Reinforcement Learning for Control with Probabilistic Stability Guarantee: A Finite-Sample Approach
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908856784781312 |
|---|---|
| author | Han, Minghao Zhang, Lixian Liu, Chenliang Zhou, Zhipeng Wang, Jun Pan, Wei |
| author_facet | Han, Minghao Zhang, Lixian Liu, Chenliang Zhou, Zhipeng Wang, Jun Pan, Wei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00043 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reinforcement Learning for Control with Probabilistic Stability Guarantee: A Finite-Sample Approach Han, Minghao Zhang, Lixian Liu, Chenliang Zhou, Zhipeng Wang, Jun Pan, Wei Machine Learning Artificial Intelligence 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. |
| title | Reinforcement Learning for Control with Probabilistic Stability Guarantee: A Finite-Sample Approach |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2603.00043 |