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Theoretical analysis demonstrates normal approximation convergence rates in online linear regression, indicating explicit error bounds scaling with problem dimension.
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 logn/n, provided that the sample size n is large enough.
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Sheshukova et al. (2026) studied this question.
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