LeanMachineLearning

Learning.IsAlgEnvSeqπŸ”—

Structure

An algorithm-environment sequence: a sequence of actions and feedbacks generated by an algorithm interacting with an environment.

πŸ”—structure
Learning.IsAlgEnvSeq.{u_1, u_2, u_3} {𝓐 : Type u_1} {𝓨 : Type u_2}
  {Ξ© : Type u_3} {m𝓐 : MeasurableSpace 𝓐} {m𝓨 : MeasurableSpace 𝓨}
  {mΞ© : MeasurableSpace Ξ©} (A : β„• β†’ Ξ© β†’ 𝓐) (Y : β„• β†’ Ξ© β†’ 𝓨)
  (alg : Algorithm 𝓐 𝓨) (env : Environment 𝓐 𝓨)
  (P : MeasureTheory.Measure Ξ©) [MeasureTheory.IsFiniteMeasure P] : Prop
Learning.IsAlgEnvSeq.{u_1, u_2, u_3}
  {𝓐 : Type u_1} {𝓨 : Type u_2}
  {Ξ© : Type u_3} {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨}
  {mΞ© : MeasurableSpace Ξ©} (A : β„• β†’ Ξ© β†’ 𝓐)
  (Y : β„• β†’ Ξ© β†’ 𝓨) (alg : Algorithm 𝓐 𝓨)
  (env : Environment 𝓐 𝓨)
  (P : MeasureTheory.Measure Ξ©)
  [MeasureTheory.IsFiniteMeasure P] : Prop

Code

structure IsAlgEnvSeq (A : β„• β†’ Ξ© β†’ 𝓐) (Y : β„• β†’ Ξ© β†’ 𝓨) (alg : Algorithm 𝓐 𝓨) (env : Environment 𝓐 𝓨) (P : Measure Ξ©) [IsFiniteMeasure P] : Prop where /-- The action sequence is measurable. -/ measurable_action n : Measurable (A n) := by fun_prop /-- The feedback sequence is measurable. -/ measurable_feedback n : Measurable (Y n) := by fun_prop /-- The first action has the correct law. -/ hasLaw_action_zero : HasLaw (fun Ο‰ ↦ (A 0 Ο‰)) alg.p0 P /-- The first feedback has the correct conditional distribution. -/ hasCondDistrib_feedback_zero : HasCondDistrib (Y 0) (A 0) env.Ξ½0 P /-- The next action has the correct conditional distribution given the history. -/ hasCondDistrib_action n : HasCondDistrib (A (n + 1)) (history A Y n) (alg.policy n) P /-- The next feedback has the correct conditional distribution given the history and next action. -/ hasCondDistrib_feedback n : HasCondDistrib (Y (n + 1)) (fun Ο‰ ↦ (history A Y n Ο‰, A (n + 1) Ο‰)) (env.feedback n) 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: 3 project declarations, 39 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.