Global Convergence for Average Reward Constrained MDPs with Primal-Dual Actor Critic Algorithm
Yang Xu, Swetha Ganesh, Washim Uddin Mondal, Qinbo Bai, Vaneet Aggarwal
Abstract
This paper investigates infinite-horizon average reward Constrained Markov Decision Processes (CMDPs) under general parametrized policies with smooth and bounded policy gradients. We propose a Primal-Dual Natural Actor-Critic algorithm that adeptly manages constraints while ensuring a high convergence rate. In particular, our algorithm achieves global convergence and constraint violation rates of $\tilde{\mathcal{O}}(1/\sqrt{T})$ over a horizon of length $T$ when the mixing time, $\tau_{\mathrm{mix}}$, is known to the learner. In absence of knowledge of $\tau_{\mathrm{mix}}$, the achievable rates change to $\tilde{\mathcal{O}}(1/T^{0.5-\epsilon})$ provided that $T \geq \tilde{\mathcal{O}}\left(\tau_{\mathrm{mix}}^{2/\epsilon}\right)$. Our results match the theoretical lower bound for Markov Decision Processes and establish a new benchmark in the theoretical exploration of average reward CMDPs.
BibTeX
@inproceedings{
xu2025global,
title={Global Convergence for Average Reward Constrained {MDP}s with Primal-Dual Actor Critic Algorithm},
author={Yang Xu and Swetha Ganesh and Washim Uddin Mondal and Qinbo Bai and Vaneet Aggarwal},
booktitle={The Thirty-ninth Annual Conference on Neural Information Processing Systems},
year={2025},
url={https://openreview.net/forum?id=9I1XjEEtsh}
}