Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/88214
PIRA download icon_1.1View/Download Full Text
Title: Convergence of the randomized kaczmarz algorithm in Hilbert space
Authors: Guo, X 
Lin, J
Zhou, DX
Issue Date: 27-May-2017
Source: Paper presented at International Conference on Computational Harmonic Analysis 2017, Shanghai, China, 24-28 May 2017
Abstract: The randomized Kaczmarz algorithm recently draws much attention. Existing results on anal-ysis suffer from condition numbers of the linear equation systems. Although the randomized Kacz-marz algorithm has a natural generalization to Hilbert spaces (which covers online learning algo-rithms for a particular instance), the existing analysis does not. Although the large-scale linear equation system is an ideal scenario for the randomized Kaczmarz algorithm to outperform direct solvers, it is also a scenario the existing analysis is not satisfactory. In this research, we introduce the regularity assumption widely adopted in learning theory and obtain the polynomial convergence rate of the randomized Kaczmarz algorithm in Hilbert space under noise-free setting. We find that by nature, the randomized Kaczmarz algorithm converges weakly. Meanwhile, with noisy data, we study the relaxation method and obtain a strong convergence arbitrarily close to the minimax optimal rate. The result applies to online gradient descent learning algorithms and significantly improves the existing learning rate in literature.
Appears in Collections:Presentation

Files in This Item:
File Description SizeFormat 
FudanShanghai2017May.pdf93.13 kBAdobe PDFView/Open
Open Access Information
Status open access
File Version Other Version
Show full item record

Page views

38
Citations as of May 22, 2022

Downloads

14
Citations as of May 22, 2022

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.