  We propose a method to encourage safety in Model Predictive Control
(MPC)-based Reinforcement Learning (RL) via Gaussian Process (GP) regression.
This framework consists of 1) a parametric MPC scheme that is employed as
model-based controller with approximate knowledge on the real system's
dynamics, 2) an episodic RL algorithm tasked with adjusting the MPC
parametrization in order to increase its performance, and lastly, 3) GP
regressors used to estimate, directly from data, constraints on the MPC
parameters capable of predicting, up to some probability, whether the
parametrization is likely to yield a safe or unsafe policy. These constraints
are then enforced onto the RL updates in an effort to enhance the learning
method with a probabilistic safety mechanism. Compared to other recent
publications combining safe RL with MPC, our method does not require further
assumptions on, e.g., the prediction model in order to retain computational
tractability. We illustrate the results of our method in a numerical example on
the control of a quadrotor drone in a safety-critical environment.
