Learning to accelerate distributed ADMM using graph neural networks

Henri Doerks, Paul Häusner, Daniel Hernández Escobar, Jens Sjölund
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1995-2020, 2026.

Abstract

Distributed optimization is fundamental to large-scale machine learning and control applications. Among existing methods, the alternating direction method of multipliers (ADMM) has gained popularity due to its strong convergence guarantees and suitability for decentralized computation. However, ADMM can suffer from slow convergence and high sensitivity to hyperparameter choices. In this work, we show that distributed ADMM iterations can be naturally expressed within the message-passing framework of graph neural networks (GNNs). Building on this connection, we propose learning adaptive step sizes and communication weights through a GNN that predicts these yperparameters based on the current iterates. By unrolling ADMM for a fixed number of iterations, we train the network end-to-end to minimize the solution distance after these iterations for a given problem class, while preserving the algorithm’s convergence properties. Numerical experiments demonstrate that our learned variant consistently improves convergence speed and solution quality compared to standard ADMM, both within the trained computational budget and beyond.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-doerks26a, title = {Learning to accelerate distributed ADMM using graph neural networks}, author = {Doerks, Henri and H\"ausner, Paul and Escobar, Daniel Hern\'andez and Sj\"olund, Jens}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1995--2020}, 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/doerks26a/doerks26a.pdf}, url = {https://proceedings.mlr.press/v331/doerks26a.html}, abstract = {Distributed optimization is fundamental to large-scale machine learning and control applications. Among existing methods, the alternating direction method of multipliers (ADMM) has gained popularity due to its strong convergence guarantees and suitability for decentralized computation. However, ADMM can suffer from slow convergence and high sensitivity to hyperparameter choices. In this work, we show that distributed ADMM iterations can be naturally expressed within the message-passing framework of graph neural networks (GNNs). Building on this connection, we propose learning adaptive step sizes and communication weights through a GNN that predicts these yperparameters based on the current iterates. By unrolling ADMM for a fixed number of iterations, we train the network end-to-end to minimize the solution distance after these iterations for a given problem class, while preserving the algorithm’s convergence properties. Numerical experiments demonstrate that our learned variant consistently improves convergence speed and solution quality compared to standard ADMM, both within the trained computational budget and beyond.} }
Endnote
%0 Conference Paper %T Learning to accelerate distributed ADMM using graph neural networks %A Henri Doerks %A Paul Häusner %A Daniel Hernández Escobar %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-doerks26a %I PMLR %P 1995--2020 %U https://proceedings.mlr.press/v331/doerks26a.html %V 331 %X Distributed optimization is fundamental to large-scale machine learning and control applications. Among existing methods, the alternating direction method of multipliers (ADMM) has gained popularity due to its strong convergence guarantees and suitability for decentralized computation. However, ADMM can suffer from slow convergence and high sensitivity to hyperparameter choices. In this work, we show that distributed ADMM iterations can be naturally expressed within the message-passing framework of graph neural networks (GNNs). Building on this connection, we propose learning adaptive step sizes and communication weights through a GNN that predicts these yperparameters based on the current iterates. By unrolling ADMM for a fixed number of iterations, we train the network end-to-end to minimize the solution distance after these iterations for a given problem class, while preserving the algorithm’s convergence properties. Numerical experiments demonstrate that our learned variant consistently improves convergence speed and solution quality compared to standard ADMM, both within the trained computational budget and beyond.
APA
Doerks, H., Häusner, P., Escobar, D.H. & Sjölund, J.. (2026). Learning to accelerate distributed ADMM using graph neural networks. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1995-2020 Available from https://proceedings.mlr.press/v331/doerks26a.html.

Related Material