A game theoretic perspective on Bayesian multi-objective optimization

Mickael Binois (1) , Abderrahmane Habbal (1) , Victor Picheny (2)

1 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
2 Secondmind

This chapter addresses the question of how to efficiently solve many-objective optimization problems in a computationally demanding black-box simulation context. We shall motivate the question by applications in machine learning and engineering, and discuss specific harsh challenges in using classical Pareto approaches when the number of objectives is four or more. Then, we review solutions combining approaches from Bayesian optimization, e.g., with Gaussian processes, and concepts from game theory like Nash equilibria, Kalai-Smorodinsky solutions and detail extensions like Nash-Kalai-Smorodinsky solutions. We finally introduce the corresponding algorithms and provide some illustrating results.

Domaines: Optimisation et contrôle [math.OC]

Mickael Binois, Abderrahmane Habbal, Victor Picheny. A game theoretic perspective on Bayesian multi-objective optimization. Many-Criteria Optimization and Decision Analysis: State-of-the-Art, Present Challenges, and Future Perspectives, 2023, 978-3-031-25263-1. ⟨10.1007/978-3-031-25263-1_11⟩. ⟨hal-03206174⟩