2021/04/29 by Mickaël Binois, Binois, Mickael, Abderrahmane Habbal +3
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Advanced Multi-Objective Optimization Algorithms #FOS: Mathematics #Machine Learning and Algorithms #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2104.14456
openalex publication_date 2021/04/29 · openalex created_date 2023/07/29 · openalex updated_date 2026/07/28
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.