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Learning.measurable_pullCount'๐Ÿ”—

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Minimal Lean file

measurable_pullCount'๐Ÿ”—

LemmaLearning.measurable_pullCount'
Details

No docstring.

๐Ÿ”—theorem
Learning.measurable_pullCount'.{u_1, u_2} {๐“ : Type u_1} {R : Type u_2}
  {m๐“ : MeasurableSpace ๐“} {mR : MeasurableSpace R} [DecidableEq ๐“]
  [MeasurableSingletonClass ๐“] (n : โ„•) (a : ๐“) :
  Measurable fun h => pullCount' n h a
Learning.measurable_pullCount'.{u_1, u_2}
  {๐“ : Type u_1} {R : Type u_2}
  {m๐“ : MeasurableSpace ๐“}
  {mR : MeasurableSpace R} [DecidableEq ๐“]
  [MeasurableSingletonClass ๐“] (n : โ„•)
  (a : ๐“) :
  Measurable fun h => pullCount' n h a

Code

lemma measurable_pullCount' [MeasurableSingletonClass ๐“] (n : โ„•) (a : ๐“) :
    Measurable (fun h : Iic n โ†’ ๐“ ร— R โ†ฆ pullCount' n h a)
Type uses (1)
Body uses (1)
Used by (3)

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Proof
by
  simp_rw [pullCount'_eq_sum]
  have h_meas s : Measurable (fun (h : Iic n โ†’ ๐“ ร— R) โ†ฆ if (h s).1 = a then 1 else 0) := by
    refine Measurable.ite ?_ (by fun_prop) (by fun_prop)
    exact (measurableSet_singleton _).preimage (by fun_prop)
  fun_prop

Dependency graph

Type dependencies (1)

pullCount'๐Ÿ”—

DefinitionLearning.pullCount'
Details

Number of pulls of arm a up to (and including) time n. This is the number of entries in h in which the arm is a.

๐Ÿ”—def
Learning.pullCount'.{u_1, u_2} {๐“ : Type u_1} {R : Type u_2}
  [DecidableEq ๐“] (n : โ„•) (h : โ†ฅ(Finset.Iic n) โ†’ ๐“ ร— R) (a : ๐“) : โ„•
Learning.pullCount'.{u_1, u_2}
  {๐“ : Type u_1} {R : Type u_2}
  [DecidableEq ๐“] (n : โ„•)
  (h : โ†ฅ(Finset.Iic n) โ†’ ๐“ ร— R) (a : ๐“) :
  โ„•

Code

noncomputable
def pullCount' (n : โ„•) (h : Iic n โ†’ ๐“ ร— R) (a : ๐“) := #{s | (h s).1 = a}
Used by (29)

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