Trade-offs in Bayesian active learning for feasible region identification

Abstract

Typical engineering design problems, such as designing an aeroplane engine or testing an automated driving system, often involve multiple design constraints that define feasible solutions in the design space. Modern data-driven approaches allow for the effective characterisation of the (corresponding) feasible region(s), often by exploring the trade-off in regions of the design space with high expected performance and high uncertainty. Bayesian active learning is a data-efficient method that iteratively learns a surrogate model based on limited input-output data. Acquisition functions select samples based on a trade-off between exploration of the design space and exploitation of the feasible region. In this work, we consider this trade-off as a bi-objective maximization problem and show that existing acquisition functions choose samples on this Pareto front. We introduce two novel acquisition functions based on multi-objective scalarization methods for identifying the feasible region. The acquisition functions are compared against the state-of-the-art on several engineering benchmarks, as well as for testing an automated driving system. The results show that the novel acquisition methods are generally at least as effective as the state-of-the-art, while they select more feasible designs than boundary-focused acquisition functions.