Improved Model-based Reinforcement Learning with Smooth Kernels
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914543046754304 |
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| author | Long, Kun Li, Yuqiang Wu, Xianyi |
| author_facet | Long, Kun Li, Yuqiang Wu, Xianyi |
| contents | For continuous state-action space scenarios, classical reinforcement learning (RL) theory predominantly focuses on low-rank Markov decision processes (MDPs), which provide sample-efficient guarantees at the expense of restrictive structural assumptions. Kernel smoothing model-based approaches offer a promising alternative paradigm that instead leverages the smoothness of the MDP and employs non-parametric kernel smoothing estimates of transition dynamics. This paper proposes a new kernel-smoothing model-based approach for online reinforcement learning in finite-horizon settings under Lipschitz continuity assumptions on the MDP. By incorporating a Bernstein-style exploration bonus into the kernel smoothing framework, our method achieves a regret bound which improves upon the state-of-the-art regret bound in its dependence on the horizon. The theoretical advancement relies on a delicate analysis of the synergy between Bernstein-style bonuses and kernel smoothing, where a new tight Bernstein-type concentration inequality for martingales may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07218 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Improved Model-based Reinforcement Learning with Smooth Kernels Long, Kun Li, Yuqiang Wu, Xianyi Machine Learning 35A01, 65L10, 65L12, 65L20, 65L70 For continuous state-action space scenarios, classical reinforcement learning (RL) theory predominantly focuses on low-rank Markov decision processes (MDPs), which provide sample-efficient guarantees at the expense of restrictive structural assumptions. Kernel smoothing model-based approaches offer a promising alternative paradigm that instead leverages the smoothness of the MDP and employs non-parametric kernel smoothing estimates of transition dynamics. This paper proposes a new kernel-smoothing model-based approach for online reinforcement learning in finite-horizon settings under Lipschitz continuity assumptions on the MDP. By incorporating a Bernstein-style exploration bonus into the kernel smoothing framework, our method achieves a regret bound which improves upon the state-of-the-art regret bound in its dependence on the horizon. The theoretical advancement relies on a delicate analysis of the synergy between Bernstein-style bonuses and kernel smoothing, where a new tight Bernstein-type concentration inequality for martingales may be of independent interest. |
| title | Improved Model-based Reinforcement Learning with Smooth Kernels |
| topic | Machine Learning 35A01, 65L10, 65L12, 65L20, 65L70 |
| url | https://arxiv.org/abs/2605.07218 |