Reviewer 1: Q1: I wonder if their analysis tricks of AC/NAC when applied to PG methods improve their guarantees

If their analysis tricks do improve PG guarantees, how does it compare then? Reviewer 2: Q1: It would be interesting to complement the theoretical results with empirical results in toy problem. We are working on experiments and will add these results to the revision. Q2: For the error term that disappears with a larger mini-batch (line 211). A2: Y es, this error term should be called as variance error.