首次为联邦线性随机逼近提供高斯近似，量化通信与计算权衡。
Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximation
- 基于联邦学习的线性随机逼近，建立带通信-计算权衡的高斯近似
- 揭示局部步长、本地迭代次数和异质性对收敛速率的影响
- 提出在线乘子自助法，无需估计协方差矩阵即可推断最终结果
本文建立了联邦线性随机逼近（LSA）的Berry-Esseen型边界。我们的结果首次提供了显式捕捉通信-计算权衡和异质性感知误差项的联邦高斯近似，量化了局部步长、本地更新次数及异质性对收敛速率的影响。针对两种情形：(i) 固定步长，(ii) 步长递减且本地迭代次数增加，结果恢复了Bonnerjee等[2025]的近期率作为特例。作为主要应用，我们开发了一种针对最后迭代值的在线乘子自助程序，避免显式估计渐近协方差矩阵，并获得了该方法的非渐近有效性保证。
原文摘要 · Abstract (English)
In this paper, we establish Berry-Esseen-type bounds for federated linear stochastic approximation (LSA). Our results provide the first federated Gaussian approximations for LSA that explicitly capture communication-computation trade-offs and heterogeneity-aware error terms, quantifying the effects of local step size, number of local updates, and heterogeneity on convergence rates. We present results for both (i) constant step size regime and (ii) decreasing step size with an increasing number of local iterations, recovering the recent rates of Bonnerjee et al. [2025] as a special case. As a primary application of our results, we develop an online multiplier bootstrap procedure for inference on the last iterate, which avoids explicit estimation of the asymptotic covariance matrix, and obtain non-asymptotic validity guarantees for this procedure.
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