English

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

Machine Learning 2024-07-02 v3

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.

Keywords

Cite

@article{arxiv.2401.17780,
  title  = {A Policy Gradient Primal-Dual Algorithm for Constrained MDPs with Uniform PAC Guarantees},
  author = {Toshinori Kitamura and Tadashi Kozuno and Masahiro Kato and Yuki Ichihara and Soichiro Nishimori and Akiyoshi Sannai and Sho Sonoda and Wataru Kumagai and Yutaka Matsuo},
  journal= {arXiv preprint arXiv:2401.17780},
  year   = {2024}
}
R2 v1 2026-06-28T14:32:58.638Z