Non-Asymptotic Gap-Dependent Regret Bounds for Tabular MDPs
This work provides improved theoretical guarantees for reinforcement learning algorithms in tabular MDPs, addressing a specific bottleneck in regret analysis.
The paper tackles the problem of achieving gap-dependent and non-asymptotic logarithmic regret bounds for episodic Markov Decision Processes (MDPs) using optimistic algorithms, resulting in bounds that avoid dependencies on diameter-like quantities and smoothly interpolate between logarithmic and minimax rates.
This paper establishes that optimistic algorithms attain gap-dependent and non-asymptotic logarithmic regret for episodic MDPs. In contrast to prior work, our bounds do not suffer a dependence on diameter-like quantities or ergodicity, and smoothly interpolate between the gap dependent logarithmic-regret, and the $\widetilde{\mathcal{O}}(\sqrt{HSAT})$-minimax rate. The key technique in our analysis is a novel "clipped" regret decomposition which applies to a broad family of recent optimistic algorithms for episodic MDPs.