Non-Asymptotic Gap-Dependent Regret Bounds for Tabular MDPs

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-r...

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Bibliographic Details
Published in:arXiv.org 2019-10
Main Authors: Simchowitz, Max, Jamieson, Kevin
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic properties
Dependence
Minimax technique
Online Access:Get full text
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Summary: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.
ISSN:2331-8422