In current model-free reinforcement learning (RL) algorithms, stability criteria based on sampling methods are commonly utilized to guide policy optimization. However, these criteria only guarantee the infinite-time convergence of the system's state to an equilibrium point, which leads to sub-optimality of the policy. In this paper, we propose a policy optimization technique incorporating sampling-based Lyapunov stability. Our approach enables the system's state to reach an equilibrium point within an optimal time and maintain stability thereafter, referred to as "optimal-time stability". To achieve this, we integrate the optimization method into the Actor-Critic framework, resulting in the development of the Adaptive Lyapunov-based Actor-Critic (ALAC) algorithm. Through evaluations conducted on ten robotic tasks, our approach outperforms previous studies significantly, effectively guiding the system to generate stable patterns.
@article{arxiv.2301.00521,
title = {A Policy Optimization Method Towards Optimal-time Stability},
author = {Shengjie Wang and Fengbo Lan and Xiang Zheng and Yuxue Cao and Oluwatosin Oseni and Haotian Xu and Tao Zhang and Yang Gao},
journal= {arXiv preprint arXiv:2301.00521},
year = {2023}
}