Neur2BiLO: Neural Bilevel Optimization
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912098859089920 |
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| author | Dumouchelle, Justin Julien, Esther Kurtz, Jannis Khalil, Elias B. |
| author_facet | Dumouchelle, Justin Julien, Esther Kurtz, Jannis Khalil, Elias B. |
| contents | Bilevel optimization deals with nested problems in which a leader takes the first decision to minimize their objective function while accounting for a follower's best-response reaction. Constrained bilevel problems with integer variables are particularly notorious for their hardness. While exact solvers have been proposed for mixed-integer linear bilevel optimization, they tend to scale poorly with problem size and are hard to generalize to the non-linear case. On the other hand, problem-specific algorithms (exact and heuristic) are limited in scope. Under a data-driven setting in which similar instances of a bilevel problem are solved routinely, our proposed framework, Neur2BiLO, embeds a neural network approximation of the leader's or follower's value function, trained via supervised regression, into an easy-to-solve mixed-integer program. Neur2BiLO serves as a heuristic that produces high-quality solutions extremely fast for four applications with linear and non-linear objectives and pure and mixed-integer variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02552 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neur2BiLO: Neural Bilevel Optimization Dumouchelle, Justin Julien, Esther Kurtz, Jannis Khalil, Elias B. Optimization and Control Artificial Intelligence Machine Learning Bilevel optimization deals with nested problems in which a leader takes the first decision to minimize their objective function while accounting for a follower's best-response reaction. Constrained bilevel problems with integer variables are particularly notorious for their hardness. While exact solvers have been proposed for mixed-integer linear bilevel optimization, they tend to scale poorly with problem size and are hard to generalize to the non-linear case. On the other hand, problem-specific algorithms (exact and heuristic) are limited in scope. Under a data-driven setting in which similar instances of a bilevel problem are solved routinely, our proposed framework, Neur2BiLO, embeds a neural network approximation of the leader's or follower's value function, trained via supervised regression, into an easy-to-solve mixed-integer program. Neur2BiLO serves as a heuristic that produces high-quality solutions extremely fast for four applications with linear and non-linear objectives and pure and mixed-integer variables. |
| title | Neur2BiLO: Neural Bilevel Optimization |
| topic | Optimization and Control Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2402.02552 |