After thorough discussions among the area chair and reviewers, we concur that, albeit there remain several open questions, the paper provides a substantial contribution at the intersection of DRO and ML. Since the DRO has been neglected by the ML community despite its relevance in many ML applications, this work could potentially stimulate future work along this direction. Hence, I recommend that the paper gets accepted for publication at NeurIPS. Nevertheless, I would urge the authors, in the camera-ready version, to be candid about the limitations of their analysis and the need for future work. For example, the authors should explicitly mention the limitations of the loose upper bound in Theorem 3.1 as well as the fact that the constant M in Corollary 3.1 often depends on the dimension which is suboptimal.