On the Rate of Gaussian Approximation for Online Linear Regression Problems
Marina Sheshukova
Alain Durmus
Marat Khusainov
Sergey Samsonov
Nov 2026
Machine Learning
Data Science
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.
