Probability of Matching for Batch Multi-Objective Bayesian Optimization

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 (POM), which evaluates both batch candidate quality and diversity by explicitly capturing 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 non-replacement sampling principles, resulting in our new POM-guided batch MOBO method. Across synthetic benchmarks and real-world tasks, our method 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.

Multi-objective optimization is widely used in science and engineering when several competing goals, such as cost, strength, or efficiency must be optimized simultaneously. Existing optimization methods typically rely on additional hyperparameters or hybrid strategies to balance solutions' “diversity” and “quality.” However, the true distribution of optimal solutions is generally unknown beforehand, making such assumptions difficult to justify. This paper introduces Probability of Matching (POM), the first unified optimization strategy that directly searches for the complete Pareto front by estimating and maximizing the probability that an acquired batch matches the true Pareto-optimal set, without requiring separate diversity tuning or policy switching. Experiments on benchmark and real-world materials design problems show that POM consistently discovers broader and higher-quality Pareto fronts than existing methods while maintaining similar computational cost.