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We consider the problem of unconstrained minimization of finite sums offunctions. We propose a simple, yet, practical way to incorporate variancereduction techniques into SignSGD, guaranteeing convergence that is similar tothe full sign gradient descent. The core idea is first instantiated on theproblem of minimizing sums of convex and Lipschitz functions and is thenextended to the smooth case via variance reduction. Our analysis is elementaryand much simpler than the typical proof for variance reduction methods. We showthat for smooth functions our method gives $\mathcal{O}(1 / \sqrt{T})$ rate forexpected norm of the gradient and $\mathcal{O}(1/T)$ rate in the case of smoothconvex functions, recovering convergence results of deterministic methods,while preserving computational advantages of SignSGD.

SignSVRG: fixing SignSGD via variance reduction