Global Convergence for Average Reward Constrained MDPs with Primal-Dual Actor Critic Algorithm
Yang Xu, Swetha Ganesh, Washim Uddin Mondal, Qinbo Bai, Vaneet Aggarwal
TL;DR
This work addresses infinite-horizon average-reward CMDPs under general policy parameterizations by introducing a Primal-Dual Natural Actor-Critic (PDNAC) algorithm. The method combines a primal-dual update on policy parameters with MLMC-based estimators for the critic and natural policy gradient directions, enabling efficient handling of average-reward objectives and average-cost constraints. The authors prove global convergence with rates matching the MDP lower bound: $ ilde{\mathcal{O}}(1/\sqrt{T})$ when the mixing time $τ_{mix}$ is known, and $ ilde{\mathcal{O}}(1/T^{0.5-\varepsilon})$ without such knowledge at the cost of larger horizon, $T$. These results significantly improve over prior general-parameterization CMDP rates and establish near-optimal performance benchmarks while avoiding explicit mixing-time oracles.
Abstract
This paper investigates infinite-horizon average reward Constrained Markov Decision Processes (CMDPs) with general parametrization. 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, $τ_{\mathrm{mix}}$, is known to the learner. In absence of knowledge of $τ_{\mathrm{mix}}$, the achievable rates change to $\tilde{\mathcal{O}}(1/T^{0.5-ε})$ provided that $T \geq \tilde{\mathcal{O}}\left(τ_{\mathrm{mix}}^{2/ε}\right)$. Our results match the theoretical lower bound for Markov Decision Processes and establish a new benchmark in the theoretical exploration of average reward CMDPs.