arXiv Machine Learning By Joseph Keslin, Wei Biao Wu

Strong Gaussian Approximation of Constant Learning Rate SGD: Bias and Trajectory Inference

Read the original on arXiv Machine Learning →

arXiv:2610. 14567v2 Announce Type: replace-cross Abstract: This paper develops strong Gaussian approximations (KMT type) for constant learning rate stochastic gradient descent (SGD).

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arXiv Machine Learning
5d ago

Stochastic Gradient Descent: A Nonlinear Time Series Perspective

This paper studies the statistical properties of Stochastic Gradient Descent (SGD) with a constant step size using the framework of iterated random functions. It demonstrates convergence in Euclidean distance via Geometric Moment Contraction, establishes quenched central limit theorems, invariance principles, and α-stable convergence for averaged SGD regardless of initialization, and explores the effect of step sizes through derivative processes. The authors further develop a Richardson-Romberg extrapolation with multiple step sizes, propose a bias-reduced variant, and introduce an online inference method that yields empirical confidence intervals with coverage approaching nominal levels as sample size increases.

By Jiaqi Li, Zhipeng Lou, Stefan Richter, Wei Biao Wu