Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates
Abstract
Quasi-Newton (qN) techniques approximate the Newton step by estimating the Hessian using the so-called secant equations. Some of these methods compute the Hessian using several secant equations but produce non-symmetric updates. Other quasi-Newton schemes, such as BFGS, enforce symmetry but cannot satisfy more than one secant equation. We propose a new type of quasi-Newton symmetric update using several secant equations in a least-squares sense. Our approach generalizes and unifies the design of quasi-Newton updates and satisfies provable robustness guarantees.
Cite
Text
Scieur et al. " Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates ." Artificial Intelligence and Statistics, 2021.Markdown
[Scieur et al. " Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates ." Artificial Intelligence and Statistics, 2021.](https://mlanthology.org/aistats/2021/scieur2021aistats-generalization/)BibTeX
@inproceedings{scieur2021aistats-generalization,
title = {{ Generalization of Quasi-Newton Methods: Application to Robust Symmetric Multisecant Updates }},
author = {Scieur, Damien and Liu, Lewis and Pumir, Thomas and Boumal, Nicolas},
booktitle = {Artificial Intelligence and Statistics},
year = {2021},
pages = {550-558},
volume = {130},
url = {https://mlanthology.org/aistats/2021/scieur2021aistats-generalization/}
}