Mini-batch stochastic Nesterov's smoothing method for constrained convex stochastic composite optimization

TL;DR

This paper introduces a mini-batch stochastic Nesterov's smoothing method for constrained convex stochastic composite optimization, providing convergence guarantees and demonstrating efficiency on SVM models.

Contribution

The paper proposes a novel MSNS method that handles nonsmooth convex components with max structure without requiring explicit proximal mappings.

Findings

Convergence and optimal iteration complexity are established.

Numerical results show the method's efficiency on SVM models.

The method effectively manages nonsmooth components in stochastic optimization.

Abstract

This paper considers a class of constrained convex stochastic composite optimization problems whose objective function is given by the summation of a differentiable convex component, together with a nonsmooth but convex component. The nonsmooth component has an explicit max structure that may not easy to compute its proximal mapping. In order to solve these problems, we propose a mini-batch stochastic Nesterov's smoothing (MSNS) method. Convergence and the optimal iteration complexity of the method are established. Numerical results are provided to illustrate the efficiency of the proposed MSNS method for a support vector machine (SVM) model.