A fully Bayesian approach to bilevel problems

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dc.contributor.authorDogan, Vedaten
dc.contributor.authorPrestwich, Stevenen
dc.contributor.authorO'Sullivan, Barryen
dc.contributor.funderScience Foundation Irelanden
dc.date.accessioned2024-11-27T09:21:00Z
dc.date.available2024-11-27T09:21:00Z
dc.date.issued2024-10-16en
dc.description.abstractThe mathematical models of many real-world decision-making problems contain two levels of optimization. In these models, one of the optimization problems appears as a constraint of the other one, called follower and leader, respectively. These problems are known as bilevel optimization problems (BOPs) in mathematical programming and are widely studied by both classical and evolutionary optimization communities. The nested nature of these problems causes many difficulties such as non-convexity and disconnectedness for traditional methods, and requires a huge number of function evaluations for evolutionary algorithms. This paper proposes a fully Bayesian optimization approach, called FB-BLO. We aim to reduce the necessary function evaluations for both upper and lower level problems by iteratively approximating promising solutions with Gaussian process surrogate models at both levels. The proposed FB-BLO algorithm uses the other decision-makers’ observations in its Gaussian process model to leverage the correlation between decisions and objective values. This allows us to extract knowledge from previous decisions for each level. The algorithm has been evaluated on numerous benchmark problems and compared with existing state-of-the-art algorithms. Our evaluation demonstrates the success of our proposed FB-BLO algorithm in terms of both effectiveness and efficiency.en
dc.description.sponsorshipScience Foundation Ireland (12/RC/2289-P2)en
dc.description.statusPeer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationDogan, V., Prestwich, S. and O'Sullivan, B. (2024) 'A fully Bayesian approach to bilevel problems', in Freeman, R. and Mattei, N. (eds) Algorithmic Decision Theory. ADT 2024. Lecture Notes in Computer Science, 15248, pp. 144-159. Springer, Cham. https://doi.org/10.1007/978-3-031-73903-3_10en
dc.identifier.doi10.1007/978-3-031-73903-3_10en
dc.identifier.eissn1611-3349en
dc.identifier.endpage159en
dc.identifier.isbn9783031739026en
dc.identifier.isbn9783031739033en
dc.identifier.issn0302-9743en
dc.identifier.journaltitleLecture Notes in Computer Scienceen
dc.identifier.startpage144en
dc.identifier.urihttps://hdl.handle.net/10468/16681
dc.identifier.volume15248en
dc.language.isoenen
dc.publisherSpringer Natureen
dc.relation.ispartofLecture Notes in Computer Scienceen
dc.relation.ispartofAlgorithmic Decision Theoryen
dc.rights© 2024 The Author(s). Version of Record published under exclusive license to Springer Nature Switzerland. For Open Access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.en
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subjectBilevel decision-makingen
dc.subjectBayesian optimizationen
dc.subjectGaussian processen
dc.subjectStackelberg gamesen
dc.titleA fully Bayesian approach to bilevel problemsen
dc.typeArticle (peer-reviewed)en
dc.typeBook chapteren
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