Non-Asymptotic Gap-Dependent Regret Bounds for Tabular MDPs
Abstract
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.
Cite
Text
Simchowitz and Jamieson. "Non-Asymptotic Gap-Dependent Regret Bounds for Tabular MDPs." Neural Information Processing Systems, 2019.Markdown
[Simchowitz and Jamieson. "Non-Asymptotic Gap-Dependent Regret Bounds for Tabular MDPs." Neural Information Processing Systems, 2019.](https://mlanthology.org/neurips/2019/simchowitz2019neurips-nonasymptotic/)BibTeX
@inproceedings{simchowitz2019neurips-nonasymptotic,
title = {{Non-Asymptotic Gap-Dependent Regret Bounds for Tabular MDPs}},
author = {Simchowitz, Max and Jamieson, Kevin G.},
booktitle = {Neural Information Processing Systems},
year = {2019},
pages = {1153-1162},
url = {https://mlanthology.org/neurips/2019/simchowitz2019neurips-nonasymptotic/}
}