Together with Lenaic Chizat, François-Xavier Vialard and Bernhard Schmitzer, we released our paper “Scaling Algorithms for Unbalanced Transport Problems”. It is the third and last paper about generalized “unbalanced” optimal transport, which is a recently hot topic in the (small but rapidly growing!) world of optimal transport (OT) theorists and practitioners.
- In the first paper “An Interpolating Distance between Optimal Transport and Fisher-Rao”, we proposed (simultaneously and independently with two other groups of researchers) a new geodesic distance between two arbitrary positive measures, generalizing OT to the unblanced cases (i.e. when the measures are not normalized to unit mass).
- In the second paper “Unbalanced Optimal Transport: Geometry and Kantorovich Formulation”, we showed (simultaneously and independently with another group of researchers) that this distance is a special case of a generic class of “static” OT problems, which generalizes the linear programming formulation of OT.
- In this last paper, “Scaling Algorithms for Unbalanced Transport Problems”, we show how to solve efficiently these problems, and many more (in particular also barycenters and gradient flows) using entropic regularization, a recent computational technic championed by Marco Cuturi. The resulting algorithm is a far reaching generalization of Sinkhorn iterative scaling method.