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Learning.IsBayesAlgEnvSeq.regret🔗

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Minimal Lean file

regret🔗

DefinitionLearning.IsBayesAlgEnvSeq.regret
Details

A random variable that gives the regret at time n.

🔗def
Learning.IsBayesAlgEnvSeq.regret.{u_1, u_2, u_4} {𝓔 : Type u_1}
  {𝓐 : Type u_2} {Ω : Type u_4} [MeasurableSpace 𝓔] [MeasurableSpace 𝓐]
  (κ : ProbabilityTheory.Kernel (𝓔 × 𝓐) ℝ) (E : Ω → 𝓔) (A : ℕ → Ω → 𝓐)
  (n : ℕ) (ω : Ω) : ℝ
Learning.IsBayesAlgEnvSeq.regret.{u_1,
    u_2, u_4}
  {𝓔 : Type u_1} {𝓐 : Type u_2}
  {Ω : Type u_4} [MeasurableSpace 𝓔]
  [MeasurableSpace 𝓐]
  (κ : ProbabilityTheory.Kernel (𝓔 × 𝓐) ℝ)
  (E : Ω → 𝓔) (A : ℕ → Ω → 𝓐) (n : ℕ)
  (ω : Ω) : ℝ

Code

noncomputable
def regret (κ : Kernel (𝓔 × 𝓐) ℝ) (E : Ω → 𝓔) (A : ℕ → Ω → 𝓐) (n : ℕ) (ω : Ω) : ℝ :=
  Bandits.regret (κ.sectR (E ω)) A n ω
Body uses (1)
Used by (6)

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Dependency graph

All dependencies, transitively (1)

regret🔗

DefinitionBandits.regret
Details

Regret of a sequence of pulls k : ℕ → 𝓐 at time t for the reward kernel ν ; Kernel 𝓐 ℝ.

🔗def
Bandits.regret.{u_1, u_2} {𝓐 : Type u_1} {Ω : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐} (ν : ProbabilityTheory.Kernel 𝓐 ℝ)
  (A : ℕ → Ω → 𝓐) (t : ℕ) (ω : Ω) : ℝ
Bandits.regret.{u_1, u_2} {𝓐 : Type u_1}
  {Ω : Type u_2} {m𝓐 : MeasurableSpace 𝓐}
  (ν : ProbabilityTheory.Kernel 𝓐 ℝ)
  (A : ℕ → Ω → 𝓐) (t : ℕ) (ω : Ω) : ℝ

Code

noncomputable
def regret (ν : Kernel 𝓐 ℝ) (A : ℕ → Ω → 𝓐) (t : ℕ) (ω : Ω) : ℝ :=
  t * (⨆ a, (ν a)[id]) - ∑ s ∈ range t, (ν (A s ω))[id]
Used by (11)

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