The Uniform algorithm

An algorithm that chooses actions uniformly at random in every situation.

Main definitions

• uniformAlgorithm: a uniform algorithm with actions in a finite non-empty type 𝓐.

Main results

• absolutelyContinuous_uniformAlgorithm: every algorithm with actions in 𝓐 is absolutely continuous with respect to the uniform algorithm with the same type of feedback.

noncomputable def Learning.uniformAlgorithm {𝓐 : Type u_1} {𝓨 : Type u_2} {m𝓐 : MeasurableSpace 𝓐} {m𝓨 : MeasurableSpace 𝓨} [Finite 𝓐] [Nonempty 𝓐] : Algorithm 𝓐 𝓨

The Uniform algorithm: actions are chosen uniformly at random.

Equations

• Learning.uniformAlgorithm = Learning.randomSampling (ProbabilityTheory.uniformOn Set.univ)

theorem Learning.absolutelyContinuous_uniformAlgorithm {𝓐 : Type u_1} {𝓨 : Type u_2} {m𝓐 : MeasurableSpace 𝓐} {m𝓨 : MeasurableSpace 𝓨} [Finite 𝓐] [Nonempty 𝓐] {alg : Algorithm 𝓐 𝓨} : alg.AbsolutelyContinuous uniformAlgorithm