Inexact Tensor Methods and Their Application to Stochastic Convex Optimization

Authors

Artem Agafonov, Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation & Mohamed bin Zayed University of Artificial IntelligenceFollow
Dmitry Kamzolov, Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation & Mohamed bin Zayed University of Artificial Intelligence
Pavel Dvurechensky, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Alexander Gasnikov, Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation & Institute for Information Transmission Problems, Moscow, Russian Federation & HSE University, Moscow, Russian Federation
Martin Takac, Mohamed Bin Zayed University of Artificial IntelligenceFollow

Document Type

Article

Publication Title

arXiv

Abstract

We propose general non-accelerated and accelerated tensor methods under inexact information on the derivatives of the objective, analyze their convergence rate. Further, we provide conditions for the inexactness in each derivative that is sufficient for each algorithm to achieve a desired accuracy. As a corollary, we propose stochastic tensor methods for convex optimization and obtain sufficient mini-batch sizes for each derivative. © 2020, CC BY.

DOI

10.48550/arXiv.2012.15636

Publication Date

12-31-2020

Keywords

Stochastic systems, Tensors, Condition, Convergence rates, Convex optimisation, High-order methods, Higher-order methods, Inexact derivative, Objective analysis, Stochastic optimizations, Stochastics, Tensor method, Convex optimization, Optimization and Control (math.OC)

Comments

Preprint: arXiv

Archived with thanks to arXiv

Preprint License: CC by 4.0

Uploaded 13 July 2022

Recommended Citation

A. Agafonov, D. Kamzolov, P. Dvurechensky, A. Gasnikov, and M. Takac, "Inexact Tensor Methods and Their Application to Stochastic Convex Optimization", 2020, arXiv:2012.15636