The paper analyzes the bias and variance of a biased batch gradient estimator for solving DRO with CVaR and chisquare divergence uncertainty sets, and provides the upper/lower complexity bounds for the associated batch gradient methods. All reviewers found the algorithmic results interesting, given the growing relevance of DRO in ML research community. Please take the reviewers' comments into consideration in the revision and include numerical comparisons against previous methods as suggested by R3 and R5.