Section: New Results

The Kalai-Smorodinski solution for many-objective Bayesian optimization

Participants : Mickael Binois [Univ. Chicago] , Victor Picheny [INRA, Toulouse] , Abderrahmane Habbal.

Bayesian optimization methods are efficient to find solutions of multi-objective problems under very limited budgets of evaluation. An ongoing scope of research in multi-objective Bayesian optimization is to extend its applicability to a large number of objectives.

We have proposed in [127] a novel approach to solve Nash games with drastically limited budgets of evaluations based on GP regression, taking the form of a Bayesian optimization algorithm. Experiments on challenging benchmark problems demonstrate the potential of this approach compared to classical, derivative-based algorithms.

Regarding the harsh many-objective optimization problems, the recovering of the set of optimal compromise solution generally requires lots of observations while being less interpretable, since this set tends to grow larger with the number of objectives. We thus propose to focus on a choice of a specific solution originating from game theory, the Kalai-Smorodinski solution, that possesses attractive properties [22] [19]. We further make it insensitive to a monotone transformation of the objectives by considering the objectives in the copula space. A tailored algorithm is proposed to search for the solution, which is tested on a synthetic problem.