Algorithm for Constrained Markov Decision Process with Linear Convergence
Egor Gladin, Maksim Lavrik-Karmazin, Karina Zainullina, Varvara Rudenko, Alexander Gasnikov, Martin Takac
Abstract
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual approach is proposed with the integration of two ingredients: entropy-regularized policy optimizer and Vaidya’s dual optimizer, both of which are critical to achieve faster convergence. The finite-time error bound of the proposed approach is provided. Despite the challenge of the nonconcave objective subject to nonconcave constraints, the proposed approach is shown to converge (with linear rate) to the global optimum. The complexity expressed in terms of the optimality gap and the constraint violation significantly improves upon the existing primal-dual approaches.
BibTeX
@InProceedings{pmlr-v206-gladin23a,
title = {Algorithm for Constrained Markov Decision Process with Linear Convergence},
author = {Gladin, Egor and Lavrik-Karmazin, Maksim and Zainullina, Karina and Rudenko, Varvara and Gasnikov, Alexander and Takac, Martin},
booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
pages = {11506--11533},
year = {2023},
editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem},
volume = {206},
series = {Proceedings of Machine Learning Research},
month = {25--27 Apr},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v206/gladin23a/gladin23a.pdf},
url = {https://proceedings.mlr.press/v206/gladin23a.html},
abstract = {The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual approach is proposed with the integration of two ingredients: entropy-regularized policy optimizer and Vaidya’s dual optimizer, both of which are critical to achieve faster convergence. The finite-time error bound of the proposed approach is provided. Despite the challenge of the nonconcave objective subject to nonconcave constraints, the proposed approach is shown to converge (with linear rate) to the global optimum. The complexity expressed in terms of the optimality gap and the constraint violation significantly improves upon the existing primal-dual approaches.}
}