  This paper presents a safe learning framework that employs an adaptive model
learning algorithm 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. We use the learned model in combination
with control barrier certificates which constrain policies (feedback
controllers) in order to maintain safety, which refers to avoiding particular
undesirable 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 an 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 the greedy policy improvement under mild conditions. The resulting
framework is validated via simulations of a quadrotor, which has previously
been used under stationarity assumptions in the safe learnings literature, and
is then tested on a real robot, the brushbot, whose dynamics is unknown, highly
complex and nonstationary.
