Title: Probability of Matching for Pareto Coverage
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Multi-objective Bayesian Optimization, Pareto front, Probability of Matching, Hypervolume, Space filling

Abstract: In batch multi-objective Bayesian optimization (MOBO), it is often desirable to identify the whole Pareto optimal set, especially when considering the complicated interplay between different design criteria and constraints. This poses unique challenges in acquiring batches of both high quality and diversity to cover the Pareto front. We propose a novel acquisition strategy, Probability of Matching, which evaluates both batch candidate quality and diversity by explicitly capturing the likelihood that a batch matches the true Pareto set. This is achieved by factorizing the probability into two components: the likelihood that all batch points are Pareto optimal, and the probability that they collectively cover the full Pareto set. To estimate the coverage probability and promote diversity, we incorporate space-filling design principles, resulting in our space-filling qEHVI (qEHVI-SF), a new batch MOBO method. Across synthetic benchmarks and real-world tasks, qEHVI-SF consistently outperforms state-of-the-art baselines on standard MOBO metrics as well as a new design-space coverage metric, Expected Minimum Distance (EMD), with comparable computational efficiency.