On the Rate of Gaussian Approximation for Online Linear Regression Problems

Abstract

In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant stepsize and study the explicit dependence of the convergence rate on the problem dimension $d$ and quantities related to the design matrix. When the number of iterations $n$ is known in advance, our results yield a normal approximation rate of order $\sqrt{\log n/n}$, provided that the sample size $n$ is large enough.

arXiv commentPublished in Statistics (Taylor & Francis, 2026)