Logarithmic regret bounds for continuous-time average-reward Markov decision processes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909236873658368 |
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| author | Gao, Xuefeng Zhou, Xun Yu |
| author_facet | Gao, Xuefeng Zhou, Xun Yu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_11168 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Logarithmic regret bounds for continuous-time average-reward Markov decision processes Gao, Xuefeng Zhou, Xun Yu Machine Learning Optimization and Control 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. |
| title | Logarithmic regret bounds for continuous-time average-reward Markov decision processes |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2205.11168 |