  Learning a dynamical system requires stabilizing the unknown dynamics to
avoid state blow-ups. However, current reinforcement learning (RL) methods lack
stabilization guarantees, which limits their applicability for the control of
safety-critical systems. We propose a model-based RL framework with formal
stability guarantees, Krasovskii Constrained RL (KCRL), that adopts
Krasovskii's family of Lyapunov functions as a stability constraint. The
proposed method learns the system dynamics up to a confidence interval using
feature representation, e.g. Random Fourier Features. It then solves a
constrained policy optimization problem with a stability constraint based on
Krasovskii's method using a primal-dual approach to recover a stabilizing
policy. We show that KCRL is guaranteed to learn a stabilizing policy in a
finite number of interactions with the underlying unknown system. We also
derive the sample complexity upper bound for stabilization of unknown nonlinear
dynamical systems via the KCRL framework.
