{"ID":2864906,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.21725","arxiv_id":"2509.21725","title":"Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems","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.","short_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 invo...","url_abs":"https://arxiv.org/abs/2509.21725","url_pdf":"https://arxiv.org/pdf/2509.21725v2","authors":"[\"Takuya Kanayama\",\"Yuki Ito\",\"Tomoyuki Tamura\",\"Masayuki Karasuyama\"]","published":"2025-09-26T00:52:14Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}