Bayesian Optimization of Bilevel Problems

• URL: http://arxiv.org/abs/2412.18518v1
• Date: Tue, 24 Dec 2024 15:55:30 GMT
• Title: Bayesian Optimization of Bilevel Problems
• Authors: Omer Ekmekcioglu, Nursen Aydin, Juergen Branke,
• Abstract summary: This paper focuses on bilevel optimization where both upper-level and lower-level functions are black boxes and expensive to evaluate. We propose a Bayesian Optimization framework that models the upper and lower-level functions as Gaussian processes over the combined space of upper and lower-level decisions. Our experimental results demonstrate that the proposed algorithm is highly sample-efficient and outperforms existing methods in finding high-quality solutions.
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• Abstract: Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics, engineering, and machine learning. This paper focuses on bilevel optimization where both upper-level and lower-level functions are black boxes and expensive to evaluate. We propose a Bayesian Optimization framework that models the upper and lower-level functions as Gaussian processes over the combined space of upper and lower-level decisions, allowing us to exploit knowledge transfer between different sub-problems. Additionally, we propose a novel acquisition function for this model. Our experimental results demonstrate that the proposed algorithm is highly sample-efficient and outperforms existing methods in finding high-quality solutions.

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