Logarithmic regret bounds for continuous-time average-reward Markov decision processes

Xuefeng Gao; Xun Yu Zhou

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arXiv · 2205.11168

Logarithmic regret bounds for continuous-time average-reward Markov decision processes

Xuefeng Gao·Xun Yu Zhou

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Abstract

We consider reinforcement learning for continuous-time Markov decision processes (MDPs) in the infinite-horizon, average-reward setting. In contrast to discrete-time MDPs, a continuous-time process moves to a state and stays there for a random holding time after an action is taken. With unknown transition probabilities and rates of exponential holding times, we derive instance-dependent regret lower bounds that are logarithmic in the time horizon. Moreover, we design a learning algorithm and establish a finite-time regret bound that achieves the logarithmic growth rate. Our analysis builds upon upper confidence reinforcement learning, a delicate estimation of the mean holding times, and stochastic comparison of point processes.

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Xuefeng Gao, Xun Yu Zhou. 2022-05-23. Logarithmic regret bounds for continuous-time average-reward Markov decision processes. https://arxiv.org/abs/2205.11168

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