Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems

Takuya Kanayama, Yuki Ito, Tomoyuki Tamura, Masayuki Karasuyama
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:2661-2687, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-kanayama26a, title = {Information-Theoretic {Bayesian} Optimization for Bilevel Optimization Problems}, author = {Kanayama, Takuya and Ito, Yuki and Tamura, Tomoyuki and Karasuyama, Masayuki}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {2661--2687}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/kanayama26a/kanayama26a.pdf}, url = {https://proceedings.mlr.press/v337/kanayama26a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems %A Takuya Kanayama %A Yuki Ito %A Tomoyuki Tamura %A Masayuki Karasuyama %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-kanayama26a %I PMLR %P 2661--2687 %U https://proceedings.mlr.press/v337/kanayama26a.html %V 337 %X 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.
APA
Kanayama, T., Ito, Y., Tamura, T. & Karasuyama, M.. (2026). Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:2661-2687 Available from https://proceedings.mlr.press/v337/kanayama26a.html.

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