. Figure 1 m n 100 1000 10 29 4 s 33 6 s 50 8 1 min 9 1 min 100 15 1 min 24 2 min Table 2: Time to reach relative improvement 10

We thank the reviewers for their comments. We then address reviewer's comments individually (due to space limits please zoom in the tiny figures). For [18] we used Alg. 2 We thank the reviewer for the additional reference, which we will add to the paper. Gradient Descent) applied in parallel to multiple starting points. We thank R2 for the reference "Entropic regularization of continuous optimal transport problems".