A fully Bayesian approach to bilevel problems
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Accepted Version
Date
2024-10-16
Authors
Dogan, Vedat
Prestwich, Steven
O’Sullivan, Barry
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Nature
Published Version
Abstract
The 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.
Description
Keywords
Bilevel decision-making , Bayesian optimization , Gaussian process , Stackelberg games
Citation
Dogan, 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_10