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arXiv · 2610.28157

Worst-Case Bayesian CVaR Regret Bounds for Episodic Markov Decision Processes

Raghav Bongole·Amirreza Zamani·Tobias J. Oechtering·Mikael Skoglund
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Abstract

We study the worst-case, over priors, Bayesian conditional value-at-risk (CVaR) of cumulative pseudo-regret in time-homogeneous finite-horizon episodic Markov decision processes. A high-probability guarantee for UCBVI-BF yields a prior-predictive upper bound. A lower bound follows by a three-state MDP and applying a reverse-KL inequality. For a constant number of states, the bounds have the same polynomial dependence on horizon, actions, and episodes, with a logarithmic gap in the risk level.

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Raghav Bongole, Amirreza Zamani, Tobias J. Oechtering, Mikael Skoglund. 2026-10-20. Worst-Case Bayesian CVaR Regret Bounds for Episodic Markov Decision Processes. https://arxiv.org/abs/2610.28157

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