NeurIPS 2020

Online Sinkhorn: Optimal Transport distances from sample streams

Meta Review

This paper gives a streaming estimator of entropy-regularized optimal transport, which allows for continuous distributions, gives better estimates of the transport plan than previous approaches, and enjoys strong theoretical guarantees. Although the numerical experiments are somewhat limited, they are more than sufficient to show the value of the new estimator. As a whole, then, the paper is clearly worthy of inclusion at NeurIPS, and should be quite useful to practitioners in certain settings. One remaining comment was brought up in discussion: Proposition 2 and Proposition 4, though not contradictory, seem to give different conclusions about a constant batch size with \iota nearly 0: Proposition 2, constant batch size with \iota = 0, gives no convergence, while taking \iota \to 0 in Proposition 4 gives n(t) -> B, a constant batch size, and a convergence rate of D / N. It would be helpful to add a brief discussion explaining this unintuitive discontinuity in the final version of the paper. (Is it simply that D and/or N_0 explode as iota -> 0?) Additionally, one very minor note: in your author response you used "his" to refer to a reviewer; since you presumably do not know the gender of the reviewer, it is preferable to use gender-neutral language, the preferred form of which in contemporary English is "they"/"them"/"their".