2024/02/04 by Justin Dumouchelle, Esther Julien, Dumouchelle, Justin +5 · 1 citation
Computer Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2402.02552
openalex publication_date 2024/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.