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Learning.detEnvironmentπŸ”—

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detEnvironmentπŸ”—

DefinitionLearning.detEnvironment
Details

A deterministic environment, where the feedback is given by evaluating fixed measurable functions.

πŸ”—def
Learning.detEnvironment.{u_1, u_2} {𝓐 : Type u_1} {𝓨 : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐} {m𝓨 : MeasurableSpace 𝓨} (f0 : 𝓐 β†’ 𝓨)
  (hf0 : Measurable f0)
  (f : (n : β„•) β†’ (β†₯(Finset.Iic n) β†’ 𝓐 Γ— 𝓨) Γ— 𝓐 β†’ 𝓨)
  (hf : βˆ€ (n : β„•), Measurable (f n)) : Environment 𝓐 𝓨
Learning.detEnvironment.{u_1, u_2}
  {𝓐 : Type u_1} {𝓨 : Type u_2}
  {m𝓐 : MeasurableSpace 𝓐}
  {m𝓨 : MeasurableSpace 𝓨} (f0 : 𝓐 β†’ 𝓨)
  (hf0 : Measurable f0)
  (f :
    (n : β„•) β†’
      (β†₯(Finset.Iic n) β†’ 𝓐 Γ— 𝓨) Γ— 𝓐 β†’ 𝓨)
  (hf : βˆ€ (n : β„•), Measurable (f n)) :
  Environment 𝓐 𝓨

Code

noncomputable def detEnvironment
    (f0 : 𝓐 β†’ 𝓨) (hf0 : Measurable f0)
    (f : (n : β„•) β†’ ((Iic n β†’ 𝓐 Γ— 𝓨) Γ— 𝓐) β†’ 𝓨) (hf : βˆ€ n, Measurable (f n)) :
    Environment 𝓐 𝓨 where
  feedback n := (Kernel.deterministic (f n) (hf n))
  Ξ½0 := Kernel.deterministic f0 hf0
Type uses (1)
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Dependency graph

Type dependencies (1)

EnvironmentπŸ”—

StructureLearning.Environment
Details

A stochastic environment.

πŸ”—structure
Learning.Environment.{u_4, u_5} (𝓐 : Type u_4) (𝓨 : Type u_5)
  [MeasurableSpace 𝓐] [MeasurableSpace 𝓨] : Type (max u_4 u_5)
Learning.Environment.{u_4, u_5}
  (𝓐 : Type u_4) (𝓨 : Type u_5)
  [MeasurableSpace 𝓐]
  [MeasurableSpace 𝓨] : Type (max u_4 u_5)

Code

structure Environment (𝓐 𝓨 : Type*) [MeasurableSpace 𝓐] [MeasurableSpace 𝓨] where
  /-- Distribution of the next observation as function of the past history. -/
  feedback : (n : β„•) β†’ Kernel ((Iic n β†’ 𝓐 Γ— 𝓨) Γ— 𝓐) 𝓨
  /-- The feedback kernels are Markov kernels. -/
  [h_feedback : βˆ€ n, IsMarkovKernel (feedback n)]
  /-- Distribution of the first observation given the first action. -/
  Ξ½0 : Kernel 𝓐 𝓨
  /-- The initial observation kernel is a Markov kernel. -/
  [hp0 : IsMarkovKernel Ξ½0]
Used by (128)

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