On Scaled Methods for Saddle Point Problems

Authors

Aleksandr Beznosikov, oscow Institute of Physics and Technology (MIPT), Moscow, Russian FederationFollow
Aibek Alanov, Artificial Intelligence Research Institute (AIRI), Higher School of Economics (HSE), Moscow, Russian Federation
Dmitry Kovalev, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia
Martin Takac, Mohamed Bin Zayed University of Artificial IntelligenceFollow
Alexander Gasnikov, Moscow Institute of Physics and Technology (MIPT), Moscow, Russian Federation

Document Type

Article

Publication Title

arXiv

Abstract

Methods with adaptive scaling of different features play a key role in solving saddle point problems, primarily due to Adam’s popularity for solving adversarial machine learning problems, including GANS training. This paper carries out a theoretical analysis of the following scaling techniques for solving SPPs: the well-known Adam and RmsProp scaling and the newer AdaHessian and OASIS based on Hutchison approximation. We use the Extra Gradient and its improved version with negative momentum as the basic method. Experimental studies on GANs show good applicability not only for Adam, but also for other less popular methods. Copyright © 2022, The Authors. All rights reserved.

DOI

10.48550/arXiv.2206.08303

Publication Date

6-16-2022

Keywords

Adaptive scaling, Hutchison, Machine learning problem, Saddle point problems, Scaled methods, Scalings, Machine learning, Machine Learning (cs.LG), Optimization and Control (math.OC)

Comments

IR Deposit conditions: non-described

Preprint available on arXiv

Recommended Citation

A. Beznosikov, A. Alanov, D. Kovalev, M. Takac, and A. Gasnikov, "On Scaled Methods for Saddle Point Problems", 2022, arXiv:2206.08303