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We study optimization algorithms based on variance reduction for stochasticgradient descent (SGD). Remarkable recent progress has been made in thisdirection through development of algorithms like SAG, SVRG, SAGA. Thesealgorithms have been shown to outperform SGD, both theoretically andempirically. However, asynchronous versions of these algorithms---a crucialrequirement for modern large-scale applications---have not been studied. Webridge this gap by presenting a unifying framework for many variance reductiontechniques. Subsequently, we propose an asynchronous algorithm grounded in ourframework, and prove its fast convergence. An important consequence of ourgeneral approach is that it yields asynchronous versions of variance reductionalgorithms such as SVRG and SAGA as a byproduct. Our method achieves nearlinear speedup in sparse settings common to machine learning. We demonstratethe empirical performance of our method through a concrete realization ofasynchronous SVRG.

On Variance Reduction in Stochastic Gradient Descent and its Asynchronous Variants