Lyapunov-Constrained Action Sets for Reinforcement Learning
Lyapunov analysis is a standard approach to studying the stability of dynamical systems and to designing controllers. We propose to design the actions of a reinforcement learning (RL) agent to be descending on a Lyapunov function. For minimum cost-to-target problems, this has the theoretical benefit of guaranteeing that the agent will reach a goal state on every trial, regardless of the RL algorithm it uses. In practice, Lyapunov-descent constraints can significantly shorten learning trials, improve initial and worst-case performance, and accelerate learning. Although this method of constraining actions may limit the extent to which an RL agent can minimize cost, it allows one to construct robust RL systems for problems in which Lyapunov domain knowledge is available. This includes many important individual problems as well as general classes of problems, such as the control of feedback linearizable systems (e.g., industrial robots) and continuous-state path-planning problems. We demonstrate the general approach on two simulated control problems: pendulum swing-up and robot arm control.