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arXiv · 2603.00043

Reinforcement Learning for Control with Probabilistic Stability Guarantee: A Finite-Sample Approach

Minghao Han·Lixian Zhang·Chenliang Liu·Zhipeng Zhou·Jun Wang·Wei Pan
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Abstract

This paper presents a novel approach to reinforcement learning (RL) for control systems that provides probabilistic stability guarantees using finite data. Leveraging Lyapunov's method, we propose a probabilistic stability theorem that ensures mean square stability using only a finite number of sampled trajectories. The probability of stability increases with the number and length of trajectories, converging to certainty as data size grows. Additionally, we derive a policy gradient theorem for stabilizing policy learning and develop an RL algorithm, L-REINFORCE, that extends the classical REINFORCE algorithm to stabilization problems. The effectiveness of L-REINFORCE is demonstrated through simulations on a Cartpole task, where it outperforms the baseline in ensuring stability. This work bridges a critical gap between RL and control theory, enabling stability analysis and controller design in a model-free framework with finite data.

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Minghao Han, Lixian Zhang, Chenliang Liu, Zhipeng Zhou, Jun Wang, Wei Pan. 2026-02-09. Reinforcement Learning for Control with Probabilistic Stability Guarantee: A Finite-Sample Approach. https://arxiv.org/abs/2603.00043

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