Neur2BiLO: Neural Bilevel Optimization

Bilevel optimization deals with nested problems in which 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.

Authors

• Justin Dumouchelle
• Esther Julien
• Jannis Kurtz University of Amsterdam, Amsterdam Business School, Business Analytics Section
• Elias B. Khalil Department of Mechanical and Industrial Engineering, University of Toronto

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