Monge solutions

On the Gromov-Wasserstein problem, existence of Monge maps. On a statistical estimation of smooth optimal transport.

This talk has two parts. In the first part, we study the existence of Monge maps as optimizer of the standard Gromov-Wasserstein problem for two different costs in euclidean spaces, in two important cases. The second part of the talk presents how to use sum of squares in RKHS to design computationnally efficient statistical estimators of smooth optimal transport.