A Dual Approach to Constrained Markov Decision Processes with Entropy Regularization

Donghao Ying, Yuhao Ding, Javad Lavaei
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:1887-1909, 2022.

Abstract

We study entropy-regularized constrained Markov decision processes (CMDPs) under the soft-max parameterization, in which an agent aims to maximize the entropy-regularized value function while satisfying constraints on the expected total utility. By leveraging the entropy regularization, our theoretical analysis shows that its Lagrangian dual function is smooth and the Lagrangian duality gap can be decomposed into the primal optimality gap and the constraint violation. Furthermore, we propose an accelerated dual-descent method for entropy-regularized CMDPs. We prove that our method achieves the global convergence rate $\widetilde{\mathcal{O}}(1/T)$ for both the optimality gap and the constraint violation for entropy-regularized CMDPs. A discussion about a linear convergence rate for CMDPs with a single constraint is also provided.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-ying22a, title = { A Dual Approach to Constrained Markov Decision Processes with Entropy Regularization }, author = {Ying, Donghao and Ding, Yuhao and Lavaei, Javad}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {1887--1909}, 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/ying22a/ying22a.pdf}, url = {https://proceedings.mlr.press/v151/ying22a.html}, abstract = { We study entropy-regularized constrained Markov decision processes (CMDPs) under the soft-max parameterization, in which an agent aims to maximize the entropy-regularized value function while satisfying constraints on the expected total utility. By leveraging the entropy regularization, our theoretical analysis shows that its Lagrangian dual function is smooth and the Lagrangian duality gap can be decomposed into the primal optimality gap and the constraint violation. Furthermore, we propose an accelerated dual-descent method for entropy-regularized CMDPs. We prove that our method achieves the global convergence rate $\widetilde{\mathcal{O}}(1/T)$ for both the optimality gap and the constraint violation for entropy-regularized CMDPs. A discussion about a linear convergence rate for CMDPs with a single constraint is also provided. } }
Endnote
%0 Conference Paper %T A Dual Approach to Constrained Markov Decision Processes with Entropy Regularization %A Donghao Ying %A Yuhao Ding %A Javad Lavaei %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-ying22a %I PMLR %P 1887--1909 %U https://proceedings.mlr.press/v151/ying22a.html %V 151 %X We study entropy-regularized constrained Markov decision processes (CMDPs) under the soft-max parameterization, in which an agent aims to maximize the entropy-regularized value function while satisfying constraints on the expected total utility. By leveraging the entropy regularization, our theoretical analysis shows that its Lagrangian dual function is smooth and the Lagrangian duality gap can be decomposed into the primal optimality gap and the constraint violation. Furthermore, we propose an accelerated dual-descent method for entropy-regularized CMDPs. We prove that our method achieves the global convergence rate $\widetilde{\mathcal{O}}(1/T)$ for both the optimality gap and the constraint violation for entropy-regularized CMDPs. A discussion about a linear convergence rate for CMDPs with a single constraint is also provided.
APA
Ying, D., Ding, Y. & Lavaei, J.. (2022). A Dual Approach to Constrained Markov Decision Processes with Entropy Regularization . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:1887-1909 Available from https://proceedings.mlr.press/v151/ying22a.html.

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