The Kalai-Smorodinski solution for many-objective Bayesian optimization - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles (Review Article) Journal of Machine Learning Research Year : 2020

The Kalai-Smorodinski solution for many-objective Bayesian optimization

Abstract

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame.
Fichier principal
Vignette du fichier
ks_arxiv_v3.pdf (3.02 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01656393 , version 1 (05-12-2017)
hal-01656393 , version 2 (18-02-2019)
hal-01656393 , version 3 (02-10-2019)

Identifiers

  • HAL Id : hal-01656393 , version 3
  • ARXIV : 1902.06565
  • WOS : 000570113800001

Cite

Mickaël Binois, Victor Picheny, Patrick Taillandier, Abderrahmane Habbal. The Kalai-Smorodinski solution for many-objective Bayesian optimization. Journal of Machine Learning Research, 2020, 21 (150), pp.1-42. ⟨hal-01656393v3⟩
382 View
366 Download

Altmetric

Share

Gmail Facebook X LinkedIn More