Evolving Robustness--Exploration Trade-off in Online Reinforcement Learning via Quantile Bayesian Risk MDPs

• URL: http://arxiv.org/abs/2605.24345v1
• Date: Sat, 23 May 2026 02:12:00 GMT
• Title: Evolving Robustness--Exploration Trade-off in Online Reinforcement Learning via Quantile Bayesian Risk MDPs
• Abstract summary: In online reinforcement learning, data scarcity creates uncertainty that makes robustness important early in learning, whereas sufficient exploration is needed to learn the true-environment optimal policy.<n>We study this time-varying robustness--a trade-off through a quantile Bayesian risk-aware Markov decision process (BR-MDP)<n>We propose an online Bayesian risk-aware algorithm with an adaptive quantile schedule that emphasizes early and gradually encourages exploration of less-visited state-action pairs.
• Score: 8.44570722529746
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In online reinforcement learning, data scarcity creates epistemic uncertainty that makes robustness important early in learning, whereas sufficient exploration is needed to learn the true-environment optimal policy. We study this time-varying robustness--exploration trade-off through a quantile Bayesian risk-aware Markov decision process (BR-MDP), in which the quantile level controls how posterior uncertainty enters the Bellman backup. We characterize this control through an asymptotic normality result for the difference between the quantile BR-MDP value and the value in the true environment. The result implies that upper/lower-tail quantiles induce optimism/pessimism towards epistemic uncertainty, and the magnitude of the optimism/pessimism decreases as data accumulate. Building on this characterization, we propose an online Bayesian risk-aware algorithm with an adaptive quantile schedule that emphasizes robustness early and gradually encourages exploration of less-visited state--action pairs. We establish sublinear Bayesian regret bounds with respect to both the true optimal value and the optimal BR-MDP robust value. Numerical experiments demonstrate strong performance in both exploration-demanding and exploration-costly environments.

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