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arXiv · 2210.00832

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

Xuefeng Gao·Xun Yu Zhou
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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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Xuefeng Gao, Xun Yu Zhou. 2022-10-03. Square-root regret bounds for continuous-time episodic Markov decision processes. https://arxiv.org/abs/2210.00832

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