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

2026-02-09 · Minghao Han, Lixian Zhang, Chenliang Liu, Zhipeng Zhou, Jun Wang, Wei Pan arxiv

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.

📄 PDF Abstract BibTeX arXiv:2603.00043

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Reinforcement Learning

Reinforcement Learning for Control with Probabilistic Stability Guarantee

2021-01-01 · Minghao Han, Zhipeng Zhou, Lixian Zhang, Jun Wang 외

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