Covering Multiple Objectives with a Small Set of Solutions Using Bayesian Optimization

In multi-objective black-box optimization, the goal is typically to find solutions that optimize a set of T black-box objective functions, $f_1$, ..., $f_T$, simultaneously. Traditional approaches often seek a single Pareto-optimal set that balances trade-offs among all objectives. In this work, we introduce a novel problem setting that departs from this paradigm: finding a smaller set of K solutions, where K < T, that collectively "covers" the T objectives. A set of solutions is defined as "covering" if, for each objective $f_1$, ..., $f_T$, there is at least one good solution. A motivating example for this problem setting occurs in drug design. For example, we may have T pathogens and aim to identify a set of K < T antibiotics such that at least one antibiotic can be used to treat each pathogen. To address this problem, we propose Multi-Objective Coverage Bayesian Optimization (MOCOBO), a principled algorithm designed to efficiently find a covering set. We validate our approach through extensive experiments on challenging high-dimensional tasks, including applications in peptide and molecular design. Experiments demonstrate MOCOBO's ability to find high-performing covering sets of solutions. Additionally, we show that the small sets of K < T solutions found by MOCOBO can match or nearly match the performance of T individually optimized solutions for the same objectives. Our results highlight MOCOBO's potential to tackle complex multi-objective problems in domains where finding at least one high-performing solution for each objective is critical.