arXiv:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).
By Steffen Dereich, Arnulf Jentzen, Adrian Riekert
arXiv:2605. 27991v2 Announce Type: replace-cross Abstract: Gradient-flow optimization is usually viewed as an algorithmic procedure for minimizing empirical loss, with training duration selected by validation or heuristic early-stopping rules.
By Minhao Yao, Ruoyu Wang, Xihong Lin, Lin Liu, Zhonghua Liu
The paper studies a variant of stochastic gradient descent called SGDIR, which incorporates initial regularization. It derives dimension‑free upper bounds on the expected excess risk for the squared loss, providing new rates for both averaged and non‑averaged SGDIR under various assumptions. The authors also establish matching lower bounds in certain regimes and compare SGDIR to ridge regression in noisy settings, showing comparable performance up to a polylogarithmic factor.
By Nabil Kahal\'e
arXiv:2610.00446v1 Announce Type: cross
Abstract: As an alternative to the standard geometric analyses, we give an exact, information-theoretic analysis of stochastic gradient descent (SGD) and its v...
By Akshay Balsubramani
arXiv:2510. 14074v2 Announce Type: replace-cross Abstract: We develop a framework for analyzing the learning dynamics of high-dimensional problems trained using one-pass stochastic gradient descent (SGD) with data from multiple anisotropic classes.
By Elizabeth Collins-Woodfin, Inbar Seroussi
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.
By Junyu Zhou, Puyu Wang, Dennis Wagner, Yunwen Lei, Marius Kloft, Yiming Ying