Algorithms for Weak Optimal Transport with an Application to Economics

The theory of weak optimal transport (WOT), introduced by [Gozlan et al., 2017], generalizes the classic Monge-Kantorovich framework by allowing the transport cost between one point and the points it is matched with to be nonlinear. In the so-called barycentric version of WOT, the cost for transporting a point $x$ only depends on $x$ and on the barycenter of the points it is matched with. This aggregation property of WOT is appealing in machine learning, economics and finance. Yet algorithms to ...