Bilevel optimization by conditional Bayesian optimization

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Date
2024-02-16
Authors
Dogan, Vedat
Prestwich, Steven
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Springer Nature Ltd.
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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.
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Keywords
Bilevel optimization , Conditional Bayesian optimization , Stackelberg Games , Gaussian process
Citation
Dogan, V. and Prestwich, S. (2024)'Bilevel optimization by conditional Bayesian optimization', in Nicosia, G., Ojha, V., La Malfa, E., La Malfa, G., Pardalos, P. M. and Umeton, R. (eds) Machine Learning, Optimization, and Data Science. LOD 2023. Lecture Notes in Computer Science, 14505, pp. 243-258. Springer, Cham. https://doi.org/10.1007/978-3-031-53969-5_19
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