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Learning.pullCount'_eq_sum๐Ÿ”—

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pullCount'_eq_sum๐Ÿ”—

LemmaLearning.pullCount'_eq_sum
Details

No docstring.

๐Ÿ”—theorem
Learning.pullCount'_eq_sum.{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“) :
  pullCount' n h a = โˆ‘ s, if Prod.fst (h s) = a then 1 else 0
Learning.pullCount'_eq_sum.{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“) :
  pullCount' n h a =
    โˆ‘ s,
      if Prod.fst (h s) = a then 1 else 0

Code

lemma pullCount'_eq_sum (n : โ„•) (h : Iic n โ†’ ๐“ ร— R) (a : ๐“) :
    pullCount' n h a = โˆ‘ s : Iic n, if (h s).1 = a then 1 else 0
Type uses (1)
Used by (3)

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Proof
by simp [pullCount']

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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