First-Order Methods for Wasserstein Distributionally Robust MDP

Julien Grand Clement, Christian Kroer
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:2010-2019, 2021.

Abstract

Markov decision processes (MDPs) are known to be sensitive to parameter specification. Distributionally robust MDPs alleviate this issue by allowing for \textit{ambiguity sets} which give a set of possible distributions over parameter sets. The goal is to find an optimal policy with respect to the worst-case parameter distribution. We propose a framework for solving Distributionally robust MDPs via first-order methods, and instantiate it for several types of Wasserstein ambiguity sets. By developing efficient proximal updates, our algorithms achieve a convergence rate of $O\left(NA^{2.5}S^{3.5}\log(S)\log(\epsilon^{-1})\epsilon^{-1.5} \right)$ for the number of kernels $N$ in the support of the nominal distribution, states $S$, and actions $A$; this rate varies slightly based on the Wasserstein setup. Our dependence on $N,A$ and $S$ is significantly better than existing methods, which have a complexity of $O\left(N^{3.5}A^{3.5}S^{4.5}\log^{2}(\epsilon^{-1}) \right)$. Numerical experiments show that our algorithm is significantly more scalable than state-of-the-art approaches across several domains.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-clement21a, title = {First-Order Methods for Wasserstein Distributionally Robust MDP}, author = {Clement, Julien Grand and Kroer, Christian}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {2010--2019}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/clement21a/clement21a.pdf}, url = {https://proceedings.mlr.press/v139/clement21a.html}, abstract = {Markov decision processes (MDPs) are known to be sensitive to parameter specification. Distributionally robust MDPs alleviate this issue by allowing for \textit{ambiguity sets} which give a set of possible distributions over parameter sets. The goal is to find an optimal policy with respect to the worst-case parameter distribution. We propose a framework for solving Distributionally robust MDPs via first-order methods, and instantiate it for several types of Wasserstein ambiguity sets. By developing efficient proximal updates, our algorithms achieve a convergence rate of $O\left(NA^{2.5}S^{3.5}\log(S)\log(\epsilon^{-1})\epsilon^{-1.5} \right)$ for the number of kernels $N$ in the support of the nominal distribution, states $S$, and actions $A$; this rate varies slightly based on the Wasserstein setup. Our dependence on $N,A$ and $S$ is significantly better than existing methods, which have a complexity of $O\left(N^{3.5}A^{3.5}S^{4.5}\log^{2}(\epsilon^{-1}) \right)$. Numerical experiments show that our algorithm is significantly more scalable than state-of-the-art approaches across several domains.} }
Endnote
%0 Conference Paper %T First-Order Methods for Wasserstein Distributionally Robust MDP %A Julien Grand Clement %A Christian Kroer %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-clement21a %I PMLR %P 2010--2019 %U https://proceedings.mlr.press/v139/clement21a.html %V 139 %X Markov decision processes (MDPs) are known to be sensitive to parameter specification. Distributionally robust MDPs alleviate this issue by allowing for \textit{ambiguity sets} which give a set of possible distributions over parameter sets. The goal is to find an optimal policy with respect to the worst-case parameter distribution. We propose a framework for solving Distributionally robust MDPs via first-order methods, and instantiate it for several types of Wasserstein ambiguity sets. By developing efficient proximal updates, our algorithms achieve a convergence rate of $O\left(NA^{2.5}S^{3.5}\log(S)\log(\epsilon^{-1})\epsilon^{-1.5} \right)$ for the number of kernels $N$ in the support of the nominal distribution, states $S$, and actions $A$; this rate varies slightly based on the Wasserstein setup. Our dependence on $N,A$ and $S$ is significantly better than existing methods, which have a complexity of $O\left(N^{3.5}A^{3.5}S^{4.5}\log^{2}(\epsilon^{-1}) \right)$. Numerical experiments show that our algorithm is significantly more scalable than state-of-the-art approaches across several domains.
APA
Clement, J.G. & Kroer, C.. (2021). First-Order Methods for Wasserstein Distributionally Robust MDP. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:2010-2019 Available from https://proceedings.mlr.press/v139/clement21a.html.

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