联邦线性随机逼近的高斯近似与乘子自助法
Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximation
Ilya Levin, Maksim Shuklin, Eric Moulines, Paul Mangold, Sergey Samsonov
AI 速览：该论文为联邦线性随机逼近建立Berry-Esseen型界与联邦高斯近似，并据此提出一种无需显式估计渐近协方差矩阵的在线乘子自助推断方法。
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.