Online Sinkhorn: optimal transportation distances from sample streams
share
Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This paper introduces a new online estimator of entropy-regularized OT distances between two such arbitrary distributions. It uses streams of samples from both distributions to iteratively enrich a non-parametric representation of the transportation plan. Compared to the classic Sinkhorn algorithm, our method leverages new samples at each iteration, which enables a consistent estimation of the true regularized OT distance. We cast our algorithm as a block-convex mirror descent in the space of positive distributions, and provide a theoretical analysis of its convergence. We numerically illustrate the performance of our method in comparison with concurrent approaches.
READ FULL TEXT