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A Game Theoretic Perspective on Bayesian Many-Objective Optimization

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Many-Criteria Optimization and Decision Analysis

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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.

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Author information

Authors and Affiliations

  1. LJAD, CNRS, Inria, Université Côte d’Azur, Sophia Antipolis, Nice, France

    Mickaël Binois

  2. LJAD, UMR 7351, CNRS, Inria, Université Côte d’Azur, Nice, France

    Abderrahmane Habbal

  3. Secondmind, Cambridge, UK

    Victor Picheny

Authors
  1. Mickaël Binois
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  2. Abderrahmane Habbal
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  3. Victor Picheny
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Corresponding author

Correspondence to Mickaël Binois .

Editor information

Editors and Affiliations

  1. Inria Saclay-Île-de-France and CMAP, École Polytechnique, Palaiseau, France

    Dimo Brockhoff

  2. Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands

    Michael Emmerich

  3. Informatik und Ingenieurwissenschaften, TH Köln, Gummersbach, Germany

    Boris Naujoks

  4. Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK

    Robin Purshouse

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Binois, M., Habbal, A., Picheny, V. (2023). A Game Theoretic Perspective on Bayesian Many-Objective Optimization. In: Brockhoff, D., Emmerich, M., Naujoks, B., Purshouse, R. (eds) Many-Criteria Optimization and Decision Analysis. Natural Computing Series. Springer, Cham. https://doi.org/10.1007/978-3-031-25263-1_11

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  • DOI: https://doi.org/10.1007/978-3-031-25263-1_11

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  • Online ISBN: 978-3-031-25263-1

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