# Learning to Solve Bilevel Programs with Binary Tender

arXiv: https://arxiv.org/abs/2407.16914 · HTML: https://mlsanity.com/paper/2407.16914/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2024.

## Built on by (most cited first, 3 of 3)

- [Estimating the Unobservable Components of Electricity Demand Response with Inverse Optimization](https://mlsanity.com/paper/2410.02774/) (2024)
- [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)

## Abstract (arXiv)

Bilevel programs (BPs) find a wide range of applications in fields such as energy, transportation, and machine learning. As compared to BPs with continuous (linear/convex) optimization problems in both levels, the BPs with discrete decision variables have received much less attention, largely due to the ensuing computational intractability and the incapability of gradient-based algorithms for handling discrete optimization formulations. In this paper, we develop deep learning techniques to address this challenge. Specifically, we consider a BP with binary tender, wherein the upper and lower levels are linked via binary variables. We train a neural network to approximate the optimal value of the lower-level problem, as a function of the binary tender. Then, we obtain a single-level reformulation of the BP through a mixed-integer representation of the value function. Furthermore, we conduct a comparative analysis between two types of neural networks: general neural networks and the novel input supermodular neural networks, studying their representational capacities. To solve high-dimensional BPs, we introduce an enhanced sampling method to generate higher-quality samples and implement an iterative process to refine solutions. We demonstrate the performance of these approaches through extensive numerical experiments, whose lower-level problems are linear and mixed-integer programs, respectively.