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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.08671 |
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| _version_ | 1866908780400214016 |
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| author | Arif, Huzaifa |
| author_facet | Arif, Huzaifa |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08671 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | DS FedProxGrad: Asymptotic Stationarity Without Noise Floor in Fair Federated Learning Arif, Huzaifa Machine Learning 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. |
| title | DS FedProxGrad: Asymptotic Stationarity Without Noise Floor in Fair Federated Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2512.08671 |