Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximation
Authors: Ilya Levin, Maksim Shuklin, Eric Moulines et al.
Summary
arXiv:2605. 19629v1 Announce Type: new Abstract: In this paper, we establish Berry-Esseen-type bounds for federated linear stochastic approximation (LSA).
Relevance
Read next because Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximation overlaps with clean result "The marker is a representational handle, not a behavioural one — sharing it between a villain persona and the assistant transfers no misalignment (HIGH confidence)", experiment "#351 follow-up: broader-vocab position-0 sweep at T=1.0 + position-1 suffix isolation". Matching terms: line, rate. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.19629v1 Announce Type: new Abstract: 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.