LeanMachineLearning exposition

Learning.pullCount_add_one🔗

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Minimal Lean file

pullCount_add_one🔗

LemmaLearning.pullCount_add_one
Details

No docstring.

🔗theorem
Learning.pullCount_add_one.{u_1, u_3} {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} {a : 𝓐} {t : ℕ} {ω : Ω} :
  pullCount A a (t + 1) ω =
    pullCount A a t ω + if A t ω = a then 1 else 0
Learning.pullCount_add_one.{u_1, u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} {a : 𝓐}
  {t : ℕ} {ω : Ω} :
  pullCount A a (t + 1) ω =
    pullCount A a t ω +
      if A t ω = a then 1 else 0

Code

lemma pullCount_add_one :
    pullCount A a (t + 1) ω = pullCount A a t ω + if A t ω = a then 1 else 0
Type uses (1)
Body uses (2)
Used by (7)

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Proof
by
  split_ifs with h
  · rw [← h, pullCount_action_eq_pullCount_add_one]
  · rw [pullCount_eq_pullCount_of_action_ne h, add_zero]

Dependency graph

Type dependencies (1)

pullCount🔗

DefinitionLearning.pullCount
Details

Number of times action a was chosen up to time t (excluding t).

🔗def
Learning.pullCount.{u_1, u_3} {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] (A : ℕ → Ω → 𝓐) (a : 𝓐) (t : ℕ) (ω : Ω) : ℕ
Learning.pullCount.{u_1, u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] (A : ℕ → Ω → 𝓐) (a : 𝓐)
  (t : ℕ) (ω : Ω) : ℕ

Code

noncomputable
def pullCount (A : ℕ → Ω → 𝓐) (a : 𝓐) (t : ℕ) (ω : Ω) : ℕ :=
  #(filter (fun s ↦ A s ω = a) (range t))
Used by (146)

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