解决联邦学习中公平优化的噪声干扰问题，实现真正渐近平稳收敛。
DS FedProxGrad: Asymptotic Stationarity Without Noise Floor in Fair Federated Learning
- 采用衰减步长与局部近似误差控制，改进联邦近端梯度算法。
- 证明算法在无穷迭代下梯度范数期望趋于零，突破噪声下界限制。
- 适合关注公平性保障与理论稳健性的联邦学习研究者。
近期工作提出了联邦近端梯度（FedProxGrad）方法，用于求解群体公平联邦学习中的非凸复合优化问题。然而，原始分析仅能收敛到受方差驱动的噪声邻域，且存在显式的噪声下界。本文针对一种包含不精确局部近端解和显式公平正则化的广义FedProxGrad框架，提出改进的渐近收敛分析。该框架称为DS FedProxGrad（衰减步长FedProxGrad）。在Robbins-Monro型步长调度及局部近似误差的温和衰减条件下，证明了当迭代次数趋于无穷时，梯度范数期望的下极限为零（即 ↔∞ → Ε[∥∇F(ℓ)∥²] = 0），表明算法达到渐近平稳，且收敛速率不再受方差引起的噪声下界影响。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。