mlsanityData to 14 Oct 2026

On the Rate of Gaussian Approximation for Linear Regression Problems

arXiv 2509.14039 ↗First posted 17 Sep 2025stat.ML cs.LG math.OCcited by 2

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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.

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

12 of 23 references.

References · 12

  1. 2018A Finite Time Analysis of Temporal Difference Learning With Linear Function Approximationcited by 229
  2. 2020On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentrationcited by 68
  3. 2020An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Biascited by 48
  4. 2022Finite-time High-probability Bounds for Polyak-Ruppert Averaged Iterates of Linear Stochastic Approximationcited by 41
  5. 2019A Tale of Two-Timescale Reinforcement Learning with the Tightest Finite-Time Boundcited by 31
  6. 2019Normal Approximation for Stochastic Gradient Descent via Non-Asymptotic Rates of Martingale CLTcited by 30
  7. 2021Tight High Probability Bounds for Linear Stochastic Approximation with Fixed Stepsizecited by 27
  8. 2024Gaussian Approximation and Multiplier Bootstrap for Polyak-Ruppert Averaged Linear Stochastic Approximation with Applications to TD Learningcited by 19
  9. 2024Rates of Convergence in the Central Limit Theorem for Markov Chains, with an Application to TD Learningcited by 17
  10. 2024Statistical Inference for Policy Evaluation with Temporal Difference Learningcited by 15
  11. 2025Gaussian Approximation and Multiplier Bootstrap for Stochastic Gradient Descentcited by 10
  12. 2024Asymptotics of Stochastic Gradient Descent with Dropout Regularization in Linear Modelscited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Statistical Inference for Linear Functionals of Online Least-squares SGD when t gtrsim d1+δcited by 1
  2. 2026Gaussian Limits for SGD Without Stationary Momentscited by 0