# Neur2BiLO: Neural Bilevel Optimization

arXiv: https://arxiv.org/abs/2402.02552 · HTML: https://mlsanity.com/paper/2402.02552/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 62 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 19 of 19)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond](https://mlsanity.com/paper/2101.11517/) (2021)
- [A Fully First-Order Method for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2301.10945/) (2023)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)
- [Mixed-Integer Optimization with Constraint Learning](https://mlsanity.com/paper/2111.04469/) (2021)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [JANOS: An Integrated Predictive and Prescriptive Modeling Framework](https://mlsanity.com/paper/1911.09461/) (2019)
- [Neur2SP: Neural Two-Stage Stochastic Programming](https://mlsanity.com/paper/2205.12006/) (2022)
- [PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs](https://mlsanity.com/paper/2312.08074/) (2023)
- [A Branch-and-Cut Algorithm for Mixed Integer Bilevel Linear Optimization Problems and Its Implementation](https://mlsanity.com/paper/2104.09010/) (2021)
- [Alternating mixed-integer programming and neural network training for approximating stochastic two-stage problems](https://mlsanity.com/paper/2305.06785/) (2023)
- [Bilevel Optimization based on Iterative Approximation of Multiple Mappings](https://mlsanity.com/paper/1702.03394/) (2017)
- [A Double-oracle, Logic-based Benders decomposition approach to solve the K-adaptability problem](https://mlsanity.com/paper/2209.02936/) (2022)
- [Solving Bilevel Knapsack Problem using Graph Neural Networks](https://mlsanity.com/paper/2211.13436/) (2022)
- [Deep Learning for Two-Stage Robust Integer Optimization](https://mlsanity.com/paper/2310.04345/) (2023)
- [An Exact Method for Fortification Games](https://mlsanity.com/paper/2111.13400/) (2021)
- [Integer Programming Games: A Gentle Computational Overview](https://mlsanity.com/paper/2306.02817/) (2023)

## Built on by (most cited first, 4 of 4)

- [Synergistic Localization and Sensing in MIMO-OFDM Systems via Mixed-Integer Bilevel Learning](https://mlsanity.com/paper/2507.07118/) (2025)
- [Graph4BiLO: Graph Neural Network Approximation for Bilevel Mixed-Integer Linear Optimization](https://mlsanity.com/paper/2608.30103/) (2026)
- [Probabilistic Multi-Source Data Selection via Learnable Categorical Priors: Variance Reduction and Guaranteed Derandomization](https://mlsanity.com/paper/2610.14942/) (2026)
- [Optimization for One, Feasibility for Most: Decoupling Optimization from Feasibility in Chance-Constrained Programs](https://mlsanity.com/paper/2610.19027/) (2026)

## Abstract (arXiv)

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.