Model-Free Robust Average-Reward Reinforcement Learning

Yue Wang, Alvaro Velasquez, George K. Atia, Ashley Prater-Bennette, Shaofeng Zou
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:36431-36469, 2023.

Abstract

Robust Markov decision processes (MDPs) address the challenge of model uncertainty by optimizing the worst-case performance over an uncertainty set of MDPs. In this paper, we focus on the robust average-reward MDPs under the model-free setting. We first theoretically characterize the structure of solutions to the robust average-reward Bellman equation, which is essential for our later convergence analysis. We then design two model-free algorithms, robust relative value iteration (RVI) TD and robust RVI Q-learning, and theoretically prove their convergence to the optimal solution. We provide several widely used uncertainty sets as examples, including those defined by the contamination model, total variation, Chi-squared divergence, Kullback-Leibler (KL) divergence, and Wasserstein distance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-wang23am, title = {Model-Free Robust Average-Reward Reinforcement Learning}, author = {Wang, Yue and Velasquez, Alvaro and Atia, George K. and Prater-Bennette, Ashley and Zou, Shaofeng}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {36431--36469}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/wang23am/wang23am.pdf}, url = {https://proceedings.mlr.press/v202/wang23am.html}, abstract = {Robust Markov decision processes (MDPs) address the challenge of model uncertainty by optimizing the worst-case performance over an uncertainty set of MDPs. In this paper, we focus on the robust average-reward MDPs under the model-free setting. We first theoretically characterize the structure of solutions to the robust average-reward Bellman equation, which is essential for our later convergence analysis. We then design two model-free algorithms, robust relative value iteration (RVI) TD and robust RVI Q-learning, and theoretically prove their convergence to the optimal solution. We provide several widely used uncertainty sets as examples, including those defined by the contamination model, total variation, Chi-squared divergence, Kullback-Leibler (KL) divergence, and Wasserstein distance.} }
Endnote
%0 Conference Paper %T Model-Free Robust Average-Reward Reinforcement Learning %A Yue Wang %A Alvaro Velasquez %A George K. Atia %A Ashley Prater-Bennette %A Shaofeng Zou %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-wang23am %I PMLR %P 36431--36469 %U https://proceedings.mlr.press/v202/wang23am.html %V 202 %X Robust Markov decision processes (MDPs) address the challenge of model uncertainty by optimizing the worst-case performance over an uncertainty set of MDPs. In this paper, we focus on the robust average-reward MDPs under the model-free setting. We first theoretically characterize the structure of solutions to the robust average-reward Bellman equation, which is essential for our later convergence analysis. We then design two model-free algorithms, robust relative value iteration (RVI) TD and robust RVI Q-learning, and theoretically prove their convergence to the optimal solution. We provide several widely used uncertainty sets as examples, including those defined by the contamination model, total variation, Chi-squared divergence, Kullback-Leibler (KL) divergence, and Wasserstein distance.
APA
Wang, Y., Velasquez, A., Atia, G.K., Prater-Bennette, A. & Zou, S.. (2023). Model-Free Robust Average-Reward Reinforcement Learning. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:36431-36469 Available from https://proceedings.mlr.press/v202/wang23am.html.

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