Learning.instIsMarkovKernelProdHistFeedback
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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env : Environment ๐ ๐ ๐จA stochastic environment. -
n : โ
Then
ProbabilityTheory.IsMarkovKernel (env.feedback n)MeasurableSpace : Type u_6 โ Type u_6A measurable space is a space equipped with a ฯ-algebra.
Learning.Environment : (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 environment. At each round, an observation is drawn prior to the algorithm taking an action. Then the environment provides feedback based on the observation and the action.Go to its page
Nat : TypeThe natural numbers, starting at zero. This type is special-cased by both the kernel and the compiler, and overridden with an efficient implementation. Both use a fast arbitrary-precision arithmetic library (usually [GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.
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.
Code
instance (env : Environment ๐ ๐ ๐จ) (n : โ) : IsMarkovKernel (env.feedback n)
Proof
env.isMarkovKernel_feedback n
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: 3 project declarations, 8 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.