`Learning.sum_pullCount`🔗

This page has the declaration's own card below, then its dependency graph, then a card for each dependency (type dependencies first, then the rest of the transitive closure). For a theorem, the graph and the dependency cards only follow its statement's dependencies (its proof is replaced by sorry, so what it proves doesn't depend on how); for everything else, both the type and the body/value are followed, since their content is part of what later declarations build on.

Minimal Lean file

`sum_pullCount`🔗

LemmaLearning.sum_pullCount

Details

No docstring.

theorem

Learning.sum_pullCount.{u_1, u_3} {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} {t : ℕ} [Fintype 𝓐] {ω : Ω} :
  ∑ a, pullCount A a t ω = t
Learning.sum_pullCount.{u_1, u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} {t : ℕ}
  [Fintype 𝓐] {ω : Ω} :
  ∑ a, pullCount A a t ω = t

Code

lemma sum_pullCount [Fintype 𝓐] {ω : Ω} : ∑ a, pullCount A a t ω = t

Type uses (1)

pullCount

Body uses (1)

sum_pullCount_mul

Used by (1)

sum_ucb_sub_mean_le

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Proof

by
  suffices ∑ a, pullCount A a t ω * (1 : ℝ) = t by norm_cast at this; simpa
  rw [sum_pullCount_mul]
  simp

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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Learning.sum_pullCount🔗

sum_pullCount🔗

pullCount🔗

`Learning.sum_pullCount`🔗

`sum_pullCount`🔗

`pullCount`🔗