Greedy stochastic algorithms for entropy-regularized optimal transport problems
This incremental improvement addresses computational efficiency for machine learning and computer vision applications that use optimal transport distances.
The authors tackled the computational bottleneck of entropy-regularized optimal transport by developing a family of fast stochastic algorithms, extending the Greenkhorn algorithm, with convergence rates matching state-of-the-art methods and showing speed improvements in certain penalization regimes.
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.