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

arXiv:2603.00043v1 Announce Type: new 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 · · 1 min read · 2 views
#cs.LG #cs.AI

arXiv:2603.00043v1 Announce Type: new 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.

Executive Summary

This article presents a novel approach to reinforcement learning (RL) for control systems, providing probabilistic stability guarantees using finite data. Leveraging Lyapunov's method, the authors propose a probabilistic stability theorem and derive a policy gradient theorem for stabilizing policy learning. They develop an RL algorithm, L-REINFORCE, extending the classical REINFORCE algorithm to stabilization problems. Simulations on a Cartpole task demonstrate the effectiveness of L-REINFORCE 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. The approach has potential applications in robotics, autonomous systems, and other domains requiring stable control.

Key Points

  • ▸ The authors propose a probabilistic stability theorem for RL control systems using Lyapunov's method.
  • ▸ They derive a policy gradient theorem for stabilizing policy learning.
  • ▸ L-REINFORCE is developed as an extension of the classical REINFORCE algorithm for stabilization problems.

Merits

Strength

The approach provides probabilistic stability guarantees using finite data, addressing a critical gap between RL and control theory.

Originality

The development of L-REINFORCE and the probabilistic stability theorem offer novel contributions to the field of RL and control theory.

Applicability

The approach has potential applications in robotics, autonomous systems, and other domains requiring stable control.

Demerits

Limitation

The approach may not be suitable for high-dimensional or complex control systems, requiring significant computational resources.

Assumptions

The probabilistic stability theorem relies on assumptions about the control system and the Lyapunov function, which may not always hold in practice.

Expert Commentary

The article presents a significant contribution to the field of RL and control theory, bridging a critical gap between the two. The development of L-REINFORCE and the probabilistic stability theorem offer novel approaches to stability analysis and controller design in a model-free framework with finite data. While the approach has potential applications in various domains, its limitations and assumptions must be carefully considered. The ongoing research in stability analysis for RL algorithms and model-free control methods will continue to drive innovation in this area. As the field progresses, it is essential to address the challenges associated with high-dimensional or complex control systems and to develop more robust and generalizable approaches.

Recommendations

  • ✓ Further research is needed to extend the approach to high-dimensional or complex control systems.
  • ✓ The development of more robust and generalizable approaches to stability analysis and controller design is essential for widespread adoption in industries requiring stable control systems.

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