| import Mathlib |
| import OAI.Probability.LogConcave.OraclePrograms.RoutineKind |
| import OAI.Probability.LogConcave.Numerics.CompileDeclaredRootShift |
| import OAI.Probability.LogConcave.OraclePrograms.TerminalMeanProgram |
| import OAI.Probability.LogConcave.Sampling.SampleCorrelation |
|
|
| namespace OAI |
|
|
| section |
| noncomputable section |
| namespace LogConcaveSampling.OracleCompiler |
| open MeanTree Quadrature |
| open scoped Classical |
|
|
| structure CircuitParameters where |
| n : ℕ |
| m : ℕ |
| N : ℕ |
| nc : ℕ |
| Nc : ℕ |
| T : ℝ |
| h : ℝ |
| ψ : ℝ |
| v : ℝ |
| D : ℝ |
| A : ℝ |
| Af : ℝ |
| T_lower : 1/2≤T |
| T_upper : T<1 |
| h_pos : 0<h |
| v_nonneg : 0≤v |
| angle_bound : ∀j : Fin (m+1),|ψ*angleNodes m j|≤v |
| angle_small : v^2≤Real.sqrt (1-T^2) |
|
|
| namespace CircuitParameters |
| variable (C : CircuitParameters) {d : ℕ} |
|
|
| def meanEndpoint : ProbabilityNode C.T C.h (C.n+1) := |
| probabilityEndpoint (by linarith [C.T_lower]) C.T_upper C.h_pos (C.n+1) |
|
|
| def meanTree (r σ : ℝ) : MeanTree (MeanInput d) d := |
| literalMean r C.T C.h C.ψ σ C.n C.m C.N C.nc C.Nc C.meanEndpoint |
|
|
| def meanDrift (r σ : ℝ) (hr : 0<r) : DriftData (C.meanTree (d:=d) r σ) := |
| (literalMean_drift hr C.T_lower C.T_upper C.h_pos C.v_nonneg C.angle_small C.angle_bound C.meanEndpoint).choose |
|
|
| lemma meanDrift_spec (r σ : ℝ) (hr : 0<r) : |
| DriftValid (meanInputMove r C.T) (C.meanTree (d:=d) r σ) (C.meanDrift r σ hr) ∧ |
| (C.meanDrift (d:=d) r σ hr).root _=0 ∧ DriftBound 3 _ (C.meanDrift (d:=d) r σ hr) := |
| (literalMean_drift hr C.T_lower C.T_upper C.h_pos C.v_nonneg C.angle_small C.angle_bound C.meanEndpoint).choose_spec |
|
|
| def sampleEndpoint (η : ℝ) (hη : 0<η) (hη1 : η≤1) : |
| ProbabilityNode (sampleCorrelation η) C.h (C.n+1) := |
| probabilityEndpoint (by linarith [(sampleCorrelation_properties hη hη1).1]) |
| (sampleCorrelation_properties hη hη1).2.1 C.h_pos (C.n+1) |
|
|
| def sampleTree (r η : ℝ) (hη : 0<η) (hη1 : η≤1) : MeanTree (SampleInput d) d := |
| literalSample r (sampleCorrelation η) C.h (C.n+1) C.N (C.sampleEndpoint η hη hη1) |
|
|
| def sampleDrift (r η : ℝ) (hr : 0<r) (hη : 0<η) (hη1 : η≤1) : |
| DriftData (C.sampleTree (d:=d) r η hη hη1) := |
| (literalSample_drift hr (Nat.succ_pos C.n) |
| (by linarith [(sampleCorrelation_properties hη hη1).1]) |
| (sampleCorrelation_properties hη hη1).2.1 C.h_pos (C.sampleEndpoint η hη hη1)).choose |
|
|
| def meanCenterBudget (r σ : ℝ) : ℝ := C.A*(r/σ+r^2) |
| def sampleCenterBudget (r : ℝ) : ℝ := C.A*r^2 |
| def sampleFinalBudget (r : ℝ) : ℝ := C.Af*r |
|
|
| def meanFrom (Mf Mi : ℝ → ℝ → SeedProgram d) (S : ℝ → ℝ → ReservedProgram d) |
| (r σ : ℝ) : SeedProgram d := |
| if hr : 0<r then |
| let E := C.meanTree r σ |
| let p := C.meanDrift r σ hr |
| let noise := Real.sqrt 3*σ/2 |
| let B := compileDeclaredRoot C.D (C.meanCenterBudget r σ) C.Af Mf Mi E noise |
| let v := compileDeclaredRootShift C.D (C.meanCenterBudget r σ) C.Af Mf Mi E noise p |
| let R := Real.sqrt (1-C.T^2) |
| let anchor := S r (R/C.T) |
| meanParent anchor.full B (anchor.extraShift (-2*R/C.T)) v C.T |
| else terminalMeanProgram d r σ |
|
|
| def sampleFrom (Mf Mi : ℝ → ℝ → SeedProgram d) (r η : ℝ) : ReservedProgram d := |
| if hv : 0<r ∧ 0<η ∧ η≤1 then |
| let E := C.sampleTree r η hv.2.1 hv.2.2 |
| let p := C.sampleDrift r η hv.1 hv.2.1 hv.2.2 |
| let noise := η/Real.sqrt 2 |
| let B := compileDeclaredRoot C.D (C.sampleCenterBudget r) (C.sampleFinalBudget r) Mf Mi E noise |
| let v := compileDeclaredRootShift C.D (C.sampleCenterBudget r) (C.sampleFinalBudget r) Mf Mi E noise p |
| sampleParent B v (sampleCorrelation η) η |
| else terminalReservedProgram d r η |
| end CircuitParameters |
|
|
| def RoutineValue (d : ℕ) : RoutineKind → Type |
| | .mean => ℝ → ℝ → SeedProgram d |
| | .sample => ℝ → ℝ → ReservedProgram d |
|
|
| def constructRoutine (d : ℕ) (C : CircuitParameters) {t : ℝ} (ht : 0<t) (hs : t≤1/44) |
| (L : RoutineLabel) : RoutineValue d L.kind := |
| if _ : L.terminal then |
| match L.kind with |
| | .mean => terminalMeanProgram d |
| | .sample => terminalReservedProgram d |
| else |
| match hk : L.kind with |
| | .mean => C.meanFrom |
| (constructRoutine d C ht hs ⟨.mean,L.b+t,L.p⟩) |
| (constructRoutine d C ht hs ⟨.mean,L.b-10*t,L.p-1/4⟩) |
| (constructRoutine d C ht hs ⟨.sample,L.b-10*t,L.p-1/4⟩) |
| | .sample => C.sampleFrom |
| (constructRoutine d C ht hs ⟨.mean,L.b,L.p⟩) |
| (constructRoutine d C ht hs ⟨.mean,L.b-10*t,L.p-1/4⟩) |
| termination_by L.rank t |
| decreasing_by |
| all_goals apply RoutineStep.rank_lt ht hs (by assumption) |
| · simpa only [←hk] using (RoutineStep.meanFinal (t:=t) L.b L.p) |
| · simpa only [←hk] using (RoutineStep.internal (t:=t) RoutineKind.mean RoutineKind.mean L.b L.p) |
| · simpa only [←hk] using (RoutineStep.internal (t:=t) RoutineKind.mean RoutineKind.sample L.b L.p) |
| · simpa only [←hk] using (RoutineStep.sampleFinal (t:=t) L.b L.p) |
| · simpa only [←hk] using (RoutineStep.internal (t:=t) RoutineKind.sample RoutineKind.mean L.b L.p) |
| end LogConcaveSampling.OracleCompiler |
|
|
| end |
|
|
| end |
|
|
| end OAI |
|
|
