Warm-starting active-set solvers using graph neural networks

Ella J. Schmidtobreick, Daniel Arnström, Paul Häusner, Jens Sjölund
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:662-677, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-schmidtobreick26a, title = {Warm-starting active-set solvers using graph neural networks}, author = {Schmidtobreick, Ella J. and Arnstr\"om, Daniel and H\"ausner, Paul and Sj\"olund, Jens}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {662--677}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/schmidtobreick26a/schmidtobreick26a.pdf}, url = {https://proceedings.mlr.press/v331/schmidtobreick26a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Warm-starting active-set solvers using graph neural networks %A Ella J. Schmidtobreick %A Daniel Arnström %A Paul Häusner %A Jens Sjölund %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-schmidtobreick26a %I PMLR %P 662--677 %U https://proceedings.mlr.press/v331/schmidtobreick26a.html %V 331 %X 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.
APA
Schmidtobreick, E.J., Arnström, D., Häusner, P. & Sjölund, J.. (2026). Warm-starting active-set solvers using graph neural networks. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:662-677 Available from https://proceedings.mlr.press/v331/schmidtobreick26a.html.

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