neural-net backgammon programs such as Neurogammon (also written by Tesauro), where an expert trained the program by supplying the "correct" evaluation of each position, TD-Gammon was at first programmed "knowledge-free". In early experimentation, using only a raw board encoding with no huma... |
TD-Gammon : TD-Gammon's exclusive training through self-play (rather than tutelage) enabled it to explore strategies that humans previously had not considered or had ruled out erroneously. Its success with unorthodox strategies had a significant impact on the backgammon community. For example, on the opening play, the ... |
TD-Gammon : World Backgammon Federation |
TD-Gammon : TD-Gammon at IBM TD-Gammon on GitHub |
Temporal difference learning : Temporal difference (TD) learning refers to a class of model-free reinforcement learning methods which learn by bootstrapping from the current estimate of the value function. These methods sample from the environment, like Monte Carlo methods, and perform updates based on current estimate... |
Temporal difference learning : The tabular TD(0) method is one of the simplest TD methods. It is a special case of more general stochastic approximation methods. It estimates the state value function of a finite-state Markov decision process (MDP) under a policy π . Let V π denote the state value function of the MDP ... |
Temporal difference learning : TD-Lambda is a learning algorithm invented by Richard S. Sutton based on earlier work on temporal difference learning by Arthur Samuel. This algorithm was famously applied by Gerald Tesauro to create TD-Gammon, a program that learned to play the game of backgammon at the level of expert h... |
Temporal difference learning : The TD algorithm has also received attention in the field of neuroscience. Researchers discovered that the firing rate of dopamine neurons in the ventral tegmental area (VTA) and substantia nigra (SNc) appear to mimic the error function in the algorithm. The error function reports back th... |
Temporal difference learning : PVLV Q-learning Rescorla–Wagner model State–action–reward–state–action (SARSA) |
Temporal difference learning : Meyn, S. P. (2007). Control Techniques for Complex Networks. Cambridge University Press. ISBN 978-0521884419. See final chapter and appendix. Sutton, R. S.; Barto, A. G. (1990). "Time Derivative Models of Pavlovian Reinforcement" (PDF). Learning and Computational Neuroscience: Foundations... |
Temporal difference learning : Connect Four TDGravity Applet (+ mobile phone version) – self-learned using TD-Leaf method (combination of TD-Lambda with shallow tree search) Self Learning Meta-Tic-Tac-Toe Example web app showing how temporal difference learning can be used to learn state evaluation constants for a mini... |
KAON : KAON (Karlsruhe ontology) is an ontology infrastructure developed by the University of Karlsruhe and the Research Center for Information Technologies in Karlsruhe. Its first incarnation was developed in 2002 and supported an enhanced version of RDF ontologies. Several tools like the graphical ontology editor OIM... |
KAON : KAON home page KAON2 home page Archived 2006-01-06 at the Wayback Machine |
Markov model : In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property). Generally, this assumption enables reasoning ... |
Markov model : There are four common Markov models used in different situations, depending on whether every sequential state is observable or not, and whether the system is to be adjusted on the basis of observations made: |
Markov model : The simplest Markov model is the Markov chain. It models the state of a system with a random variable that changes through time. In this context, the Markov property indicates that the distribution for this variable depends only on the distribution of a previous state. An example use of a Markov chain is... |
Markov model : A hidden Markov model is a Markov chain for which the state is only partially observable or noisily observable. In other words, observations are related to the state of the system, but they are typically insufficient to precisely determine the state. Several well-known algorithms for hidden Markov models... |
Markov model : A Markov decision process is a Markov chain in which state transitions depend on the current state and an action vector that is applied to the system. Typically, a Markov decision process is used to compute a policy of actions that will maximize some utility with respect to expected rewards. |
Markov model : A partially observable Markov decision process (POMDP) is a Markov decision process in which the state of the system is only partially observed. POMDPs are known to be NP complete, but recent approximation techniques have made them useful for a variety of applications, such as controlling simple agents o... |
Markov model : A Markov random field, or Markov network, may be considered to be a generalization of a Markov chain in multiple dimensions. In a Markov chain, state depends only on the previous state in time, whereas in a Markov random field, each state depends on its neighbors in any of multiple directions. A Markov r... |
Markov model : Hierarchical Markov models can be applied to categorize human behavior at various levels of abstraction. For example, a series of simple observations, such as a person's location in a room, can be interpreted to determine more complex information, such as in what task or activity the person is performing... |
Markov model : A Tolerant Markov model (TMM) is a probabilistic-algorithmic Markov chain model. It assigns the probabilities according to a conditioning context that considers the last symbol, from the sequence to occur, as the most probable instead of the true occurring symbol. A TMM can model three different natures:... |
Markov model : Markov-chains have been used as a forecasting methods for several topics, for example price trends, wind power and solar irradiance. The Markov-chain forecasting models utilize a variety of different settings, from discretizing the time-series to hidden Markov-models combined with wavelets and the Markov... |
Markov model : Markov chain Monte Carlo Markov blanket Andrey Markov Variable-order Markov model == References == |
Absorbing Markov chain : In the mathematical theory of probability, an absorbing Markov chain is a Markov chain in which every state can reach an absorbing state. An absorbing state is a state that, once entered, cannot be left. Like general Markov chains, there can be continuous-time absorbing Markov chains with an in... |
Absorbing Markov chain : A Markov chain is an absorbing chain if there is at least one absorbing state and it is possible to go from any state to at least one absorbing state in a finite number of steps. In an absorbing Markov chain, a state that is not absorbing is called transient. |
Absorbing Markov chain : Discrete phase-type distribution Absorbing set (random dynamical systems) |
Absorbing Markov chain : Wolfram Demonstration Project: Absorbing Markov Chain Monopoly as a Markov chain |
Algorithmic composition : Algorithmic composition is the technique of using algorithms to create music. Algorithms (or, at the very least, formal sets of rules) have been used to compose music for centuries; the procedures used to plot voice-leading in Western counterpoint, for example, can often be reduced to algorith... |
Algorithmic composition : Compositional algorithms are usually classified by the specific programming techniques they use. The results of the process can then be divided into 1) music composed by computer and 2) music composed with the aid of computer. Music may be considered composed by computer when the algorithm is ... |
Algorithmic composition : AIVA Change ringing Computational creativity David Cope Euclidean rhythm (traditional musical rhythms that are generated by Euclid's algorithm) Generative music Musical dice game Pop music automation List of music software |
Algorithmic composition : "Algorithmic Composition: Computational Thinking in Music" by Michael Edwards. Communications of the ACM, vol. 54, no. 7, pp. 58–67, July 2011 doi:10.1145/1965724.1965742 Karlheinz Essl: Algorithmic Composition. in: Cambridge Companion to Electronic Music, ed. by Nicholas Collins and Julio d'E... |
Algorithmic composition : Drew Krause: Introduction to Algorithmic Composition on Vimeo Algorithmic Composer, series of algorithmic composition tutorials |
Baum–Welch algorithm : In electrical engineering, statistical computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics fo... |
Baum–Welch algorithm : The Baum–Welch algorithm was named after its inventors Leonard E. Baum and Lloyd R. Welch. The algorithm and the Hidden Markov models were first described in a series of articles by Baum and his peers at the IDA Center for Communications Research, Princeton in the late 1960s and early 1970s. One ... |
Baum–Welch algorithm : A hidden Markov model describes the joint probability of a collection of "hidden" and observed discrete random variables. It relies on the assumption that the i-th hidden variable given the (i − 1)-th hidden variable is independent of previous hidden variables, and the current observation variabl... |
Baum–Welch algorithm : Suppose we have a chicken from which we collect eggs at noon every day. Now whether or not the chicken has laid eggs for collection depends on some unknown factors that are hidden. We can however (for simplicity) assume that the chicken is always in one of two states that influence whether the ch... |
Baum–Welch algorithm : Accord.NET in C# ghmm C library with Python bindings that supports both discrete and continuous emissions. hmmlearn Python library that implements Baum-Welch on various discrete-time HMMs Jajapy Python library that implements Baum-Welch on various kind of Markov Models ( HMM, MC, MDP, CTMC). Hidd... |
Baum–Welch algorithm : Viterbi algorithm Hidden Markov model EM algorithm Maximum likelihood Speech recognition Bioinformatics Cryptanalysis |
Baum–Welch algorithm : A comprehensive review of HMM methods and software in bioinformatics – Profile Hidden Markov Models Early HMM publications by Baum: A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains An inequality with applications to statistical estimation ... |
Bernoulli scheme : In mathematics, the Bernoulli scheme or Bernoulli shift is a generalization of the Bernoulli process to more than two possible outcomes. Bernoulli schemes appear naturally in symbolic dynamics, and are thus important in the study of dynamical systems. Many important dynamical systems (such as Axiom A... |
Bernoulli scheme : A Bernoulli scheme is a discrete-time stochastic process where each independent random variable may take on one of N distinct possible values, with the outcome i occurring with probability p i , with i = 1, ..., N, and ∑ i = 1 N p i = 1. ^p_=1. The sample space is usually denoted as X = Z ^ as a s... |
Bernoulli scheme : The Hamming distance provides a natural metric on a Bernoulli scheme. Another important metric is the so-called f ¯ metric, defined via a supremum over string matches. Let A = a 1 a 2 ⋯ a m a_\cdots a_ and B = b 1 b 2 ⋯ b n b_\cdots b_ be two strings of symbols. A match is a sequence M of pairs ( i ... |
Bernoulli scheme : Most of the properties of the Bernoulli scheme follow from the countable direct product, rather than from the finite base space. Thus, one may take the base space to be any standard probability space ( Y , B , ν ) ,\nu ) , and define the Bernoulli scheme as ( X , A , μ ) = ( Y , B , ν ) Z ,\mu )=(Y,,... |
Bernoulli scheme : Ya. Sinai demonstrated that the Kolmogorov entropy of a Bernoulli scheme is given by H = − ∑ i = 1 N p i log p i . ^p_\log p_. This may be seen as resulting from the general definition of the entropy of a Cartesian product of probability spaces, which follows from the asymptotic equipartition prope... |
Bernoulli scheme : The Ornstein isomorphism theorem states that two Bernoulli schemes with the same entropy are isomorphic. The result is sharp, in that very similar, non-scheme systems, such as Kolmogorov automorphisms, do not have this property. The Ornstein isomorphism theorem is in fact considerably deeper: it prov... |
Bernoulli scheme : An invertible, measure-preserving transformation of a standard probability space (Lebesgue space) is called a Bernoulli automorphism if it is isomorphic to a Bernoulli shift. |
Bernoulli scheme : A system is termed "loosely Bernoulli" if it is Kakutani-equivalent to a Bernoulli shift; in the case of zero entropy, if it is Kakutani-equivalent to an irrational rotation of a circle. |
Bernoulli scheme : Shift of finite type Markov chain Hidden Bernoulli model == References == |
Burst error : In telecommunications, a burst error or error burst is a contiguous sequence of symbols, received over a communication channel, such that the first and last symbols are in error and there exists no contiguous subsequence of m correctly received symbols within the error burst. The integer parameter m is re... |
Burst error : The Gilbert–Elliott model is a simple channel model introduced by Edgar Gilbert and E. O. Elliott that is widely used for describing burst error patterns in transmission channels and enables simulations of the digital error performance of communications links. It is based on a Markov chain with two states... |
Burst error : Burst error-correcting code |
Burst error : The Gilbert-Elliott Model for Packet Loss in Real Time Services on the Internet at the Wayback Machine (archived 2020-07-29) A Markov-Based Channel Model Algorithm for Wireless Networks at the Wayback Machine (archived 2020-07-27) The two-state model for a fading channel |
Burstiness : In statistics, burstiness is the intermittent increases and decreases in activity or frequency of an event. One measure of burstiness is the Fano factor—a ratio between the variance and mean of counts. Burstiness is observable in natural phenomena, such as natural disasters, or other phenomena, such as net... |
Burstiness : One relatively simple measure of burstiness is burstiness score. The burstiness score of a subset t of time period T relative to an event e is a measure of how often e appears in t compared to its occurrences in T . It is defined by B u r s t ( e , t ) = ( E t E − 1 T ) (e,t)=\left(-\right) Where E ... |
Burstiness : Burst transmission Poisson clumping Time-varying network == References == |
Kruskal count : The Kruskal count (also known as Kruskal's principle, Dynkin–Kruskal count, Dynkin's counting trick, Dynkin's card trick, coupling card trick or shift coupling) is a probabilistic concept originally demonstrated by the Russian mathematician Evgenii Borisovich Dynkin in the 1950s or 1960s discussing coup... |
Kruskal count : The trick is performed with cards, but is more a magical-looking effect than a conventional magic trick. The magician has no access to the cards, which are manipulated by members of the audience. Thus sleight of hand is not possible. Rather the effect is based on the mathematical fact that the output of... |
Kruskal count : Coupling (probability) Discrete logarithm Equifinality Ergodic theory Geometric distribution Overlapping instructions Pollard's kangaroo algorithm Random walk Self-synchronizing code |
Kruskal count : Dynkin [Ды́нкин], Evgenii Borisovich [Евге́ний Бори́сович]; Uspenskii [Успе́нский], Vladimir Andreyevich [Влади́мир Андре́евич] (1963). Written at University of Moscow, Moscow, Russia. Putnam, Alfred L.; Wirszup, Izaak (eds.). Random Walks (Mathematical Conversations Part 3). Survey of Recent East Europ... |
Kruskal count : Humble, Steve "Dr. Maths" (2010). "Dr. Maths Randomness Show". YouTube (Video). Alchemist Cafe, Dublin, Ireland. Retrieved 2023-09-05. [23:40] "Mathematical Card Trick Source". Close-Up Magic. GeniiForum. 2015–2017. Archived from the original on 2023-09-04. Retrieved 2023-09-05. Behr, Denis, ed. (2023).... |
Dependability state model : A dependability state diagram is a method for modelling a system as a Markov chain. It is used in reliability engineering for availability and reliability analysis. It consists of creating a finite-state machine which represent the different states a system may be in. Transitions between sta... |
Dependability state model : A redundant computer system consist of identical two-compute nodes, which each fail with an intensity of λ . When failed, they are repaired one at the time by a single repairman with negative exponential distributed repair times with expectation μ − 1 . state 0: 0 failed units, normal stat... |
Dependability state model : Finite state models of systems are subject to state explosion. To create a realistic model of a system one ends up with a model with so many states that it is infeasible to solve or draw the model. == References == |
Detailed balance : The principle of detailed balance can be used in kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions). It states that at equilibrium, each elementary process is in equilibrium with its reverse process. |
Detailed balance : The principle of detailed balance was explicitly introduced for collisions by Ludwig Boltzmann. In 1872, he proved his H-theorem using this principle. The arguments in favor of this property are founded upon microscopic reversibility. Five years before Boltzmann, James Clerk Maxwell used the principl... |
Detailed balance : The microscopic "reversing of time" turns at the kinetic level into the "reversing of arrows": the elementary processes transform into their reverse processes. For example, the reaction ∑ i α i A i ⟶ ∑ j β j B j \alpha __\sum _\beta __ transforms into ∑ j β j B j ⟶ ∑ i α i A i \beta __\sum _\alpha __... |
Detailed balance : For many systems of physical and chemical kinetics, detailed balance provides sufficient conditions for the strict increase of entropy in isolated systems. For example, the famous Boltzmann H-theorem states that, according to the Boltzmann equation, the principle of detailed balance implies positivit... |
Detailed balance : In chemical kinetics, the elementary reactions are represented by the stoichiometric equations ∑ i α r i A i ⟶ ∑ j β r j A j ( r = 1 , … , m ) , \alpha __\sum _\beta __\;\;(r=1,\ldots ,m)\,, where A i _ are the components and α r i , β r j ≥ 0 ,\beta _\geq 0 are the stoichiometric coefficients. Here,... |
Detailed balance : To describe dynamics of the systems that obey the generalized mass action law, one has to represent the activities as functions of the concentrations cj and temperature. For this purpose, use the representation of the activity through the chemical potential: a i = exp ( μ i − μ i ⊖ R T ) =\exp \lef... |
Detailed balance : Let the principle of detailed balance be valid. Then, for small deviations from equilibrium, the kinetic response of the system can be approximated as linearly related to its deviation from chemical equilibrium, giving the reaction rates for the generalized mass action law as: w r + = w r e q ( 1 + ∑... |
Detailed balance : To formulate the principle of semi-detailed balance, it is convenient to count the direct and inverse elementary reactions separately. In this case, the kinetic equations have the form: d N i d t = V ∑ r γ r i w r = V ∑ r ( β r i − α r i ) w r =V\sum _\gamma _w_=V\sum _(\beta _-\alpha _)w_ Let us use... |
Detailed balance : Let us represent the generalized mass action law in the equivalent form: the rate of the elementary process ∑ i α r i A i ⟶ ∑ i β r i A i \alpha __\sum _\beta __ is w r = φ r exp ( ∑ i α r i μ i R T ) =\varphi _\exp \left(\sum _\mu _\right) where μ i = ∂ F ( T , V , N ) / ∂ N i =\partial F(T,V,N)/\... |
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