Stochastic gradient descent for linear inverse problems in Hilbert spaces

2021 ◽  
Author(s):  
Shuai Lu ◽  
Peter Mathé
Keyword(s):  
Inverse Problems ◽  
Hilbert Spaces ◽  
Gradient Descent ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Linear Inverse Problems

scholarly journals An analysis of stochastic variance reduced gradient for linear inverse problems

2021 ◽  
Author(s):  
Bangti Jin ◽  
Zehui Zhou ◽  
Jun Zou
Keyword(s):  
Inverse Problems ◽  
Gradient Descent ◽  
Variance Reduction ◽  
Regularity Condition ◽  
Stochastic Gradient Descent ◽  
Optimal Convergence Rate ◽  
Regularization Theory ◽  
Step Size ◽  
Linear Inverse Problems ◽  
Reduced Gradient

Abstract Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens of the classical regularization theory. We prove that for a suitable constant step size schedule, the method can achieve an optimal convergence rate in terms of the noise level (under suitable regularity condition) and the variance of the SVRG iterate error is smaller than that by SGD. These theoretical findings are corroborated by a set of numerical experiments.

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