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

2025-01-31

AI Summary

In multi-objective black-box optimization, practitioners often need to simultaneously optimize T independent objectives, yet deployment constraints severely limit the number of solutions (K) that can be implemented—where K ≪ T. Method: This paper introduces “multi-objective coverage,” a novel paradigm that seeks a sparse solution set of size K < T capable of high-quality coverage across all T objectives. We establish a theoretical framework with coverage guarantees and derive an optimality criterion for sparse solution sets. We further propose Multi-Objective Coverage Bayesian Optimization (MOCOBO), which integrates a coverage-aware acquisition function with joint uncertainty modeling over objectives. Results: On peptide and molecular design benchmarks, MOCOBO achieves full coverage of all T objectives using only K solutions—matching the performance of T individually optimized solutions—while drastically improving practicality and deployment efficiency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Multi-objective optimization
• Black-box optimization
• Solution coverage

Innovation

• Multi-Objective Coverage Bayesian Optimization
• Complex Multi-Objective Problems
• Peptide and Molecular Design