arXiv:2605.19629 · v2
Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximation
摘要
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.
作者备注：The bootstrap validity theorem in the previous version was incorrect: it omitted a heterogeneity term of the same order as the leading fluctuation term. To address this issue, we now use the same bootstrap variables across clients, at the cost of losing the $N^{-1}$ factor in the leading term