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

• URL: http://arxiv.org/abs/2505.15138v1
• Date: Wed, 21 May 2025 05:49:11 GMT
• Title: Global Convergence for Average Reward Constrained MDPs with Primal-Dual Actor Critic Algorithm
• Authors: Yang Xu, Swetha Ganesh, Washim Uddin Mondal, Qinbo Bai, Vaneet Aggarwal,
• Abstract summary: We propose a Primal-Dual Natural Actor-Critic algorithm that adeptly manages constraints while ensuring a high convergence rate.<n>Our results match the theoretical lower bound for Markov Decision Processes and establish a new benchmark in the theoretical exploration of average reward CMDPs.
• Score: 31.539921770584005
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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, $\tau_{\mathrm{mix}}$, 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.

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