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Function-Space ADMM for Decentralized Federated Learning: A Control Theoretic Perspective
Akihito Taya · 2026-05-12 · via cs.LG updates on arXiv.org

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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.
Comments: (c) 2026 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works
Subjects: Machine Learning (cs.LG); Networking and Internet Architecture (cs.NI)
Cite as: arXiv:2605.09356 [cs.LG]
  (or arXiv:2605.09356v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2605.09356

arXiv-issued DOI via DataCite (pending registration)

Journal reference: IEEE Internet of Things Journal, 2026
Related DOI: https://doi.org/10.1109/jiot.2026.3690200

DOI(s) linking to related resources

Submission history

From: Akihito Taya [view email]
[v1] Sun, 10 May 2026 06:11:46 UTC (9,421 KB)