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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper seems to essentially combine three published ideas: accelerated gradient, the stochastic gradient variance reduction technique of Johnson and Zhang, and variance reduction via minibatching. Hence, on a conceptual level at least, it's a fairly incremental paper (I don't want to minimize the effort that may have gone into developing the convergence proof). With this said, it's well-done, mostly well-written, and has good theoretical and experimental results. In terms of quality, originality and significance, it's as I said above: they're combining pre-existing ideas, but doing it well, and included a convergence proof with a slightly improved rate over the competition.