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

2025/12/09 by Arif, Huzaifa
Computer Science · #Privacy-Preserving Technologies in Data #Stochastic Gradient Optimization Techniques #Distributed Control Multi-Agent Systems

paper · doi:10.48550/arxiv.2512.08671

Abstract

Recent work \citearifgroup introduced Federated Proximal Gradient \textbf(FedProxGrad) for solving non-convex composite optimization problems in group fair federated learning. However, the original analysis established convergence only to a 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 FedProxGrad-type analytical framework with inexact local proximal solutions and explicit fairness regularization. We call this extended analytical framework \textbfDS FedProxGrad (Decay Step Size FedProxGrad). Under a Robbins-Monro step-size schedule \citerobbins1951stochastic and a mild decay condition on local inexactness, we prove that \liminf_r→∞ 𝔼[‖∇ F(x^r)‖²] = 0, i.e., the algorithm is asymptotically stationary and the convergence rate does not depend on a variance-induced noise floor.

Citations

• Federated Optimization in Heterogeneous Networks
• A Stochastic Approximation Method

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