LeanMachineLearning

Bandits.TS.policyπŸ”—

Definition

The Thompson sampling policy samples an action according to its probability of being optimal under the posterior over environments given the history so far. The posterior under a uniform algorithm is used to avoid a circular definition.

πŸ”—def
Bandits.TS.policy.{u_1} {K : β„•} {𝓔 : Type u_1} [MeasurableSpace 𝓔]
  [StandardBorelSpace 𝓔] [Nonempty 𝓔] (hK : 0 < K)
  (Q : MeasureTheory.Measure 𝓔) [MeasureTheory.IsProbabilityMeasure Q]
  (ΞΊ : ProbabilityTheory.Kernel (𝓔 Γ— Fin K) ℝ)
  [ProbabilityTheory.IsMarkovKernel ΞΊ] (n : β„•) :
  ProbabilityTheory.Kernel (β†₯(Finset.Iic n) β†’ Fin K Γ— ℝ) (Fin K)
Bandits.TS.policy.{u_1} {K : β„•}
  {𝓔 : Type u_1} [MeasurableSpace 𝓔]
  [StandardBorelSpace 𝓔] [Nonempty 𝓔]
  (hK : 0 < K)
  (Q : MeasureTheory.Measure 𝓔)
  [MeasureTheory.IsProbabilityMeasure Q]
  (ΞΊ :
    ProbabilityTheory.Kernel (𝓔 Γ— Fin K)
      ℝ)
  [ProbabilityTheory.IsMarkovKernel ΞΊ]
  (n : β„•) :
  ProbabilityTheory.Kernel
    (β†₯(Finset.Iic n) β†’ Fin K Γ— ℝ) (Fin K)

Code

noncomputable def TS.policy (hK : 0 < K) (Q : Measure 𝓔) [IsProbabilityMeasure Q] (ΞΊ : Kernel (𝓔 Γ— Fin K) ℝ) [IsMarkovKernel ΞΊ] (n : β„•) : Kernel (Iic n β†’ (Fin K) Γ— ℝ) (Fin K) := have : Nonempty (Fin K) := Fin.pos_iff_nonempty.mp hK (IT.bayesTrajMeasurePosterior Q ΞΊ uniformAlgorithm n).map (bestAction ΞΊ id)

Actions: Source Β· Open Issue

Meaning last changed in v4.34.0-rc2-1-g439785b (2026-08-23), the 4th recorded change.

Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file Β· open it in the Lean web editor.

Dependency graph

Audit surface: 17 project declarations, 73 external constants

βœ“ Proved: no sorry anywhere in its closure

This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.