MSACL: Multi-Step Actor-Critic Learning with Lyapunov Certificates for Exponentially Stabilizing Control

TL;DR

MSACL introduces a multi-step actor-critic reinforcement learning method that incorporates Lyapunov certificates to ensure exponential stability, improving efficiency, robustness, and generalization in complex control tasks.

Contribution

It presents a novel multi-step RL framework with Lyapunov certificates, enabling stable and efficient learning without elaborate reward engineering.

Findings

Consistent performance improvements over baselines.

Robustness against environmental uncertainties.

Effective generalization to unseen signals.

Abstract

For stabilizing control tasks, model-free reinforcement learning (RL) approaches face numerous challenges, particularly regarding the issues of effectiveness and efficiency in complex high-dimensional environments with limited training data. To address these challenges, we propose Multi-Step Actor-Critic Learning with Lyapunov Certificates (MSACL), a novel approach that integrates exponential stability into off-policy maximum entropy reinforcement learning (MERL). In contrast to existing RL-based approaches that depend on elaborate reward engineering and single-step constraints, MSACL adopts intuitive reward design and exploits multi-step samples to enable exploratory actor-critic learning. Specifically, we first introduce Exponential Stability Labels (ESLs) to categorize training samples and propose a $\lambda$-weighted aggregation mechanism to learn Lyapunov certificates. Based on these certificates, we further design a stability-aware advantage function to guide policy optimization, thereby promoting rapid Lyapunov descent and robust state convergence. We evaluate MSACL across six benchmarks, comprising four stabilizing and two high-dimensional tracking tasks. Experimental results demonstrate its consistent performance improvements over both standard RL baselines and state-of-the-art Lyapunov-based RL algorithms. Beyond rapid convergence, MSACL exhibits robustness against environmental uncertainties and generalization to unseen reference signals. The source code and benchmarking environments are available at \href{https://github.com/YuanZhe-Xing/MSACL}{https://github.com/YuanZhe-Xing/MSACL}.