Neur2BiLO: Neural Bilevel Optimization
<|reference_start|>Neur2BiLO: Neural Bilevel Optimization: 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 the bilevel knapsack interdiction problem, the "critical node game" from network security, a donor-recipient healthcare problem, and discrete network design from transportation planning. These problems are diverse in that they have linear or non-linear objectives/constraints and integer or mixed-integer variables, making Neur2BiLO unique in its versatility.<|reference_end|>
@article{dumouchelle2024neur2bilo:,
    title={Neur2BiLO: Neural Bilevel Optimization},
    author={Justin Dumouchelle, Esther Julien, Jannis Kurtz, Elias B. Khalil},
    journal={arXiv preprint arXiv:2402.02552},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.02552},
    primaryClass={math.OC cs.AI cs.LG}
}