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News/Online Covariance Estimation in Averaged SGD: Improved Batch-Mean Rates and Minimax Optimality via Trajectory Regression
arxiv
PublishedApril 14, 2026 at 4:00 AM

Online Covariance Estimation in Averaged SGD: Improved Batch-Mean Rates and Minimax Optimality via Trajectory Regression

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arXiv:2604.10814v1 Announce Type: new Abstract: We study online covariance matrix estimation for Polyak--Ruppert averaged stochastic gradient descent (SGD). The online batch-means estimator of Zhu, Chen and Wu (2023) achieves an operator-norm convergence rate of $O(n^{-(1-\alpha)/4})$, which yields

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