aiqbench analysis
This study analytically resolves the Mountain Car benchmark after 36 years, revealing that modern neural network agents lag significantly behind optimal control solutions in low-dimensional tasks. By introducing Chebyshev policies as a lightweight alternative to deep learning models, researchers achieve substantial gains in sample efficiency and explainability while reducing parameter counts by over two orders of magnitude. These findings suggest a promising path toward more efficient reinforcement learning architectures without relying on massive neural networks for specific control applications.
Chebyshev Policies and the Mountain Car Problem: Reinforcement Learning for Low-Dimensional Control Tasks
arXiv:2605.22305v5 Announce Type: replace Abstract: 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 6.18, 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.
Abstract: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 6.18, 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.
Machine Learning (cs.LG)
arXiv:2605.22305 [cs.LG]
(or arXiv:2605.22305v5 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.22305 Focus to learn more arXiv-issued DOI via DataCite
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