Neur2BiLO: Neural Bilevel Optimization
This provides a fast heuristic for practitioners dealing with complex bilevel optimization problems, though it is incremental as it builds on existing data-driven and neural network methods.
The paper tackles the challenge of solving constrained bilevel optimization problems with integer variables, which are notoriously hard and scale poorly, by proposing Neur2BiLO, a neural network-based heuristic that embeds approximations into mixed-integer programs to produce high-quality solutions quickly for various applications.
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.