A Parallel Technique for Multi-objective Bayesian Global Optimization: Using a Batch Selection of Probability of Improvement

TL;DR

This paper introduces five new batch Probability of Improvement methods for multi-objective Bayesian optimization, accounting for covariance among points, and demonstrates their effectiveness through extensive empirical testing on bio-objective benchmarks.

Contribution

It proposes novel q-PoI acquisition functions for parallel multi-objective Bayesian optimization, with formulas and algorithms, and evaluates their performance against existing methods.

Findings

Greedy q-PoIs excel on low-dimensional problems.

Explorative q-PoIs perform well on high-dimensional problems.

Two proposed q-PoIs outperform existing algorithms in benchmarks.

Abstract

Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluate the true-expensive objective functions in one iteration to boost the execution time. An effective and straightforward approach is to design an acquisition function that can evaluate the performance of a bath of multiple solutions, instead of a single point/solution, in one iteration. This paper proposes five alternatives of \emph{Probability of Improvement} (PoI) with multiple points in a batch (q-PoI) for multi-objective Bayesian global optimization (MOBGO), taking the covariance among multiple points into account. Both exact computational formulas and the Monte Carlo approximation algorithms for all proposed q-PoIs are provided. Based on the distribution of the multiple points relevant to the Pareto-front, the position-dependent behavior of the five q-PoIs is investigated. Moreover, the five q-PoIs are compared with the other nine state-of-the-art and recently proposed batch MOBGO algorithms on twenty bio-objective benchmarks. The empirical experiments on different variety of benchmarks are conducted to demonstrate the effectiveness of two greedy q-PoIs ($\kpoi_{\mbox{best}}$ and $\kpoi_{\mbox{all}}$) on low-dimensional problems and the effectiveness of two explorative q-PoIs ($\kpoi_{\mbox{one}}$ and $\kpoi_{\mbox{worst}}$) on high-dimensional problems with difficult-to-approximate Pareto front boundaries.