LeanMachineLearning exposition

Learning.IT.fst_comp_step๐Ÿ”—

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Minimal Lean file

fst_comp_step๐Ÿ”—

LemmaLearning.IT.fst_comp_step
Details

No docstring.

๐Ÿ”—theorem
Learning.IT.fst_comp_step.{u_1, u_2} {๐“ : Type u_1} {๐“จ : Type u_2}
  (n : โ„•) : Prod.fst โˆ˜ step n = action n
Learning.IT.fst_comp_step.{u_1, u_2}
  {๐“ : Type u_1} {๐“จ : Type u_2} (n : โ„•) :
  Prod.fst โˆ˜ step n = action n

Code

lemma fst_comp_step (n : โ„•) : Prod.fst โˆ˜ step (๐“
Type uses (2)
Used by (2)

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Proof
๐“) (๐“จ := ๐“จ) n = action n := rfl

Dependency graph

Type dependencies (2)

step๐Ÿ”—

DefinitionLearning.IT.step
Details

Action and feedback at step n.

๐Ÿ”—def
Learning.IT.step.{u_1, u_2} {๐“ : Type u_1} {๐“จ : Type u_2} (n : โ„•)
  (h : โ„• โ†’ ๐“ ร— ๐“จ) : ๐“ ร— ๐“จ
Learning.IT.step.{u_1, u_2} {๐“ : Type u_1}
  {๐“จ : Type u_2} (n : โ„•) (h : โ„• โ†’ ๐“ ร— ๐“จ) :
  ๐“ ร— ๐“จ

Code

def step (n : โ„•) (h : โ„• โ†’ ๐“ ร— ๐“จ) : ๐“ ร— ๐“จ := h n
Used by (13)

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action๐Ÿ”—

DefinitionLearning.IT.action
Details

action n is the action pulled at time n. This is a random variable on the measurable space โ„• โ†’ ๐“ ร— ๐“จ.

๐Ÿ”—def
Learning.IT.action.{u_1, u_2} {๐“ : Type u_1} {๐“จ : Type u_2} (n : โ„•)
  (h : โ„• โ†’ ๐“ ร— ๐“จ) : ๐“
Learning.IT.action.{u_1, u_2}
  {๐“ : Type u_1} {๐“จ : Type u_2} (n : โ„•)
  (h : โ„• โ†’ ๐“ ร— ๐“จ) : ๐“

Code

def action (n : โ„•) (h : โ„• โ†’ ๐“ ร— ๐“จ) : ๐“ := (h n).1
Used by (31)

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