Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917294627618816 |
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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 |