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For solving finite-sum optimization problems, SGD without replacementsampling is empirically shown to outperform SGD. Denoting by $n$ the number ofcomponents in the cost and $K$ the number of epochs of the algorithm , severalrecent works have shown convergence rates of without-replacement SGD that havebetter dependency on $n$ and $K$ than the baseline rate of $O(1/(nK))$ for SGD.However, there are two main limitations shared among those works: the rateshave extra poly-logarithmic factors on $nK$, and denoting by $\kappa$ thecondition number of the problem, the rates hold after $\kappa^c\log(nK)$ epochsfor some $c>0$. In this work, we overcome these limitations by analyzing stepsizes that vary across epochs.

On Tight Convergence Rates of Without-replacement SGD