Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method

Bruno Barracosa (1, 2, 3) , Julien Bect (2, 3) , Héloïse Dutrieux Baraffe (1) , Juliette Morin (1) , Josselin Fournel (1) , Emmanuel Vazquez (2, 3)

1 EDF R&D SYSTEME
2 L2S - Laboratoire des signaux et systèmes
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

This article focuses on the multi-objective optimization of stochastic simulators with high output variance, where the input space is finite and the objective functions are expensive to evaluate. We rely on Bayesian optimization algorithms, which use probabilistic models to make predictions about the functions to be optimized. The proposed approach is an extension of the Pareto Active Learning (PAL) algorithm for the estimation of Pareto-optimal solutions that makes it suitable for the stochastic setting. We named it Pareto Active Learning for Stochastic Simulators (PALS). The performance of PALS is assessed through numerical experiments over a set of bi-dimensional, bi-objective test problems. PALS exhibits superior performance when compared to other scalarization-based and random-search approaches.

Mots clés: Multi-objective simulation optimization; Bayesian optimization; Stochastic simulator; Gaussian process modeling; Kriging

Domaines: Machine Learning [stat.ML]; Recherche opérationnelle [math.OC]

Bruno Barracosa, Julien Bect, Héloïse Dutrieux Baraffe, Juliette Morin, Josselin Fournel, et al.. Bayesian multi-objective optimization for stochastic simulators: an extension of the Pareto Active Learning method. 2022. ⟨hal-03714535v2⟩