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Submitted by Assigned_Reviewer_1 Q1 The authors propose a non-uniform sampling scheme for variance reduced SGD type algorithms based on local smoothness and the fact that the gradient of many individual losses is constant. The authors show that such a scheme is able to outperform uniform sampling for SVRG and SDCA. Overall the idea is an interesting one and seems to perform well in practice. However, I feel that the paper has some major clarity issues. In general, I find the paper quite difficult to read.