# Learning to accelerate distributed ADMM using graph neural networks

arXiv: https://arxiv.org/abs/2509.05288 · HTML: https://mlsanity.com/paper/2509.05288/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 47 references that are in the map.
- First posted on arXiv 5 Sep 2025.

## Builds on (most cited first, 29 of 29)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Neural Algorithmic Reasoning](https://mlsanity.com/paper/2105.02761/) (2021)
- [Tutorial on amortized optimization](https://mlsanity.com/paper/2202.00665/) (2022)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [Exploring the Power of Graph Neural Networks in Solving Linear Optimization Problems](https://mlsanity.com/paper/2310.10603/) (2023)
- [Neural incomplete factorization: learning preconditioners for the conjugate gradient method](https://mlsanity.com/paper/2305.16368/) (2023)
- [Convergence Rate of Distributed ADMM over Networks](https://mlsanity.com/paper/1601.00194/) (2016)
- [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)
- [Greedy Low-Rank Gradient Compression for Distributed Learning with Convergence Guarantees](https://mlsanity.com/paper/2507.08784/) (2025)
- [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)
- [Convergence for nonconvex ADMM, with applications to CT imaging](https://mlsanity.com/paper/2006.07278/) (2020)
- [Accelerating ADMM for Efficient Simulation and Optimization](https://mlsanity.com/paper/1909.00470/) (2019)
- [Learning Algorithm Hyperparameters for Fast Parametric Convex Optimization](https://mlsanity.com/paper/2411.15717/) (2024)
- [Principled Acceleration of Iterative Numerical Methods Using Machine Learning](https://mlsanity.com/paper/2206.08594/) (2022)
- [Greedy Learning to Optimize with Convergence Guarantees](https://mlsanity.com/paper/2406.00260/) (2024)
- [A Mathematics-Inspired Learning-to-Optimize Framework for Decentralized Optimization](https://mlsanity.com/paper/2410.01700/) (2024)
- [Gradient Methods with Online Scaling Part I. Theoretical Foundations](https://mlsanity.com/paper/2505.23081/) (2025)
- [Privacy-Preserving Distributed Optimization and Learning](https://mlsanity.com/paper/2403.00157/) (2024)
- [Q-SHED: Distributed Optimization at the Edge via Hessian Eigenvectors Quantization](https://mlsanity.com/paper/2305.10852/) (2023)

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

- [Warm-starting active-set solvers using graph neural networks](https://mlsanity.com/paper/2511.13174/) (2025)
- [Learning Multi-Agent Coordination via Sheaf-ADMM](https://mlsanity.com/paper/2605.31005/) (2026)
- [Deep-Unfolded Coordination](https://mlsanity.com/paper/2606.19920/) (2026)

## Abstract (arXiv)

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. The code is available at https://github.com/paulhausner/learning-distributed-admm.