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Fix (?) condDistrib lemmas #18

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Merged
RemyDegenne merged 1 commit into from
Sep 4, 2025
Merged

Fix (?) condDistrib lemmas #18

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20 changes: 10 additions & 10 deletions LeanBandits/Bandit.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -122,22 +122,22 @@ def ℱ (α : Type*) [MeasurableSpace α] :
Filtration ℕ (inferInstance : MeasurableSpace (ℕ → α × R)) :=
MeasureTheory.Filtration.piLE (X := fun _ ↦ α × R)

lemma condDistrib_arm_reward [StandardBorelSpace α] [Nonempty α]
[StandardBorelSpace R] [Nonempty R] (alg : Algorithm α R) (ν : Kernel α R) [IsMarkovKernel ν]
(n : ℕ) :
condDistrib (fun h ↦ (arm n h, reward n h)) (hist n) (Bandit.trajMeasure alg ν)
= Bandit.stepKernel alg ν n := by
lemma condDistrib_arm_reward [StandardBorelSpace α] [Nonempty α] [StandardBorelSpace R] [Nonempty R]
(alg : Algorithm α R) (ν : Kernel α R) [IsMarkovKernel ν] (n : ℕ) :
condDistrib (fun h ↦ (arm (n + 1) h, reward (n + 1) h)) (hist n) (Bandit.trajMeasure alg ν)
=ᵐ[(Bandit.trajMeasure alg ν).map (hist n)] Bandit.stepKernel alg ν n := by
sorry

lemma condDistrib_reward [StandardBorelSpace R] [Nonempty R] (alg : Algorithm α R)
(ν : Kernel α R) [IsMarkovKernel ν] (n : ℕ) :
condDistrib (reward n) (arm n) (Bandit.trajMeasure alg ν) = ν := by
lemma condDistrib_reward [StandardBorelSpace R] [Nonempty R] (alg : Algorithm α R) (ν : Kernel α R)
[IsMarkovKernel ν] (n : ℕ) :
condDistrib (reward n) (arm n) (Bandit.trajMeasure alg ν)
=ᵐ[(Bandit.trajMeasure alg ν).map (arm n)] ν := by
sorry

lemma condDistrib_arm [StandardBorelSpace α] [Nonempty α] [StandardBorelSpace R] [Nonempty R]
(alg : Algorithm α R) (ν : Kernel α R) [IsMarkovKernel ν] (n : ℕ) :
condDistrib (arm n) (hist n) (Bandit.trajMeasure alg ν) = alg.policy n := by
rw [← Bandit.fst_stepKernel alg ν n, ← condDistrib_arm_reward alg ν n]
condDistrib (arm (n + 1)) (hist n) (Bandit.trajMeasure alg ν)
=ᵐ[(Bandit.trajMeasure alg ν).map (hist n)] alg.policy n := by
sorry

end MeasureSpace
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