Neur2BiLO: Neural Bilevel Optimization

Justin Dumouchelle, Esther Julien, Jannis Kurtz, Elias Boutros Khalil

Keywords: bilevel optimization, machine learning, discrete optimization, integer programming

TL;DR: This work proposes a learning-based approach for quickly computing high-quality solutions for several challenging classes bilevel optimization problems (linear/non-linear, integer/mixed-integer) via learning-based value function approximation.

Abstract: 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.

Primary Area: Optimization (convex and non-convex, discrete, stochastic, robust)

Submission Number: 9612