LeanMachineLearning

Bandits.ETC.pullCount_mul๐Ÿ”—

Lemma

At time K * m, the number of pulls of each arm is equal to m.

๐Ÿ”—theorem
Bandits.ETC.pullCount_mul.{u_1} {K : โ„•} {hK : 0 < K} {m : โ„•}
  {ฮฝ : ProbabilityTheory.Kernel (Fin K) โ„}
  [ProbabilityTheory.IsMarkovKernel ฮฝ] {ฮฉ : Type u_1}
  {mฮฉ : MeasurableSpace ฮฉ} {P : MeasureTheory.Measure ฮฉ}
  [MeasureTheory.IsProbabilityMeasure P] {A : โ„• โ†’ ฮฉ โ†’ Fin K}
  {R : โ„• โ†’ ฮฉ โ†’ โ„}
  (h :
    Learning.IsAlgEnvSeq A R (etcAlgorithm hK m)
      (Learning.stationaryEnv ฮฝ) P)
  (a : Fin K) : Learning.pullCount A a (K * m) =แต[P] fun x => m
Bandits.ETC.pullCount_mul.{u_1} {K : โ„•}
  {hK : 0 < K} {m : โ„•}
  {ฮฝ : ProbabilityTheory.Kernel (Fin K) โ„}
  [ProbabilityTheory.IsMarkovKernel ฮฝ]
  {ฮฉ : Type u_1} {mฮฉ : MeasurableSpace ฮฉ}
  {P : MeasureTheory.Measure ฮฉ}
  [MeasureTheory.IsProbabilityMeasure P]
  {A : โ„• โ†’ ฮฉ โ†’ Fin K} {R : โ„• โ†’ ฮฉ โ†’ โ„}
  (h :
    Learning.IsAlgEnvSeq A R
      (etcAlgorithm hK m)
      (Learning.stationaryEnv ฮฝ) P)
  (a : Fin K) :
  Learning.pullCount A a (K * m) =แต[P]
    fun x => m

Code

lemma pullCount_mul (h : IsAlgEnvSeq A R (etcAlgorithm hK m) (stationaryEnv ฮฝ) P) (a : Fin K) :
    pullCount A a (K * m) =แต[P] fun _ โ†ฆ m
Proof
RoundRobin.pullCount_mul m (isAlgEnvSeqUntil_roundRobinAlgorithm h) a

Actions: Source ยท Open Issue

Meaning last changed in v4.34.0-rc2-14-gf86702d (2026-08-25), the 5th recorded change.

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

Dependency graph

Audit surface: 17 project declarations, 110 external constants

โœ“ 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.