Asymptotically optimal regret in communicating Markov decision processes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910964621770752 |
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| author | Boone, Victor |
| author_facet | Boone, Victor |
| contents | In this paper, we present a learning algorithm that achieves asymptotically optimal regret for Markov decision processes in average reward under a communicating assumption. That is, given a communicating Markov decision process $M$, our algorithm has regret $K(M) \log(T) + \mathrm{o}(\log(T))$ where $T$ is the number of learning steps and $K(M)$ is the best possible constant. This algorithm works by explicitly tracking the constant $K(M)$ to learn optimally, then balances the trade-off between exploration (playing sub-optimally to gain information), co-exploration (playing optimally to gain information) and exploitation (playing optimally to score maximally). We further show that the function $K(M)$ is discontinuous, which is a consequence challenge for our approach. To that end, we describe a regularization mechanism to estimate $K(M)$ with arbitrary precision from empirical data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically optimal regret in communicating Markov decision processes Boone, Victor Machine Learning In this paper, we present a learning algorithm that achieves asymptotically optimal regret for Markov decision processes in average reward under a communicating assumption. That is, given a communicating Markov decision process $M$, our algorithm has regret $K(M) \log(T) + \mathrm{o}(\log(T))$ where $T$ is the number of learning steps and $K(M)$ is the best possible constant. This algorithm works by explicitly tracking the constant $K(M)$ to learn optimally, then balances the trade-off between exploration (playing sub-optimally to gain information), co-exploration (playing optimally to gain information) and exploitation (playing optimally to score maximally). We further show that the function $K(M)$ is discontinuous, which is a consequence challenge for our approach. To that end, we describe a regularization mechanism to estimate $K(M)$ with arbitrary precision from empirical data. |
| title | Asymptotically optimal regret in communicating Markov decision processes |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.18064 |