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

A research team including Minghao Han, Lixian Zhang, and Chenliang Liu has published a significant paper on arXiv titled 'Reinforcement Learning for Control with Probabilistic Stability Guarantee: A Finite-Sample Approach.' The work introduces a novel framework that marries reinforcement learning (RL) with control theory's rigorous stability analysis. The core innovation is providing probabilistic guarantees that a learned control policy will keep a physical system stable, a major hurdle preventing RL's adoption in safety-critical applications like robotics and autonomous systems. This is achieved not through infinite simulation but using only a finite number of real or simulated trajectories, making the approach practical for real-world deployment.

The team's key technical contribution is a probabilistic stability theorem based on Lyapunov's direct method, which ensures mean square stability. They prove that the probability of stability increases with both the number and length of sampled trajectories, converging to certainty as data grows. Building on this, they derived a new policy gradient theorem specifically for learning stabilizing policies and developed the L-REINFORCE algorithm, an extension of the foundational REINFORCE algorithm. In simulations on the classic Cartpole control task, L-REINFORCE successfully learned policies and demonstrably outperformed a standard baseline in ensuring system stability. This work provides a crucial, mathematically sound toolkit for developing reliable, model-free RL controllers where failure is not an option.