Stochastic Gradient Methods with Preconditioned Updates

Abdurakhmon Sadiev, Aleksandr Beznosikov (), Abdulla Jasem Almansoori, Dmitry Kamzolov, Rachael Tappenden and Martin Takáč ()
Additional contact information
Abdurakhmon Sadiev: Ivannikov Institute for System Programming of the Russian Academy of Sciences (ISP RAS)
Aleksandr Beznosikov: Moscow Institute of Physics and Technology (MIPT)
Abdulla Jasem Almansoori: Mohamed Bin Zayed University of Artificial Intelligence (MBZUAI)
Dmitry Kamzolov: Mohamed Bin Zayed University of Artificial Intelligence (MBZUAI)
Rachael Tappenden: University of Canterbury
Martin Takáč: Mohamed Bin Zayed University of Artificial Intelligence (MBZUAI)

Journal of Optimization Theory and Applications, 2024, vol. 201, issue 2, No 1, 489 pages

Abstract: Abstract This work considers the non-convex finite-sum minimization problem. There are several algorithms for such problems, but existing methods often work poorly when the problem is badly scaled and/or ill-conditioned, and a primary goal of this work is to introduce methods that alleviate this issue. Thus, here we include a preconditioner based on Hutchinson’s approach to approximating the diagonal of the Hessian and couple it with several gradient-based methods to give new ‘scaled’ algorithms: Scaled SARAH and Scaled L-SVRG. Theoretical complexity guarantees under smoothness assumptions are presented. We prove linear convergence when both smoothness and the PL-condition are assumed. Our adaptively scaled methods use approximate partial second-order curvature information and, therefore, can better mitigate the impact of badly scaled problems. This improved practical performance is demonstrated in the numerical experiments also presented in this work.

Keywords: Optimization; Non-convex optimization; Stochastic optimization; Scaled methods; Variance reduction (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-023-02365-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:201:y:2024:i:2:d:10.1007_s10957-023-02365-3

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-023-02365-3

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().