Learning.Algorithm.instIsMarkovKernelP0
Instance
No docstring.
Types
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๐ : Type u_1m๐ : MeasurableSpace ๐A measurable space is a space equipped with a ฯ-algebra. -
๐ : Type u_2m๐ : MeasurableSpace ๐ -
๐จ : Type u_3m๐จ : MeasurableSpace ๐จ
Given
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alg : Algorithm ๐ ๐ ๐จA stochastic, sequential algorithm.
Then
ProbabilityTheory.IsMarkovKernel alg.p0MeasurableSpace : Type u_6 โ Type u_6A measurable space is a space equipped with a ฯ-algebra.
Learning.Algorithm : (๐ : Type u_5) โ
(๐ : Type u_6) โ
(๐จ : Type u_7) โ [MeasurableSpace ๐] โ [MeasurableSpace ๐] โ [MeasurableSpace ๐จ] โ Type (max (max u_5 u_6) u_7)A stochastic, sequential algorithm. At each round, it sees an observation in `๐`, then takes an action in `๐`, and finally receives feedback in `๐จ`. The action is a random function of the past rounds and the current observation.Go to its page
ProbabilityTheory.IsMarkovKernel : {ฮฑ : Type u_1} โ
{ฮฒ : Type u_2} โ {mฮฑ : MeasurableSpace ฮฑ} โ {mฮฒ : MeasurableSpace ฮฒ} โ ProbabilityTheory.Kernel ฮฑ ฮฒ โ PropA kernel is a Markov kernel if every measure in its image is a probability measure.
Learning.Algorithm.p0 : {๐ : Type u_1} โ
{๐ : Type u_2} โ
{๐จ : Type u_3} โ
{m๐ : MeasurableSpace ๐} โ
{m๐ : MeasurableSpace ๐} โ {m๐จ : MeasurableSpace ๐จ} โ Learning.Algorithm ๐ ๐ ๐จ โ ProbabilityTheory.Kernel ๐ ๐Distribution of the first action given the first observation: the policy at time `0` applied to the empty history.Go to its page
Code
deriving IsMarkovKernel
Proof
deriving IsMarkovKernel
Meaning last changed in v4.34.0-rc2-76-g565f652 (2026-09-10).
Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file ยท open it in the Lean web editor.
Dependency graph
Audit surface: 5 project declarations, 16 external constants
โ Proved: no sorry anywhere in its closure
This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.