TY - JOUR
T1 - Natural policy gradient primal-dual method for constrained Markov decision processes
AU - Ding, Dongsheng
AU - Zhang, Kaiqing
AU - Basar, Tamer
AU - Jovanovic, Mihailo R.
N1 - Publisher Copyright:
© 2020 Neural information processing systems foundation. All rights reserved.
PY - 2020
Y1 - 2020
N2 - We study sequential decision-making problems in which each agent aims to maximize the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon Constrained Markov Decision Processes (CMDPs) problem. Specifically, we propose a new Natural Policy Gradient Primal-Dual (NPG-PD) method for CMDPs which updates the primal variable via natural policy gradient ascent and the dual variable via projected sub-gradient descent. Even though the underlying maximization involves a nonconcave objective function and a nonconvex constraint set under the softmax policy parametrization, we prove that our method achieves global convergence with sublinear rates regarding both the optimality gap and the constraint violation. Such a convergence is independent of the size of the state-action space, i.e., it is dimension-free. Furthermore, for the general smooth policy class, we establish sublinear rates of convergence regarding both the optimality gap and the constraint violation, up to a function approximation error caused by restricted policy parametrization. Finally, we show that two sample-based NPG-PD algorithms inherit such non-asymptotic convergence properties and provide finite-sample complexity guarantees. To the best of our knowledge, our work is the first to establish non-asymptotic convergence guarantees of policy-based primal-dual methods for solving infinite-horizon discounted CMDPs. We also provide computational results to demonstrate merits of our approach.
AB - We study sequential decision-making problems in which each agent aims to maximize the expected total reward while satisfying a constraint on the expected total utility. We employ the natural policy gradient method to solve the discounted infinite-horizon Constrained Markov Decision Processes (CMDPs) problem. Specifically, we propose a new Natural Policy Gradient Primal-Dual (NPG-PD) method for CMDPs which updates the primal variable via natural policy gradient ascent and the dual variable via projected sub-gradient descent. Even though the underlying maximization involves a nonconcave objective function and a nonconvex constraint set under the softmax policy parametrization, we prove that our method achieves global convergence with sublinear rates regarding both the optimality gap and the constraint violation. Such a convergence is independent of the size of the state-action space, i.e., it is dimension-free. Furthermore, for the general smooth policy class, we establish sublinear rates of convergence regarding both the optimality gap and the constraint violation, up to a function approximation error caused by restricted policy parametrization. Finally, we show that two sample-based NPG-PD algorithms inherit such non-asymptotic convergence properties and provide finite-sample complexity guarantees. To the best of our knowledge, our work is the first to establish non-asymptotic convergence guarantees of policy-based primal-dual methods for solving infinite-horizon discounted CMDPs. We also provide computational results to demonstrate merits of our approach.
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M3 - Conference article
AN - SCOPUS:85098818074
SN - 1049-5258
VL - 2020-December
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 34th Conference on Neural Information Processing Systems, NeurIPS 2020
Y2 - 6 December 2020 through 12 December 2020
ER -