Skip to content

feat: the rounds, states and state-action pairs of a stationary policy are Markov chains #295

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
RemyDegenne wants to merge 1 commit into
base: main
Choose a base branch
from
+492 −0
Open

feat: the rounds, states and state-action pairs of a stationary policy are Markov chains #295

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
6 changes: 6 additions & 0 deletions LMLExplore/MarkovDecisionProcess/Basic.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -206,6 +206,12 @@ lemma env_feedback_apply (M : MDP 𝓢 𝓐 𝓡) (μ₀ : Measure 𝓢) (n :
(M.env μ₀).feedback n p = M.R (p.1.2, p.2) := by
rw [env_feedback, Kernel.comap_apply]

/-- The reward of round `0` of the environment of `M` has law `M.R` at the state and action. -/
@[simp]
lemma feedbackZero_env (M : MDP 𝓢 𝓐 𝓡) (μ₀ : Measure 𝓢) : (M.env μ₀).feedbackZero = M.R := by
ext p : 1
rw [Environment.feedbackZero_apply, env_feedback_apply]

/-- The environment of an MDP depends measurably on the initial law. -/
lemma measurable_env (M : MDP 𝓢 𝓐 𝓡) : Measurable M.env := by
rw [measurable_environment_iff]
Expand Down
Loading
Loading