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Remove last sorry in UCB file #48

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Merged
RemyDegenne merged 2 commits into from
Dec 29, 2025
Merged

Remove last sorry in UCB file #48

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1f79b72
remove sorry in UCB file
RemyDegenne Dec 29, 2025
7a384ff
Merge remote-tracking branch 'origin/main' into work
RemyDegenne Dec 29, 2025
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21 changes: 19 additions & 2 deletions LeanBandits/BanditAlgorithms/UCB.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -468,8 +468,25 @@ lemma pullCount_le_add (a : Fin K) (n C : ℕ) (ω : ℕ → Fin K × ℝ) :
rw [Finset.sum_add_distrib]
_ ≤ C + 1 + ∑ s ∈ range n, {s | arm s ω = a ∧ C < pullCount a s ω}.indicator 1 s := by
gcongr
simp_rw [pullCount_eq_sum]
sorry
have h_le n : ∑ s ∈ range n, {s | arm s ω = a ∧ pullCount a s ω ≤ C}.indicator 1 s ≤
pullCount a n ω := by
rw [pullCount_eq_sum]
gcongr with s hs
simp only [Set.indicator_apply, Set.mem_setOf_eq, Pi.one_apply]
grind
induction n with
| zero => simp
| succ n hn =>
rw [Finset.sum_range_succ]
rcases le_or_gt (pullCount a n ω) C with h_pc | h_pc
· have hn' : ∑ s ∈ range n, {s | arm s ω = a ∧ pullCount a s ω ≤ C}.indicator 1 s ≤ C :=
(h_le n).trans h_pc
grw [hn']
gcongr
simp only [Set.indicator_apply, Set.mem_setOf_eq, Pi.one_apply]
grind
· refine le_trans ?_ hn
simp [h_pc]

omit [IsMarkovKernel ν] in
lemma pullCount_le_add_three [Nonempty (Fin K)] (a : Fin K) (n C : ℕ) (ω : ℕ → Fin K × ℝ) :
Expand Down