Stability-Certified Reinforcement Learning: A Control-Theoretic Perspective

We investigate the important problem of certifying stability of reinforcement learning policies when interconnected with nonlinear dynamical systems. We show that by regulating the partial gradients of policies, strong guarantees of robust stability can be obtained based on a proposed semidefinite programming feasibility problem. The method is able to certify a large set of stabilizing controllers by exploiting problem-specific structures; furthermore, we analyze and establish its (non)conservatism. Empirical evaluations on two decentralized control tasks, namely multi-flight formation and power system frequency regulation, demonstrate that the reinforcement learning agents can have high performance within the stability-certified parameter space and also exhibit stable learning behaviors in the long run.