Review for NeurIPS paper: Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation

Weaknesses: There are a few concerns with the paper that the authors should address: (1) Regarding the formulation of robust optimal transport in equation (5), when the probability measures P_{X} and P_{Y} are discrete, the objective function with \pi is a linear programming problem. Solving directly the linear programming problem can be expensive as the standard interior point methods have complexity of order n 3 where n is the maximum number of supports of P_{X} and P_{Y} . For this reason, we can utilize the entropic regularized approach to equation (5). Here, H(\pi) stands for the entropy of \pi . The objective function is strongly convex with respect to \pi .