Relative-Error Composite Federated Optimization with One Server-Side Proximal Step per Round
Abstract
We consider deterministic composite federated optimization, in which distributed smooth client objectives are combined with a shared, possibly nonsmooth, regularizer. We propose Relative-Error Composite FedDyn (REC-FedDyn), an inexact method that supports partial participation, with one server-side proximal evaluation per communication round. REC-FedDyn employs a directly testable relative-error criterion that allows each client to independently control the accuracy of its local subproblem, without a server-side acceptance test. We establish almost-sure iterate convergence for strongly convex and convex problems, almost-sure asymptotic stationarity for nonconvex problems, and communication and parallel gradient-evaluation complexity bounds, all under partial participation and without assuming bounded data heterogeneity. Experiments on image inpainting, fMRI prediction, and neural-network classification with structured regularization demonstrate efficiency and robustness across levels of data heterogeneity and client participation.
Related
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BibTeX
@misc{dai2026relativeerror,
title = {{Relative-Error Composite Federated Optimization with One Server-Side Proximal Step per Round}},
author = {Sirong Dai and Jianting Pan and Ming Yan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04448},
eprint = {2611.04448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04448},
}
RIS
TY - UNPB
TI - Relative-Error Composite Federated Optimization with One Server-Side Proximal Step per Round
AU - Sirong Dai
AU - Jianting Pan
AU - Ming Yan
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04448
UR - https://arxiv.org/abs/2611.04448
AB - We consider deterministic composite federated optimization, in which distributed smooth client objectives are combined with a shared, possibly nonsmooth, regularizer. We propose Relative-Error Composite FedDyn (REC-FedDyn), an inexact method that supports partial participation, with one server-side proximal evaluation per communication round. REC-FedDyn employs a directly testable relative-error criterion that allows each client to independently control the accuracy of its local subproblem, without a server-side acceptance test. We establish almost-sure iterate convergence for strongly convex and convex problems, almost-sure asymptotic stationarity for nonconvex problems, and communication and parallel gradient-evaluation complexity bounds, all under partial participation and without assuming bounded data heterogeneity. Experiments on image inpainting, fMRI prediction, and neural-network classification with structured regularization demonstrate efficiency and robustness across levels of data heterogeneity and client participation.
ER -