  Optimal transport (OT) distances are finding evermore applications in machine
learning and computer vision, but their wide spread use in larger-scale
problems is impeded by their high computational cost. In this work we develop a
family of fast and practical stochastic algorithms for solving the optimal
transport problem with an entropic penalization. This work extends the recently
developed Greenkhorn algorithm, in the sense that, the Greenkhorn algorithm is
a limiting case of this family. We also provide a simple and general
convergence theorem for all algorithms in the class, with rates that match the
best known rates of Greenkorn and the Sinkhorn algorithm, and conclude with
numerical experiments that show under what regime of penalization the new
stochastic methods are faster than the aforementioned methods.
