Learning to accelerate distributed ADMM using graph neural networks

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.