Barrier-Certified Adaptive Reinforcement Learning with Applications to Brushbot Navigation

This paper presents a safe learning framework that employs an adaptive model learning method together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use a sparse optimization technique, and the resulting model will be used in combination with control barrier certificates which constrain policies (feedback controllers) in order to maintain safety, which refers to avoiding certain regions of the state space. Under certain conditions, recovery of safety in the sense of Lyapunov stability after violations of safety due to the nonstationarity is guaranteed. In addition, we reformulate action-value function approximation to make any kernel-based nonlinear function estimation method applicable to our adaptive learning framework. Lastly, solutions to the barrier-certified policy optimization are guaranteed to be globally optimal, ensuring greedy policy updates under mild conditions. The resulting framework is validated via simulations of a quadrotor, which has been used in the safe learnings literature under {\em stationarity} assumption, and then tested on a real robot called {\em brushbot}, whose dynamics is unknown, highly complex, and most probably nonstationary.