  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.
