Covering Multiple Objectives with a Small Set of Solutions Using Bayesian Optimization
Natalie Maus, Kyurae Kim, Yimeng Zeng, Haydn Jones, Fangping Wan, Marcelo Der Torossian Torres, Cesar de la Fuente-Nunez, Jacob Gardner
In multi-objective black-box optimization, the goal is typically to find solutions that optimize a set of $T$ black-box objective functions, $f_1, \ldots f_T$, 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 $f_1, \ldots f_T$, 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.