LeanMachineLearning exposition

Bandits.gap_nonneg🔗

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Minimal Lean file

gap_nonneg🔗

LemmaBandits.gap_nonneg
Details

No docstring.

🔗theorem
Bandits.gap_nonneg.{u_1} {𝓐 : Type u_1} {m𝓐 : MeasurableSpace 𝓐}
  {ν : ProbabilityTheory.Kernel 𝓐 ℝ} {a : 𝓐} [Finite 𝓐] : 0 ≤ gap ν a
Bandits.gap_nonneg.{u_1} {𝓐 : Type u_1}
  {m𝓐 : MeasurableSpace 𝓐}
  {ν : ProbabilityTheory.Kernel 𝓐 ℝ}
  {a : 𝓐} [Finite 𝓐] : 0 ≤ gap ν a

Code

lemma gap_nonneg [Finite 𝓐] : 0 ≤ gap ν a
Type uses (1)
Used by (5)

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Proof
by
  rw [gap, sub_nonneg]
  exact le_ciSup (f := fun i ↦ (ν i)[id]) (by simp) a

Dependency graph

Type dependencies (1)

gap🔗

DefinitionBandits.gap
Details

Gap of an action a: difference between the highest mean of the actions and the mean of a.

🔗def
Bandits.gap.{u_1} {𝓐 : Type u_1} {m𝓐 : MeasurableSpace 𝓐}
  (ν : ProbabilityTheory.Kernel 𝓐 ℝ) (a : 𝓐) : ℝ
Bandits.gap.{u_1} {𝓐 : Type u_1}
  {m𝓐 : MeasurableSpace 𝓐}
  (ν : ProbabilityTheory.Kernel 𝓐 ℝ)
  (a : 𝓐) : ℝ

Code

noncomputable
def gap (ν : Kernel 𝓐 ℝ) (a : 𝓐) : ℝ := (⨆ i, (ν i)[id]) - (ν a)[id]
Used by (27)

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