Provably Efficient RL under Episode-Wise Safety in Constrained MDPs with Linear Function Approximation

Yutaka Matsuo (University of Tokyo) · Toshinori Kitamura (The University of Tokyo) · Arnob Ghosh (New Jersey Institute of Technology) · Tadashi Kozuno (OMRON SINIC X) · Wataru Kumagai (RIKEN) · Kazumi Kasaura (OMRON SINIC X Corporation) · Kenta Hoshino (Institute of Science Tokyo) · Yohei Hosoe (Kyoto University)

computational efficiency constrained markov decision processconstraint violationepisode-wise zero-violation guaranteeexpected cumulative rewardexponential computational costsfunction approximationlinear cmdpspolynomial scalingproblem-dependent parametersregret analysis reinforcement learningrl algorithmstate space sizeutility value

We study the reinforcement learning (RL) problem in a constrained Markov decision process (CMDP), where an agent explores the environment to maximize the expected cumulative reward while satisfying a single constraint on the expected total utility value in every episode. While this problem is well understood in the tabular setting, theoretical results for function approximation remain scarce. This paper closes the gap by proposing an RL algorithm for linear CMDPs that achieves $\widetilde{\mathcal{O}}(\sqrt{K})$ regret with an episode-wise zero-violation guarantee. Furthermore, our method is computationally efficient, scaling polynomially with problem-dependent parameters while remaining independent of the state space size. Our results significantly improve upon recent linear CMDP algorithms, which either violate the constraint or incur exponential computational costs.