A fully Bayesian approach to bilevel problems

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dc.contributor.authorDogan, Vedaten
dc.contributor.authorPrestwich, Steven D.en
dc.contributor.authorO'Sullivan, Barryen
dc.contributor.funderScience Foundation Irelanden
dc.date.accessioned2024-10-22T15:40:08Z
dc.date.available2024-10-22T15:40:08Z
dc.date.issued2024en
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 efficiencyen
dc.description.sponsorshipScience Foundation Ireland (Grant 12/RC/2289 - P2)en
dc.description.statusPeer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationDogan V.; Preswich S. and O'Sullivan B. (2024) 'A fully Bayesian approach to bilevel problems', 9th International Conference on Algorithmic Decision Theory (ADT 2024), 14-16 October, New Jersey, USA.en
dc.identifier.issued1en
dc.identifier.startpage15en
dc.identifier.urihttps://hdl.handle.net/10468/16595
dc.language.isoenen
dc.rights© 2024 The Authors.en
dc.subjectBilevel decision-makingen
dc.subjectBayesian optimizationen
dc.subjectGaussian processen
dc.subjectStackelberg gamesen
dc.titleA fully Bayesian approach to bilevel problemsen
dc.typeConference itemen
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