Variable metric proximal stochastic gradient methods with additional sampling

Regularized empirical risk minimization problems arise in a variety of applications, including machine learning, signal processing, and image processing. Proximal stochastic gradient algorithms are a standard approach to solve these problems due to their low computational cost per iteration and a relatively simple implementation. This paper introduces a class of proximal stochastic gradient methods built … Read more

Spectral Stochastic Gradient Method with Additional Sampling for Finite and Infinite Sums

In this paper, we propose a new stochastic gradient method for numerical minimization of finite sums. We also propose a modified version of this method applicable on more general problems referred to as infinite sum problems, where the objective function is in the form of mathematical expectation. The method is based on a strategy to … Read more

A line search based proximal stochastic gradient algorithm with dynamical variance reduction

Many optimization problems arising from machine learning applications can be cast as the minimization of the sum of two functions: the first one typically represents the expected risk, and in practice it is replaced by the empirical risk, and the other one imposes a priori information on the solution. Since in general the first term … Read more