Greedy stochastic algorithms for entropy-regularized optimal transport problems

Abstract

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.

arXiv comment17 pages, 3 figures, AISTATS 2018

References in corpus (4)

• Fast Computation of Wasserstein Barycenters
• Learning with a Wasserstein Loss
• Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration
• Stochastic Optimization for Large-scale Optimal Transport

Cited by in corpus (5)

• On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms
• Domain Adaptation for Robust Workload Level Alignment Between Sessions and Subjects using fNIRS
• Screening Sinkhorn Algorithm for Regularized Optimal Transport
• Adaptive Sketch-and-Project Methods for Solving Linear Systems
• Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples