A game theoretic perspective on Bayesian multi-objective optimization

TL;DR

This paper explores how game theory and Bayesian optimization can be combined to efficiently solve many-objective black-box problems, especially when classical methods struggle with four or more objectives.

Contribution

It introduces a novel approach integrating game theory concepts with Bayesian optimization for multi-objective problems, including new algorithms and extensions.

Findings

Effective algorithms for many-objective optimization

Demonstrated improvements over classical Pareto methods

Application to machine learning and engineering problems

Abstract

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.