MLSep 17, 2025
On the Rate of Gaussian Approximation for Linear Regression ProblemsMarat Khusainov, Marina Sheshukova, Alain Durmus et al.
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 learning rate and study the explicit dependence of the convergence rate upon the problem dimension $d$ and quantities related to the design matrix. When the number of iterations $n$ is known in advance, our results yield the rate of normal approximation of order $\sqrt{\log{n}/n}$, provided that the sample size $n$ is large enough.