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In this paper we consider the question of whether it is possible to apply agradient averaging strategy to improve on the sublinear convergence rateswithout any increase in storage. Our analysis reveals that a positive answerrequires an appropriate averaging strategy and iterations that satisfy thevariance dominant condition. As an interesting fact, we show that if theiterative variance we defined is always dominant even a little bit in thestochastic gradient iterations, the proposed gradient averaging strategy canincrease the convergence rate $\mathcal{O}(1/k)$ to $\mathcal{O}(1/k^2)$ inprobability for the strongly convex objectives with Lipschitz gradients. Thisconclusion suggests how we should control the stochastic gradient iterations toimprove the rate of convergence.

Can speed up the convergence rate of stochastic gradient methods to $\mathcal{O}(1/k^2)$ by a gradient averaging strategy?