Safe learning-based control via function-based uncertainty quantification

Uncertainty quantification is essential when deploying learning-based control methods in safety-critical systems. This is commonly realized by constructing uncertainty tubes that enclose the unknown function of interest, e.g., the reward and constraint functions or the underlying dynamics model, with high probability. However, existing approaches for uncertainty quantification typically rely on restrictive assumptions that encode smoothness properties of the unknown function, such as a known norm in a function space. Moreover, these methods usually struggle with discontinuities. In this paper, we model the unknown function as a random function from which independent and identically distributed realizations can be generated. We then construct uncertainty tubes via the scenario approach that hold with high probability. Our uncertainty tubes rely solely on sampled realizations and can therefore accommodate discontinuities represented by the sampling model. We integrate these uncertainty tubes into a safe Bayesian optimization algorithm with which we safely tune control parameters on a real Furuta pendulum.