# Function-Space ADMM for Decentralized Federated Learning: A Control Theoretic Perspective Source: [Function-Space ADMM for Decentralized Federated Learning: A Control Theoretic Perspective]() Collection index: [llms.txt]() Data updated: 2026-05-13T05:00:12.693Z Authors: Akihito Taya, Yuuki Nishiyama, Kaoru Sezaki Published: 2026-05-10T06:11:46.000Z ## Abstract Decentralized federated learning (FL) is a promising approach for training machine learning models on sensor networks, Internet of Things (IoT) devices, and other edge systems where no central server exists. While federated learning offers advantages such as preserving data privacy, it often suffers from non-independent and identically distributed (IID) data distributions across devices, which cause significant performance degradation. This issue is particularly severe when directly optimizing model parameters, because neural network training is inherently non-convex and standard convergence guarantees for convex optimization do not apply. Unlike existing decentralized FL methods that primarily operate in parameter space, we propose federated function-space alternating direction method of multipliers (FedF-ADMM). FedF-ADMM exploits the convexity of loss functionals within function space to derive alternating direction method of multipliers (ADMM)-based update directions, which are subsequently projected onto the parameter space via knowledge distillation. We further introduce a stabilization coefficient to enhance robustness under severe non-IID settings and analyze its behavior from a control-theoretic perspective by interpreting it as a proportional-integral (PI) term. Experiments under challenging non-IID scenarios, including settings where each device has data from only a single label, demonstrate that FedF-ADMM achieves faster and more stable convergence than existing decentralized FL methods, while attaining higher accuracy and better consensus among devices. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on F-MNIST 500x2](): Image Classification; F-MNIST 500x2; Final Accuracy: 83.9. - [Image Classification on F-MNIST 1000x1](): Image Classification; F-MNIST 1000x1; Accuracy: 83. - [Image Classification on CIFAR-10 2500x2](): Image Classification; CIFAR-10 2500x2; Final Accuracy: 63.8. - [Image Classification on CIFAR-10 (5000x1)](): Image Classification; CIFAR-10 (5000x1); Final Accuracy: 61. - [Image Classification on F-MNIST Dirichlet](): Image Classification; F-MNIST Dirichlet; Final Accuracy (%): 84.8. - [Image Classification on CIFAR-10 Dirichlet](): Image Classification; CIFAR-10 Dirichlet; Final Accuracy: 65. ## Original sources and implementation [Original paper]() [PDF]()