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When solving finite-sum minimization problems, two common alternatives tostochastic gradient descent (SGD) with theoretical benefits are randomreshuffling (SGD-RR) and shuffle-once (SGD-SO), in which functions are sampledin cycles without replacement. Under a convenient stochastic noiseapproximation which holds experimentally, we study the stationary variances ofthe iterates of SGD, SGD-RR and SGD-SO, whose leading terms decrease in thisorder, and obtain simple approximations. To obtain our results, we study thepower spectral density of the stochastic gradient noise sequences. Our analysisextends beyond SGD to SGD with momentum and to the stochastic Nesterov'saccelerated gradient method. We perform experiments on quadratic objectivefunctions to test the validity of our approximation and the correctness of ourfindings.

Computing the Variance of Shuffling Stochastic Gradient Algorithms via Power Spectral Density Analysis