# Data-driven Projection Generation for Efficiently Solving Heterogeneous Quadratic Programming Problems

arXiv: https://arxiv.org/abs/2510.26061 · HTML: https://mlsanity.com/paper/2510.26061/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 48 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [End-to-End Learning to Warm-Start for Real-Time Quadratic Optimization](https://mlsanity.com/paper/2212.08260/) (2022)
- [Efficient differentiable quadratic programming layers: an ADMM approach](https://mlsanity.com/paper/2112.07464/) (2021)
- [Deep Graph Matching under Quadratic Constraint](https://mlsanity.com/paper/2103.06643/) (2021)
- [Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs](https://mlsanity.com/paper/2406.05938/) (2024)
- [Revocable Deep Reinforcement Learning with Affinity Regularization for Outlier-Robust Graph Matching](https://mlsanity.com/paper/2012.08950/) (2020)
- [Generalization Bound and Learning Methods for Data-Driven Projections in Linear Programming](https://mlsanity.com/paper/2309.00203/) (2023)
- [Learning context-aware adaptive solvers to accelerate quadratic programming](https://mlsanity.com/paper/2211.12443/) (2022)
- [Ensemble Quadratic Assignment Network for Graph Matching](https://mlsanity.com/paper/2403.06457/) (2024)
- [Metric Learning to Accelerate Convergence of Operator Splitting Methods for Differentiable Parametric Programming](https://mlsanity.com/paper/2404.00882/) (2024)
- [On Representing Convex Quadratically Constrained Quadratic Programs via Graph Neural Networks](https://mlsanity.com/paper/2411.13805/) (2024)
- [Provably data-driven projection method for quadratic programming](https://mlsanity.com/paper/2509.04524/) (2025)
- [Random projection of Linear and Semidefinite problem with linear inequalities](https://mlsanity.com/paper/2007.00242/) (2020)
- [Column-Randomized Linear Programs: Performance Guarantees and Applications](https://mlsanity.com/paper/2007.10461/) (2020)
- [Random projections for conic programs](https://mlsanity.com/paper/2101.04182/) (2021)
- [Convexification with bounded gap for randomly projected quadratic optimization](https://mlsanity.com/paper/2107.05272/) (2021)

## Abstract (arXiv)

We propose a data-driven framework for efficiently solving quadratic programming (QP) problems by reducing the number of variables in high-dimensional QPs using instance-specific projection. A graph neural network-based model is designed to generate projections tailored to each QP instance, enabling us to produce high-quality solutions even for previously unseen problems. The model is trained on heterogeneous QPs to minimize the expected objective value evaluated on the projected solutions. This is formulated as a bilevel optimization problem; the inner optimization solves the QP under a given projection using a QP solver, while the outer optimization updates the model parameters. We develop an efficient algorithm to solve this bilevel optimization problem, which computes parameter gradients without backpropagating through the solver. We provide a theoretical analysis of the generalization ability of solving QPs with projection matrices generated by neural networks. Experimental results demonstrate that our method produces high-quality feasible solutions with reduced computation time, outperforming existing methods.