# On the Rate of Gaussian Approximation for Linear Regression Problems

arXiv: https://arxiv.org/abs/2509.14039 · HTML: https://mlsanity.com/paper/2509.14039/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 17 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [A Finite Time Analysis of Temporal Difference Learning With Linear Function Approximation](https://mlsanity.com/paper/1806.02450/) (2018)
- [On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentration](https://mlsanity.com/paper/2004.04719/) (2020)
- [An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Bias](https://mlsanity.com/paper/2006.07904/) (2020)
- [Finite-time High-probability Bounds for Polyak-Ruppert Averaged Iterates of Linear Stochastic Approximation](https://mlsanity.com/paper/2207.04475/) (2022)
- [A Tale of Two-Timescale Reinforcement Learning with the Tightest Finite-Time Bound](https://mlsanity.com/paper/1911.09157/) (2019)
- [Normal Approximation for Stochastic Gradient Descent via Non-Asymptotic Rates of Martingale CLT](https://mlsanity.com/paper/1904.02130/) (2019)
- [Tight High Probability Bounds for Linear Stochastic Approximation with Fixed Stepsize](https://mlsanity.com/paper/2106.01257/) (2021)
- [Gaussian Approximation and Multiplier Bootstrap for Polyak-Ruppert Averaged Linear Stochastic Approximation with Applications to TD Learning](https://mlsanity.com/paper/2405.16644/) (2024)
- [Rates of Convergence in the Central Limit Theorem for Markov Chains, with an Application to TD Learning](https://mlsanity.com/paper/2401.15719/) (2024)
- [Statistical Inference for Policy Evaluation with Temporal Difference Learning](https://mlsanity.com/paper/2410.16106/) (2024)
- [Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descent](https://mlsanity.com/paper/2502.06719/) (2025)
- [Asymptotics of Stochastic Gradient Descent with Dropout Regularization in Linear Models](https://mlsanity.com/paper/2409.07434/) (2024)

## Built on by (most cited first, 2 of 2)

- [Statistical Inference for Linear Functionals of Online Least-squares SGD when t gtrsim d1+δ](https://mlsanity.com/paper/2510.19734/) (2025)
- [Gaussian Limits for SGD Without Stationary Moments](https://mlsanity.com/paper/2610.05599/) (2026)

## Abstract (arXiv)

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 √logn/n, provided that the sample size n is large enough.