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 consider a problem setting that departs from this paradigm: finding a small set of K < T solutions, 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 experiments on challenging high-dimensional tasks, including applications in peptide and molecular design, where MOCOBO is shown to find high-performing covering sets of solutions. The results show that the coverage of the K < T solutions found by MOCOBO matches or nearly matches the coverage of T solutions obtained by optimizing each objective individually. Furthermore, in in vitro experiments, the peptides found by MOCOBO exhibited high potency against drug-resistant pathogens, further demonstrating the potential of MOCOBO for drug discovery.