A Policy Gradient Primal-Dual Algorithm for Constrained MDPs with Uniform PAC Guarantees

Toshinori Kitamura, Tadashi Kozuno, Masahiro Kato, YUKI ICHIHARA, Soichiro Nishimori, Akiyoshi Sannai, Sho Sonoda, Wataru Kumagai, Yutaka Matsuo

Confirmation: Yes

Keywords: Reinforcement Learning Theory, Constrained MDP

TL;DR: We propose a policy gradient primal-dual RL algorithm for CMDPs with Uniform-PAC guarantees

Abstract: We study a primal-dual (PD) reinforcement learning (RL) algorithm for online constrained Markov decision processes (CMDPs). Despite its widespread practical use, the existing theoretical literature on PD-RL algorithms for this problem only provides sublinear regret guarantees and fails to ensure convergence to optimal policies. In this paper, we introduce a novel policy gradient PD algorithm with uniform probably approximate correctness (Uniform-PAC) guarantees, simultaneously ensuring convergence to optimal policies, sublinear regret, and polynomial sample complexity for any target accuracy. Notably, this represents the first Uniform-PAC algorithm for the online CMDP problem. In addition to the theoretical guarantees, we empirically demonstrate in a simple CMDP that our algorithm converges to optimal policies, while baseline algorithms exhibit oscillatory performance and constraint violation.

Submission Number: 1