Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement

Optimizing multiple competing black-box objectives is a challenging problem in many fields, including science, engineering, and machine learning. Multi-objective Bayesian optimization is a powerful approach for identifying the optimal trade-offs between the objectives with very few function evaluations. However, existing methods tend to perform poorly when observations are corrupted by noise, as they do not take into account uncertainty in the true Pareto frontier over the previously evaluated designs. We propose a novel acquisition function, NEHVI, that overcomes this important practical limitation by applying a Bayesian treatment to the popular expected hypervolume improvement criterion to integrate over this uncertainty in the Pareto frontier. We further argue that, even in the noiseless setting, the problem of generating multiple candidates in parallel reduces that of handling uncertainty in the Pareto frontier. Through this lens, we derive a natural parallel variant of NEHVI that can efficiently generate large batches of candidates. We provide a theoretical convergence guarantee for optimizing a Monte Carlo estimator of NEHVI using exact sample-path gradients. Empirically, we show that NEHVI achieves state-of-the-art performance in noisy and large-batch environments.