# Greedy stochastic algorithms for entropy-regularized optimal transport problems

## TL;DR

This paper introduces a family of fast stochastic algorithms for entropy-regularized optimal transport problems, extending Greenkhorn, with proven convergence rates and numerical evidence of improved speed under certain conditions.

## Contribution

It develops a new family of stochastic algorithms for entropy-regularized OT, extending Greenkhorn, with a general convergence theorem and practical speed improvements.

## Key findings

- Algorithms achieve convergence rates matching existing methods.
- Numerical experiments demonstrate faster performance in specific regimes.
- The family generalizes Greenkhorn and includes it as a special case.

## 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.