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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Summary The paper introduces a simple strategy to reduce the variance of gradients in stochastic variational inference methods. Variance reduction is achieved by storing the last L data-point's contribution to the approximated/stochastic gradient and averaging these values. There exists a bias variance trade off: variance reduction comes at the cost of increased bias in the gradient estimates. The bias-variance tradeoff can be controlled by varying the sliding window size L. Also this strategy requires storing the last L data-point gradient contributions which can be significant.