The authors propose a stochastic algorithm for generalized empirical composition problems of the form in eq. 1. The paper provides linear convergence rates for a problem (eq 1), which is more general than the problems (eq. 2) studied by the related work [8-9]. For the special case of the problem in eq. 2, the initial submission does not compare rates to [8-9]. Reviewers 2 and 6 had raised this concern and the author response provides convincing comparison. Addition of these comparisons to the revision is highly recommended.