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Efficient Exploration in Average-Reward Constrained Reinforcement Learning: Achieving Near-Optimal Regret With Posterior Sampling

29 May 2024arXiv:2405.19017archive 2025-07-28

Danil Provodin, Maurits Kaptein, Mykola Pechenizkiy

We present a new algorithm based on posterior sampling for learning in Constrained Markov Decision Processes (CMDP) in the infinite-horizon undiscounted setting. The algorithm achieves near-optimal regret bounds while being advantageous empirically compared to the existing algorithms. Our main theoretical result is a Bayesian regret bound for each cost component of Õ (DS√(AT)) for any communicating CMDP with S states, A actions, and diameter D. This regret bound matches the lower bound in order of time horizon T and is the best-known regret bound for communicating CMDPs achieved by a computationally tractable algorithm. Empirical results show that our posterior sampling algorithm outperforms the existing algorithms for constrained reinforcement learning.

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