DS FedProxGrad: Asymptotic Stationarity Without Noise Floor in Fair Federated Learning

• URL: http://arxiv.org/abs/2512.08671v3
• Date: Thu, 11 Dec 2025 02:35:40 GMT
• Title: DS FedProxGrad: Asymptotic Stationarity Without Noise Floor in Fair Federated Learning
• Abstract summary: We provide an improved convergence analysis for a Federated textttFedProxGrad-type analytical framework with inexact local solutions and explicit regularization.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent work \cite{arifgroup} introduced Federated Proximal Gradient \textbf{(\texttt{FedProxGrad})} for solving non-convex composite optimization problems in group fair federated learning. However, the original analysis established convergence only to a \textit{noise-dominated neighborhood of stationarity}, with explicit dependence on a variance-induced noise floor. In this work, we provide an improved asymptotic convergence analysis for a generalized \texttt{FedProxGrad}-type analytical framework with inexact local proximal solutions and explicit fairness regularization. We call this extended analytical framework \textbf{DS \texttt{FedProxGrad}} (Decay Step Size \texttt{FedProxGrad}). Under a Robbins-Monro step-size schedule \cite{robbins1951stochastic} and a mild decay condition on local inexactness, we prove that $\liminf_{r\to\infty} \mathbb{E}[\|\nabla F(\mathbf{x}^r)\|^2] = 0$, i.e., the algorithm is asymptotically stationary and the convergence rate does not depend on a variance-induced noise floor.

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