# Warm-starting active-set solvers using graph neural networks

arXiv: https://arxiv.org/abs/2511.13174 · HTML: https://mlsanity.com/paper/2511.13174/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 32 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 22 of 22)

- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [Large Scale Model Predictive Control with Neural Networks and Primal Active Sets](https://mlsanity.com/paper/1910.10835/) (2019)
- [End-to-End Learning to Warm-Start for Real-Time Quadratic Optimization](https://mlsanity.com/paper/2212.08260/) (2022)
- [Neural incomplete factorization: learning preconditioners for the conjugate gradient method](https://mlsanity.com/paper/2305.16368/) (2023)
- [Expressive Power of Graph Neural Networks for (Mixed-Integer) Quadratic Programs](https://mlsanity.com/paper/2406.05938/) (2024)
- [Accelerated Forward-Backward Optimization using Deep Learning](https://mlsanity.com/paper/2105.05210/) (2021)
- [Deep Distributed Optimization for Large-Scale Quadratic Programming](https://mlsanity.com/paper/2412.12156/) (2024)
- [Graph-based Neural Acceleration for Nonnegative Matrix Factorization](https://mlsanity.com/paper/2202.00264/) (2022)
- [Learning incomplete factorization preconditioners for GMRES](https://mlsanity.com/paper/2409.08262/) (2024)
- [Learning Algorithm Hyperparameters for Fast Parametric Convex Optimization](https://mlsanity.com/paper/2411.15717/) (2024)
- [An Efficiently Solvable Quadratic Program for Stabilizing Dynamic Locomotion](https://mlsanity.com/paper/1311.1839/) (2013)
- [A Dual Active-Set Solver for Embedded Quadratic Programming Using Recursive LDL' Updates](https://mlsanity.com/paper/2103.16236/) (2021)
- [TransformerMPC: Accelerating Model Predictive Control via Transformers](https://mlsanity.com/paper/2409.09266/) (2024)
- [IPM-LSTM: A Learning-Based Interior Point Method for Solving Nonlinear Programs](https://mlsanity.com/paper/2410.15731/) (2024)
- [Learning to accelerate distributed ADMM using graph neural networks](https://mlsanity.com/paper/2509.05288/) (2025)

## Built on by (most cited first, 2 of 2)

- [Memory-Computation Tradeoffs in Semi Amortized Parametric Optimization](https://mlsanity.com/paper/2607.20769/) (2026)
- [AT-SKM-Net: An Accelerated Trainable Sampling Kaczmarz-Motzkin Framework for Linear Hard-Constraint Feasibility on Dynamic Graphs](https://mlsanity.com/paper/2609.30088/) (2026)

## Abstract (arXiv)

Quadratic programming (QP) solvers are widely used in real-time control and optimization, but their computational cost often limits applicability in time-critical settings. To resolve this, we propose a learning-to-optimize approach using graph neural networks (GNNs) to predict active constraints in the dual active-set solver DAQP. Our method exploits the structural properties of QPs by representing them as bipartite graphs and learns to approximate the optimal active set for effectively warm-starting the solver. Across varying problem sizes, the GNN consistently reduces the number of solver iterations compared to cold-starting, while performance is comparable to a multilayer perceptron baseline. In contrast to the baseline, our GNN-based approach trained on varying problem sizes generalizes to unseen dimensions, demonstrating flexibility and scalability. These results highlight the potential of structure-aware learning to accelerate optimization in real-time applications such as model predictive control.