Factor Augmented High-Dimensional SGD

Shubo Li; Yuefeng Han; Xiufan Yu

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arXiv · 2605.19291

Factor Augmented High-Dimensional SGD

Shubo Li·Yuefeng Han·Xiufan Yu

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Abstract

Stochastic gradient descent (SGD) is a fundamental optimization algorithm widely used in modern machine learning. In this paper, we propose Factor-Augmented SGD (FSGD), a new optimization method that leverages latent factor representations in high-dimensional learning tasks. Unlike standard two-stage dimension reduction approaches that rely on offline representation learning and full data storage, a key novelty of FSGD is that it operates purely on streaming data, making it scalable to large-scale and high-dimensional problems. Furthermore, we establish the first theoretical framework that explicitly incorporates latent factor estimation error into the analysis of SGD, and provide moment convergence in $\ell^s$ norm under decaying step sizes and mini-batch updates. Our results provide a new foundation for employing SGD reliably and scalably in high-dimensional machine learning systems.

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BibTeX RIS

Shubo Li, Yuefeng Han, Xiufan Yu. 2026-05-19. Factor Augmented High-Dimensional SGD. https://arxiv.org/abs/2605.19291

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