Chebyshev Policies and the Mountain Car Problem: Reinforcement Learning for Low-Dimensional Control Tasks
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910278450413568 |
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| author | Huber, Stefan Unger, Hannes Schäfer, Georg Rehrl, Jakob |
| author_facet | Huber, Stefan Unger, Hannes Schäfer, Georg Rehrl, Jakob |
| contents | We analytically solve the Mountain Car problem, a canonical benchmark in RL, and derive an optimal control solution, closing a gap after 36 years. This enables us to reveal two surprising insights: The optimal control is quite simple, yet modern RL agents display a large gap to optimality. Motivated by the analysis of the optimal control, we introduce Chebyshev policies as a universal (i.e. dense) class of RL policies from first principles. They can be trained as drop-in replacements of neural nets, reducing the regret by a factor of 4.18, while requiring 277 times fewer parameters, fostering sample efficiency, explainability and realtime capability. Chebyshev policies are evaluated on further RL tasks, including a real-world nonlinear motion control testbed. They consistently improve performance over neural nets with PPO, ARS and REINFORCE. Our results demonstrate how Chebyshev policies offer a compelling and lightweight alternative or addition to neural nets for low-dimensional control tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22305 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chebyshev Policies and the Mountain Car Problem: Reinforcement Learning for Low-Dimensional Control Tasks Huber, Stefan Unger, Hannes Schäfer, Georg Rehrl, Jakob Machine Learning We analytically solve the Mountain Car problem, a canonical benchmark in RL, and derive an optimal control solution, closing a gap after 36 years. This enables us to reveal two surprising insights: The optimal control is quite simple, yet modern RL agents display a large gap to optimality. Motivated by the analysis of the optimal control, we introduce Chebyshev policies as a universal (i.e. dense) class of RL policies from first principles. They can be trained as drop-in replacements of neural nets, reducing the regret by a factor of 4.18, while requiring 277 times fewer parameters, fostering sample efficiency, explainability and realtime capability. Chebyshev policies are evaluated on further RL tasks, including a real-world nonlinear motion control testbed. They consistently improve performance over neural nets with PPO, ARS and REINFORCE. Our results demonstrate how Chebyshev policies offer a compelling and lightweight alternative or addition to neural nets for low-dimensional control tasks. |
| title | Chebyshev Policies and the Mountain Car Problem: Reinforcement Learning for Low-Dimensional Control Tasks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.22305 |