Is greed still good in multi-objective Bayesian optimisation?

Abstract

Bayesian optimisation (BO) is a popular tool for solving expensive optimisation problems. BO utilises Bayesian models and balances exploitation and exploration in searching for potential solutions. In this work, we investigate the trade-off between exploration and exploitation in multi-objective BO by comparing three different approaches: selecting points on the estimated Pareto front (PF) of the predicted values of the surrogate models, selecting points on the estimated PF of the predicted uncertainty of the models, and using an \egreedy approach to balance between the two PFs. We evaluate the performance of these approaches on a set of benchmark problems and compare them to a random baseline and expected hypervolume improvement (EHVI). It was found that the \egreedy and fully exploitative approaches were the best performing across all problem dimensionalities and that the performance of EHVI comparatively decreased as the dimensionality of the problem increased.