Sample Complexity of Robust Reinforcement Learning with a Generative Model

Kishan Panaganti, Dileep Kalathil
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:9582-9602, 2022.

Abstract

The Robust Markov Decision Process (RMDP) framework focuses on designing control policies that are robust against the parameter uncertainties due to the mismatches between the simulator model and real-world settings. An RMDP problem is typically formulated as a max-min problem, where the objective is to find the policy that maximizes the value function for the worst possible model that lies in an uncertainty set around a nominal model. The standard robust dynamic programming approach requires the knowledge of the nominal model for computing the optimal robust policy. In this work, we propose a model-based reinforcement learning (RL) algorithm for learning an $\epsilon$-optimal robust policy when the nominal model is unknown. We consider three different forms of uncertainty sets, characterized by the total variation distance, chi-square divergence, and KL divergence. For each of these uncertainty sets, we give a precise characterization of the sample complexity of our proposed algorithm. In addition to the sample complexity results, we also present a formal analytical argument on the benefit of using robust policies. Finally, we demonstrate the performance of our algorithm on two benchmark problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-panaganti22a, title = { Sample Complexity of Robust Reinforcement Learning with a Generative Model }, author = {Panaganti, Kishan and Kalathil, Dileep}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {9582--9602}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/panaganti22a/panaganti22a.pdf}, url = {https://proceedings.mlr.press/v151/panaganti22a.html}, abstract = { The Robust Markov Decision Process (RMDP) framework focuses on designing control policies that are robust against the parameter uncertainties due to the mismatches between the simulator model and real-world settings. An RMDP problem is typically formulated as a max-min problem, where the objective is to find the policy that maximizes the value function for the worst possible model that lies in an uncertainty set around a nominal model. The standard robust dynamic programming approach requires the knowledge of the nominal model for computing the optimal robust policy. In this work, we propose a model-based reinforcement learning (RL) algorithm for learning an $\epsilon$-optimal robust policy when the nominal model is unknown. We consider three different forms of uncertainty sets, characterized by the total variation distance, chi-square divergence, and KL divergence. For each of these uncertainty sets, we give a precise characterization of the sample complexity of our proposed algorithm. In addition to the sample complexity results, we also present a formal analytical argument on the benefit of using robust policies. Finally, we demonstrate the performance of our algorithm on two benchmark problems. } }
Endnote
%0 Conference Paper %T Sample Complexity of Robust Reinforcement Learning with a Generative Model %A Kishan Panaganti %A Dileep Kalathil %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-panaganti22a %I PMLR %P 9582--9602 %U https://proceedings.mlr.press/v151/panaganti22a.html %V 151 %X The Robust Markov Decision Process (RMDP) framework focuses on designing control policies that are robust against the parameter uncertainties due to the mismatches between the simulator model and real-world settings. An RMDP problem is typically formulated as a max-min problem, where the objective is to find the policy that maximizes the value function for the worst possible model that lies in an uncertainty set around a nominal model. The standard robust dynamic programming approach requires the knowledge of the nominal model for computing the optimal robust policy. In this work, we propose a model-based reinforcement learning (RL) algorithm for learning an $\epsilon$-optimal robust policy when the nominal model is unknown. We consider three different forms of uncertainty sets, characterized by the total variation distance, chi-square divergence, and KL divergence. For each of these uncertainty sets, we give a precise characterization of the sample complexity of our proposed algorithm. In addition to the sample complexity results, we also present a formal analytical argument on the benefit of using robust policies. Finally, we demonstrate the performance of our algorithm on two benchmark problems.
APA
Panaganti, K. & Kalathil, D.. (2022). Sample Complexity of Robust Reinforcement Learning with a Generative Model . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:9582-9602 Available from https://proceedings.mlr.press/v151/panaganti22a.html.

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