Continuity-Free Near-Minimax Leading-Order Regret for CVaR-UCBVI
For finite-horizon tabular CVaR reinforcement learning, prior work proves a $\widetilde{O}(τ^{-1}\sqrt{SAK})$ leading regret bound for arbitrary normalized return laws and the sharper $\widetilde{O}(\sqrt{SAK/τ})$ rate under a density lower bound. We show that the same Bernstein CVaR-UCBVI algorithm attains the sharper rate without continuity assumptions. The key is a selected-budget self-bound: the conditional variance of the episode shortfall is at most $τ$ plus the value-estimation width. Substitution into the original Bernstein decomposition yields, with high probability, $\widetilde{O}(\sqrt{SAK/τ}+(SAHK^{1/4}+S^2AH)/τ)$ regret for arbitrary normalized return laws, including atomic, ...
| Authors | Yuanlong Chen |
|---|---|
| Primary category | cs.LG |
| Published | 29 August 2026 |
| Last updated at source | 29 August 2026 |
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