Targeting Well-Balanced Solutions in Multi-Objective Bayesian Optimization under a Restricted Budget

David Gaudrie (1, 2, 3, 4, 5) , Rodolphe Le Riche (3, 1, 4, 5, 6) , Victor Picheny (7) , Benoît Enaux (2) , Vincent Herbert (2)

1 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
2 PSA Peugeot Citroën
3 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
4 FAYOL-ENSMSE - Institut Henri Fayol
5 FAYOL-ENSMSE - Département Génie mathématique et industriel
6 CNRS - Centre National de la Recherche Scientifique
7 MIAT INRA - Unité de Mathématiques et Informatique Appliquées de Toulouse

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 solutions with equilibrated trade-offs between the objectives , we define a Pareto front center. We then modify the Bayesian multi-objective optimization algorithm which uses Gaussian Processes to maximize the expected hypervolume improvement, to restrict the search to the Pareto front center. The cumulated effects of the Gaussian Processes and the center targeting strategy lead to a particularly efficient convergence to a critical part of the Pareto set.

Mots clés: Computer experiments; Preference-based optimization; Gaussian processes; Parsimonious optimization

Domaines: Autres [stat.ML]; Optimisation et contrôle [math.OC]

David Gaudrie, Rodolphe Le Riche, Victor Picheny, Benoît Enaux, Vincent Herbert. Targeting Well-Balanced Solutions in Multi-Objective Bayesian Optimization under a Restricted Budget. 12th International Conference on Learning and Intelligent Optimization, Jun 2018, Kalamata, Greece. pp 175-179, ⟨10.1007/978-3-030-05348-2_15⟩. ⟨hal-01883336⟩