LeanMachineLearning

Learning.IsBayesAlgEnvSeqπŸ”—

Structure

IsBayesAlgEnvSeq Q ΞΊ alg E A Y P states that there is a measure P : Measure Ξ© such that the parameter E : Ξ© β†’ 𝓔 has law Q and that the sequences of actions A : β„• β†’ Ξ© β†’ 𝓐 and feedbacks Y : β„• β†’ Ξ© β†’ 𝓨 are generated by the algorithm alg : Algorithm 𝓐 𝓨 interacting with an underlying environment that depends on E and ΞΊ (stationaryEnv (ΞΊ.sectR (E Ο‰))).

πŸ”—structure
Learning.IsBayesAlgEnvSeq.{u_1, u_2, u_3, u_4} {𝓔 : Type u_1}
  {𝓐 : Type u_2} {𝓨 : Type u_3} {Ξ© : Type u_4} [MeasurableSpace 𝓔]
  [MeasurableSpace 𝓐] [MeasurableSpace 𝓨] [MeasurableSpace Ξ©]
  (Q : MeasureTheory.Measure 𝓔) (ΞΊ : ProbabilityTheory.Kernel (𝓔 Γ— 𝓐) 𝓨)
  (alg : Algorithm 𝓐 𝓨) (E : Ξ© β†’ 𝓔) (A : β„• β†’ Ξ© β†’ 𝓐) (Y : β„• β†’ Ξ© β†’ 𝓨)
  (P : MeasureTheory.Measure Ξ©) [MeasureTheory.IsFiniteMeasure P] : Prop
Learning.IsBayesAlgEnvSeq.{u_1, u_2, u_3,
    u_4}
  {𝓔 : Type u_1} {𝓐 : Type u_2}
  {𝓨 : Type u_3} {Ξ© : Type u_4}
  [MeasurableSpace 𝓔] [MeasurableSpace 𝓐]
  [MeasurableSpace 𝓨] [MeasurableSpace Ξ©]
  (Q : MeasureTheory.Measure 𝓔)
  (ΞΊ : ProbabilityTheory.Kernel (𝓔 Γ— 𝓐) 𝓨)
  (alg : Algorithm 𝓐 𝓨) (E : Ξ© β†’ 𝓔)
  (A : β„• β†’ Ξ© β†’ 𝓐) (Y : β„• β†’ Ξ© β†’ 𝓨)
  (P : MeasureTheory.Measure Ξ©)
  [MeasureTheory.IsFiniteMeasure P] : Prop

Code

structure IsBayesAlgEnvSeq (Q : Measure 𝓔) (ΞΊ : Kernel (𝓔 Γ— 𝓐) 𝓨) (alg : Algorithm 𝓐 𝓨) (E : Ξ© β†’ 𝓔) (A : β„• β†’ Ξ© β†’ 𝓐) (Y : β„• β†’ Ξ© β†’ 𝓨) (P : Measure Ξ©) [IsFiniteMeasure P] : Prop where measurable_param : Measurable E := by fun_prop measurable_action n : Measurable (A n) := by fun_prop measurable_feedback n : Measurable (Y n) := by fun_prop hasLaw_env : HasLaw E Q P hasCondDistrib_action_zero : HasCondDistrib (A 0) E (Kernel.const _ alg.p0) P hasCondDistrib_feedback_zero : HasCondDistrib (Y 0) (fun Ο‰ ↦ (E Ο‰, A 0 Ο‰)) ΞΊ P hasCondDistrib_action n : HasCondDistrib (A (n + 1)) (fun Ο‰ ↦ (E Ο‰, history A Y n Ο‰)) ((alg.policy n).prodMkLeft _) P hasCondDistrib_feedback n : HasCondDistrib (Y (n + 1)) (fun Ο‰ ↦ (history A Y n Ο‰, E Ο‰, A (n + 1) Ο‰)) (ΞΊ.prodMkLeft _) P

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: 2 project declarations, 41 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.