Accelerated Sinkhorn Algorithms for Partial Optimal Transport

TL;DR

This paper introduces ASPOT, an accelerated Sinkhorn algorithm for Partial Optimal Transport, improving scalability and efficiency with theoretical complexity bounds and practical validation.

Contribution

The paper presents ASPOT, combining acceleration and minimization techniques to enhance Partial Optimal Transport computations beyond existing methods.

Findings

ASPOT achieves a complexity of O(n^{7/3} ε^{-5/3})

Informed entropic parameter choice improves classical Sinkhorn rates

Experiments validate theoretical improvements and practical performance

Abstract

Partial Optimal Transport (POT) addresses the problem of transporting only a fraction of the total mass between two distributions, making it suitable when marginals have unequal size or contain outliers. While Sinkhorn-based methods are widely used, their complexity bounds for POT remain suboptimal and can limit scalability. We introduce Accelerated Sinkhorn for POT (ASPOT), which integrates alternating minimization with Nesterov-style acceleration in the POT setting, yielding a complexity of $\mathcal{O}(n^{7/3}\varepsilon^{-5/3})$. We also show that an informed choice of the entropic parameter $\gamma$ improves rates for the classical Sinkhorn method. Experiments on real-world applications validate our theories and demonstrate the favorable performance of our proposed methods.