Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems

Fuente: arXiv
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Hauptverfasser: Kanayama, Takuya, Ito, Yuki, Tamura, Tomoyuki, Karasuyama, Masayuki
Format: Preprint
Veröffentlicht: 2025
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author Kanayama, Takuya
Ito, Yuki
Tamura, Tomoyuki
Karasuyama, Masayuki
author_facet Kanayama, Takuya
Ito, Yuki
Tamura, Tomoyuki
Karasuyama, Masayuki
contents A bilevel optimization problem consists of two optimization problems nested as an upper- and a lower-level problem, in which the optimality of the lower-level problem defines a constraint for the upper-level problem. This paper considers Bayesian optimization (BO) for the case that both the upper- and lower-levels involve expensive black-box functions. Because of its nested structure, bilevel optimization has a complex problem definition, by which bilevel BO has not been widely studied compared with other standard extensions of BO such as multi-objective or constraint problems. We propose an information-theoretic approach that considers the information gain of both the upper- and lower-optimal solutions and values. This enables us to define a unified criterion that measures the benefit for both level problems, simultaneously. Further, we also show a practical lower bound based approach to evaluating the information gain. We empirically demonstrate the effectiveness of our proposed method through several benchmark datasets.
format Preprint
id arxiv_https___arxiv_org_abs_2509_21725
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems
Kanayama, Takuya
Ito, Yuki
Tamura, Tomoyuki
Karasuyama, Masayuki
Machine Learning
A bilevel optimization problem consists of two optimization problems nested as an upper- and a lower-level problem, in which the optimality of the lower-level problem defines a constraint for the upper-level problem. This paper considers Bayesian optimization (BO) for the case that both the upper- and lower-levels involve expensive black-box functions. Because of its nested structure, bilevel optimization has a complex problem definition, by which bilevel BO has not been widely studied compared with other standard extensions of BO such as multi-objective or constraint problems. We propose an information-theoretic approach that considers the information gain of both the upper- and lower-optimal solutions and values. This enables us to define a unified criterion that measures the benefit for both level problems, simultaneously. Further, we also show a practical lower bound based approach to evaluating the information gain. We empirically demonstrate the effectiveness of our proposed method through several benchmark datasets.
title Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems
topic Machine Learning
url https://arxiv.org/abs/2509.21725