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 three problems with respectively four, six, and ten objectives. The method is available in the package GPGame available on CRAN at
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Contributor : Mickaël Binois <>
Submitted on : Monday, February 18, 2019 - 2:23:14 PM
Last modification on : Wednesday, February 20, 2019 - 1:23:13 AM


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  • HAL Id : hal-01656393, version 2
  • ARXIV : 1902.06565


Mickaël Binois, Victor Picheny, Patrick Taillandier, Abderrahmane Habbal. The Kalai-Smorodinski solution for many-objective Bayesian optimization. BayesOpt workshop at NIPS 2017 - 31st Conference on Neural Information Processing Systems, Dec 2017, Long Beach, United States. pp.1-6. ⟨hal-01656393v2⟩



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