Global Convergence for Average Reward Constrained MDPs with Primal-Dual Actor Critic Algorithm

Yang Xu (Nanjing University) · Washim Mondal (Indian Institute of Technology Kanpur) · Vaneet Aggarwal (Purdue University) · Swetha Ganesh (Purdue University) · Qinbo Bai (Purdue University)

algorithmic performance average rewardconstrained markov decision processesconstraint violation ratesconvergence rate exploration global convergence infinite-horizonmixing timeoptimization techniquesparametrized policiespolicy gradientsprimal-dual natural actor-criticreinforcement learningtheoretical lower bound

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.