Projected Semi-Stochastic Gradient Descent Method with Mini-Batch Scheme under Weak Strong Convexity Assumption

TL;DR

This paper introduces a projected semi-stochastic gradient descent method with mini-batch scheme that achieves linear convergence under weak strong convexity, enhancing efficiency and applicability in machine learning tasks.

Contribution

It presents a novel PS2GD algorithm that improves theoretical convergence rates and practical performance for convex optimization problems without requiring strong convexity.

Findings

Proves linear convergence under weak strong convexity.

Maintains low per-iteration cost with stochastic variance reduction.

Applicable to dual SVM problems with hinge loss.

Abstract

We propose a projected semi-stochastic gradient descent method with mini-batch for improving both the theoretical complexity and practical performance of the general stochastic gradient descent method (SGD). We are able to prove linear convergence under weak strong convexity assumption. This requires no strong convexity assumption for minimizing the sum of smooth convex functions subject to a compact polyhedral set, which remains popular across machine learning community. Our PS2GD preserves the low-cost per iteration and high optimization accuracy via stochastic gradient variance-reduced technique, and admits a simple parallel implementation with mini-batches. Moreover, PS2GD is also applicable to dual problem of SVM with hinge loss.