Sketch-and-Project Meets Newton Method: Global $O(1/k^2)$ Convergence with Low-Rank Updates
Abstract
In this paper, we propose the first sketch-and-project Newton method with the fast $O(1/k^2$) global convergence rate for self-concordant functions. Our method, SGN, can be viewed in three ways: i) as a sketch-and-project algorithm projecting updates of the Newton method, ii) as a cubically regularized Newton method in the sketched subspaces, and iii) as a damped Newton method in the sketched subspaces. SGN inherits the best of all three worlds: the cheap iteration costs of the sketch-and-project methods, the state-of-the-art $O(1/k^2)$ global convergence rate of the full-rank Newton-like methods, and the algorithm simplicity of the damped Newton methods. Finally, we demonstrate its comparable empirical performance to the baseline algorithms.
BibTeX
@inproceedings{
hanzely2025sketchandproject,
title={Sketch-and-Project Meets Newton Method: Global \${\textbackslash}mathcal O {\textbackslash}left( k{\textasciicircum}\{-2\} {\textbackslash}right)\$ Convergence with Low-Rank Updates},
author={Slavomir Hanzely},
booktitle={The 28th International Conference on Artificial Intelligence and Statistics},
year={2025},
url={https://openreview.net/forum?id=cPbEcEkTYe}
}