Square-root regret bounds for continuous-time episodic Markov decision processes

2022/10/03 by Xuefeng Gao, Xun Yu Zhou, Gao, Xuefeng +1
Computer Science · Decision Sciences · Engineering · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Reinforcement Learning in Robotics #Smart Grid Energy Management

paper · pdf · doi:10.48550/arxiv.2210.00832

openalex publication_date 2022/10/03 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We study reinforcement learning for continuous-time Markov decision processes (MDPs) in the finite-horizon episodic setting. In contrast to discrete-time MDPs, the inter-transition times of a continuous-time MDP are exponentially distributed with rate parameters depending on the state--action pair at each transition. We present a learning algorithm based on the methods of value iteration and upper confidence bound. We derive an upper bound on the worst-case expected regret for the proposed algorithm, and establish a worst-case lower bound, both bounds are of the order of square-root on the number of episodes. Finally, we conduct simulation experiments to illustrate the performance of our algorithm.

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