arXiv:2503.06078cs.LGcs.IT2025-03中稿 · IEEE Transactions …被引 3

解决无线异构环境下联邦学习的偏差问题,提升模型收敛速度。

Biased Federated Learning under Wireless Heterogeneity

  • 提出新型模拟与数字通信策略,允许结构化偏差以降低更新方差。
  • 理论证明偏差与方差权衡受设计参数影响,可量化优化目标。
  • 适用于设备信道条件差异大的真实无线场景,尤其适合移动边缘计算。

联邦学习(FL)作为分布式学习的有前景框架,可在不共享私有数据的情况下实现协同模型训练。现有无线联邦学习工作主要采用两种通信策略:(1) 过空气(OTA)计算,利用无线信号叠加实现梯度同时聚合;(2) 数字通信,为梯度上传分配正交资源。以往研究通常假设无线条件同质(各设备路径损耗相等),以保证无偏差更新或容忍不可控偏差,导致在异构环境中性能下降且模型更新方差高,信道差的设备会拖慢收敛。本文针对异构无线网络中的联邦学习,提出新型的OTA和数字联邦学习更新机制,允许结构化的、时不变的模型偏差,从而减少更新方差。我们在统一框架下分析其收敛性,并推导出模型“最优性误差”的上界,明确量化了偏差与方差对设计参数的依赖关系。为优化这一权衡,我们研究一个非凸优化问题,提出基于逐次凸逼近(SCA)的联合优化框架。通过大量数值实验,对比多种设计变体与现有先进方案,结果表明,在允许结构化偏差并最小化偏差-方差权衡时,本方法比现有方案具有更优的联邦学习收敛性能。

原文摘要 · Abstract (English)

Federated learning (FL) has emerged as a promising framework for distributed learning, enabling collaborative model training without sharing private data. Existing wireless FL works primarily adopt two communication strategies: (1) over-the-air (OTA) computation, which exploits wireless signal superposition for simultaneous gradient aggregation, and (2) digital communication, which allocates orthogonal resources for gradient uploads. Prior works on both schemes typically assume \emph{homogeneous} wireless conditions (equal path loss across devices) to enforce zero-bias updates or permit uncontrolled bias, resulting in suboptimal performance and high-variance model updates in \emph{heterogeneous} environments, where devices with poor channel conditions slow down convergence. This paper addresses FL over heterogeneous wireless networks by proposing novel OTA and digital FL updates that allow a structured, time-invariant model bias, thereby reducing variance in FL updates. We analyze their convergence under a unified framework and derive an upper bound on the model ``optimality error", which explicitly quantifies the effect of bias and variance in terms of design parameters. Next, to optimize this trade-off, we study a non-convex optimization problem and develop a successive convex approximation (SCA)-based framework to jointly optimize the design parameters. We perform extensive numerical evaluations with several related design variants and state-of-the-art OTA and digital FL schemes. Our results confirm that minimizing the bias-variance trade-off while allowing a structured bias provides better FL convergence performance than existing schemes.

联邦学习无线异构偏差控制

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