A New Acquisition Function for Multi-objective Bayesian Optimization: Correlated Probability of Improvement

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Abstract

Multi-objective Bayesian optimization is a sequential optimization strategy in which an optimizer searches for optimal solutions by maximizing an acquisition function. Most existing acquisition functions assume that objectives are independent, but none of them incorporates the correlations among objectives through an explicit formula for exact computation. This paper proposes a novel acquisition function, namely, correlated probability of improvement (cPoI), for bi-objective optimization problems. The cPoI method builds on the probability of improvement and addresses the correlations between objectives by utilizing 3 distinct approaches to compute the posterior covariance matrix from a multi-task Gaussian process. This paper presents both an explicit formula for exact computation of cPoI and a Monte Carlo method for approximating it. We evaluate the performance of the proposed cPoI against 4 state-of-the-art multi-objective optimization algorithms on 8 artificial benchmarks and 1 real-world problem. Our experimental results demonstrate the effectiveness of cPoI in achieving superior optimization performance.

Original languageEnglish
Title of host publicationGECCO 2023 Companion - Proceedings of the 2023 Genetic and Evolutionary Computation Conference Companion
PublisherAssociation for Computing Machinery, Inc
Pages2308-2317
Number of pages10
ISBN (Electronic)9798400701207
DOIs
Publication statusPublished - 15 Jul 2023
Event2023 Genetic and Evolutionary Computation Conference Companion, GECCO 2023 Companion - Lisbon, Portugal
Duration: 15 Jul 202319 Jul 2023

Publication series

NameGECCO 2023 Companion - Proceedings of the 2023 Genetic and Evolutionary Computation Conference Companion

Conference

Conference2023 Genetic and Evolutionary Computation Conference Companion, GECCO 2023 Companion
Country/TerritoryPortugal
CityLisbon
Period15.07.202319.07.2023

Keywords

  • Multi-objective Bayesian Optimization
  • Multi-task Gaussian Process
  • Posterior Covariance
  • Probability of Improvement

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