Optimal Variance-Dependent Regret Bounds for Infinite-Horizon MDPs
Online reinforcement learning in infinite-horizon Markov decision processes (MDPs) remains less theoretically and algorithmically developed than its episodic counterpart, with many algorithms suffering from high ``burn-in'' costs and failing to adapt to benign instance-specific complexity. In this work, we address these shortcomings for two infinite-horizon objectives: the classical average-reward regret and the $γ$-regret. We develop a single tractable UCB-style algorithm applicable to both settings, which achieves the first optimal variance-dependent regret guarantees. Our regret bounds in both settings take the form $\tilde{O}( \sqrt{SA\,\text{Var}} + \text{lower-order terms})$, where ...
| Authors | Guy Zamir, Matthew Zurek, Yudong Chen |
|---|---|
| Primary category | cs.LG |
| Published | 25 March 2026 |
| Last updated at source | 25 March 2026 |
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