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Learning.IsDeterministicAlg๐Ÿ”—

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IsDeterministicAlg๐Ÿ”—

Type ClassLearning.IsDeterministicAlg
Details

An algorithm is deterministic if its initial action and subsequent actions are determined by measurable functions (and not possibly random kernels).

๐Ÿ”—type class
Learning.IsDeterministicAlg.{u_1, u_2} {๐“ : Type u_1} {๐“จ : Type u_2}
  {m๐“ : MeasurableSpace ๐“} {m๐“จ : MeasurableSpace ๐“จ}
  (alg : Algorithm ๐“ ๐“จ) : Prop
Learning.IsDeterministicAlg.{u_1, u_2}
  {๐“ : Type u_1} {๐“จ : Type u_2}
  {m๐“ : MeasurableSpace ๐“}
  {m๐“จ : MeasurableSpace ๐“จ}
  (alg : Algorithm ๐“ ๐“จ) : Prop

Code

class IsDeterministicAlg (alg : Algorithm ๐“ ๐“จ) : Prop where
  exists_action0 : โˆƒ action0, alg.p0 = Measure.dirac action0
  exists_nextAction n : โˆƒ (nextAction : (Iic n โ†’ ๐“ ร— ๐“จ) โ†’ ๐“) (h_meas : Measurable nextAction),
    alg.policy n = Kernel.deterministic nextAction h_meas
Type uses (1)
Used by (14)

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Dependency graph

Type dependencies (1)

Algorithm๐Ÿ”—

StructureLearning.Algorithm
Details

A stochastic, sequential algorithm.

๐Ÿ”—structure
Learning.Algorithm.{u_4, u_5} (๐“ : Type u_4) (๐“จ : Type u_5)
  [MeasurableSpace ๐“] [MeasurableSpace ๐“จ] : Type (max u_4 u_5)
Learning.Algorithm.{u_4, u_5}
  (๐“ : Type u_4) (๐“จ : Type u_5)
  [MeasurableSpace ๐“]
  [MeasurableSpace ๐“จ] : Type (max u_4 u_5)

Code

structure Algorithm (๐“ ๐“จ : Type*) [MeasurableSpace ๐“] [MeasurableSpace ๐“จ] where
  /-- Policy or sampling rule: distribution of the next action. -/
  policy : (n : โ„•) โ†’ Kernel (Iic n โ†’ ๐“ ร— ๐“จ) ๐“
  /-- The policy is a Markov kernel. -/
  [h_policy : โˆ€ n, IsMarkovKernel (policy n)]
  /-- Distribution of the first action. -/
  p0 : Measure ๐“
  /-- The first action distribution is a probability measure. -/
  [hp0 : IsProbabilityMeasure p0]
Used by (216)

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