{"ID":2831230,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.08671","arxiv_id":"2512.08671","title":"DS FedProxGrad: Asymptotic Stationarity Without Noise Floor in Fair Federated Learning","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.","short_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 explic...","url_abs":"https://arxiv.org/abs/2512.08671","url_pdf":"https://arxiv.org/pdf/2512.08671v4","authors":"[\"Huzaifa Arif\"]","published":"2025-12-09T14:55:21Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}