Sampling and Update Frequencies in Proximal Variance-Reduced Stochastic Gradient Methods

TL;DR

This paper introduces a general proximal variance-reduced stochastic gradient method, analyzing its convergence and proposing a new sampling strategy that improves efficiency, with implications for various existing algorithms like SAGA and L-SVRG.

Contribution

It presents a unified analysis of variance-reduced gradient methods, introduces a faster sampling strategy, and clarifies the impact of epoch-length and gradient storage on convergence.

Findings

Improved convergence rates over existing literature.

A new, faster sampling strategy for SAGA.

Validation on real-world data problems.

Abstract

Variance-reduced stochastic gradient methods have gained popularity in recent times. Several variants exist with different strategies for the storing and sampling of gradients and this work concerns the interactions between these two aspects. We present a general proximal variance-reduced gradient method and analyze it under strong convexity assumptions. Special cases of the algorithm include SAGA, L-SVRG and their proximal variants. Our analysis sheds light on epoch-length selection and the need to balance the convergence of the iterates with how often gradients are stored. The analysis improves on other convergence rates found in the literature and produces a new and faster converging sampling strategy for SAGA. Problem instances for which the predicted rates are the same as the practical rates are presented together with problems based on real world data.