Probability Distribution of Hypervolume Improvement in Bi-objective Bayesian Optimization

arXiv:2205.05505v3 Announce Type: replace
Abstract: Hypervolume improvement (HVI) is commonly employed in multi-objective Bayesian optimization algorithms to define acquisition functions due to its Pareto-compliant property. Rather than focusing on specific statistical moments of HVI, this work aims to provide the exact expression of HVI's probability distribution for bi-objective problems. Considering a bi-variate Gaussian random variable resulting from Gaussian process (GP) modeling, we derive the probability distribution of its hypervolume improvement via a cell partition-based method. Our exact expression is superior …

abstract acquisition algorithms arxiv bayesian cs.lg distribution functions improvement moments multi-objective optimization pareto probability property statistical stat.ml type work