Factor Augmented High-Dimensional SGD
It addresses the scalability and reliability of SGD in high-dimensional machine learning by incorporating latent factor estimation error into the analysis.
The paper proposes Factor-Augmented SGD (FSGD) for high-dimensional learning, operating on streaming data without offline dimension reduction. It provides theoretical convergence guarantees in ℓ^s norm under decaying step sizes and mini-batch updates.
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.