Probability Distribution of Hypervolume Improvement in Bi-objective Bayesian Optimization. (arXiv:2205.05505v1 [cs.LG])

This work provides the exact expression of the probability distribution of
the hypervolume improvement (HVI) for bi-objective generalization of Bayesian
optimization. Here, instead of a single-objective improvement, we consider the
improvement of the hypervolume indicator concerning the current best
approximation of the Pareto front. Gaussian process regression models are
trained independently on both objective functions, resulting in a bi-variate
separated Gaussian distribution serving as a predictive model for the
vector-valued objective function. Some commonly HVI-based acquisition functions
(probability of improvement …

arxiv bayesian bi distribution improvement optimization probability