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Bilevel Optimization by Conditional Bayesian Optimization

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Machine Learning, Optimization, and Data Science (LOD 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14505))

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Abstract

Bilevel optimization problems have two decision-makers: a leader and a follower (sometimes more than one of either, or both). The leader must solve a constrained optimization problem in which some decisions are made by the follower. These problems are much harder to solve than those with a single decision-maker, and efficient optimal algorithms are known only for special cases. A recent heuristic approach is to treat the leader as an expensive black-box function, to be estimated by Bayesian optimization. We propose a novel approach called ConBaBo to solve bilevel problems, using a new conditional Bayesian optimization algorithm to condition previous decisions in the bilevel decision-making process. This allows it to extract knowledge from earlier decisions by both the leader and follower. We present empirical results showing that this enhances search performance and that ConBaBo outperforms some top-performing algorithms in the literature on two commonly used benchmark datasets.

This publication has emanated from research conducted with the financial support of Science Foundation Ireland under Grant number 16/RC/3918.

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Acknowledgements

This publication has emanated from research conducted with the financial support of Science Foundation Ireland under Grant number 16/RC/3918 which is co-funded under the European Regional Development Fund. For the purpose of Open Access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.

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Authors and Affiliations

  1. Confirm Centre for Smart Manufacturing, School of Computer Science and Information Technology, University College Cork, Cork, Ireland

    Vedat Dogan

  2. Insight Centre for Data Analytics, School of Computer Science and Information Technology, University College Cork, Cork, Ireland

    Steven Prestwich

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  1. Vedat Dogan
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  2. Steven Prestwich
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Correspondence to Vedat Dogan .

Editor information

Editors and Affiliations

  1. University of Catania, Catania, Catania, Italy

    Giuseppe Nicosia

  2. Newcastle University, Newcastle upon Tyne, UK

    Varun Ojha

  3. University of Oxford, Oxford, UK

    Emanuele La Malfa

  4. University of Cambridge, Cambridge, UK

    Gabriele La Malfa

  5. University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  6. Dana-Farber Cancer Institute, Boston, MA, USA

    Renato Umeton

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Dogan, V., Prestwich, S. (2024). Bilevel Optimization by Conditional Bayesian Optimization. In: Nicosia, G., Ojha, V., La Malfa, E., La Malfa, G., Pardalos, P.M., Umeton, R. (eds) Machine Learning, Optimization, and Data Science. LOD 2023. Lecture Notes in Computer Science, vol 14505. Springer, Cham. https://doi.org/10.1007/978-3-031-53969-5_19

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  • DOI: https://doi.org/10.1007/978-3-031-53969-5_19

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