Bayesian Quadrature for Probability Threshold Robustness of Partially Undefined Functions

Jonathan Sadeghi, Romain Mueller, John Redford

Abstract: In engineering design, one often wishes to calculate the probability that the performance of a system is satisfactory under uncertainty. State of the art algorithms exist to solve this problem using active learning with Gaussian process models. However, these algorithms cannot be applied to problems which often occur in the autonomous vehicle domain where the performance of a system may be undefined under certain circumstances. To solve this problem, we introduce a hierarchical model for the system performance, where undefined performance is classified before the performance is regressed. This enables active learning Gaussian process methods to be applied to problems where the performance of the system is sometimes undefined, and we demonstrate the effectiveness of our approach by testing our methodology on synthetic numerical examples for the autonomous driving domain.