LeanMachineLearning exposition

Learning.monotone_pullCount๐Ÿ”—

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

monotone_pullCount๐Ÿ”—

LemmaLearning.monotone_pullCount
Details

No docstring.

๐Ÿ”—theorem
Learning.monotone_pullCount.{u_1, u_3} {๐“ : Type u_1} {ฮฉ : Type u_3}
  [DecidableEq ๐“] {A : โ„• โ†’ ฮฉ โ†’ ๐“} (a : ๐“) (ฯ‰ : ฮฉ) :
  Monotone fun x => pullCount A a x ฯ‰
Learning.monotone_pullCount.{u_1, u_3}
  {๐“ : Type u_1} {ฮฉ : Type u_3}
  [DecidableEq ๐“] {A : โ„• โ†’ ฮฉ โ†’ ๐“} (a : ๐“)
  (ฯ‰ : ฮฉ) :
  Monotone fun x => pullCount A a x ฯ‰

Code

lemma monotone_pullCount (a : ๐“) (ฯ‰ : ฮฉ) : Monotone (pullCount A a ยท ฯ‰)
Type uses (1)
Used by (5)

Actions: Source ยท Open Issue

Proof
fun _ _ _ โ†ฆ card_le_card (filter_subset_filter _ (by simpa))

Dependency graph

Type dependencies (1)

pullCount๐Ÿ”—

DefinitionLearning.pullCount
Details

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

๐Ÿ”—def
Learning.pullCount.{u_1, u_3} {๐“ : Type u_1} {ฮฉ : Type u_3}
  [DecidableEq ๐“] (A : โ„• โ†’ ฮฉ โ†’ ๐“) (a : ๐“) (t : โ„•) (ฯ‰ : ฮฉ) : โ„•
Learning.pullCount.{u_1, u_3}
  {๐“ : Type u_1} {ฮฉ : Type u_3}
  [DecidableEq ๐“] (A : โ„• โ†’ ฮฉ โ†’ ๐“) (a : ๐“)
  (t : โ„•) (ฯ‰ : ฮฉ) : โ„•

Code

noncomputable
def pullCount (A : โ„• โ†’ ฮฉ โ†’ ๐“) (a : ๐“) (t : โ„•) (ฯ‰ : ฮฉ) : โ„• :=
  #(filter (fun s โ†ฆ A s ฯ‰ = a) (range t))
Used by (146)

Actions: Source ยท Open Issue