LeanMachineLearning exposition

Learning.exists_pullCount_eq_of_le🔗

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Minimal Lean file

exists_pullCount_eq_of_le🔗

LemmaLearning.exists_pullCount_eq_of_le
Details

No docstring.

🔗theorem
Learning.exists_pullCount_eq_of_le.{u_1, u_3} {𝓐 : Type u_1}
  {Ω : Type u_3} [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} {a : 𝓐} {n t : ℕ}
  {ω : Ω} (hnm : t ≤ pullCount A a (n + 1) ω) (ht : t ≠ 0) :
  ∃ s, pullCount A a (s + 1) ω = t
Learning.exists_pullCount_eq_of_le.{u_1,
    u_3}
  {𝓐 : Type u_1} {Ω : Type u_3}
  [DecidableEq 𝓐] {A : ℕ → Ω → 𝓐} {a : 𝓐}
  {n t : ℕ} {ω : Ω}
  (hnm : t ≤ pullCount A a (n + 1) ω)
  (ht : t ≠ 0) :
  ∃ s, pullCount A a (s + 1) ω = t

Code

lemma exists_pullCount_eq_of_le (hnm : t ≤ pullCount A a (n + 1) ω) (ht : t ≠ 0) :
    ∃ s, pullCount A a (s + 1) ω = t
Type uses (1)
Body uses (1)
Used by (1)

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Proof
by
  by_contra! h_contra
  refine lt_irrefl (pullCount A a (n + 1) ω) ?_
  refine lt_of_lt_of_le ?_ hnm
  exact pullCount_lt_of_forall_ne h_contra ht

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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