Targeting solutions in Bayesian multi-objective optimization: sequential and batch versions

• Published in: Annals of mathematics and artificial intelligence Vol. 88; no. 1-3; pp. 187 - 212
• Main Authors: Gaudrie, David, Le Riche, Rodolphe, Picheny, Victor, Enaux, Benoît, Herbert, Vincent
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2020; Springer; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Approximation; Artificial Intelligence; Bayesian analysis; Complex Systems; Computer Science; Design of experiments; Expected values; Gaussian process; Mathematics; Multiple objective analysis; Objectives; Optimization; Optimization and Control; Other Statistics; Pareto optimization; Pareto optimum; Statistics; Preference-based optimization; Computer experiments; Bayesian optimization; Parallel optimization; 65Kxx; Gaussian processes
• ISSN: 1012-2443; 1573-7470
• DOI: 10.1007/s10472-019-09644-8

Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for the entire set. As an end-user would typically prefer a certain part of the objective space, we modify the Bayesian multi-objective optimization algorithm which uses Gaussian Processes and works by maximizing the Expected Hypervolume Improvement, to focus the search in the preferred region. The cumulated effects of the Gaussian Processes and the targeting strategy lead to a particularly efficient convergence to the desired part of the Pareto set. To take advantage of parallel computing, a multi-point extension of the targeting criterion is proposed and analyzed.