Faster Computation of Entropic Optimal Transport via Stable Low Frequency Modes

TL;DR

This paper introduces a spectral warm-start strategy to accelerate the Sinkhorn algorithm for Entropic Optimal Transport, significantly improving convergence especially as regularization weakens.

Contribution

It presents a novel spectral warm-start approach that mitigates slow convergence in the Sinkhorn algorithm when regularization diminishes.

Findings

Faster convergence demonstrated in numerical experiments

Spectral insights improve warm-start effectiveness

Method outperforms standard Sinkhorn algorithm in weak regularization regime

Abstract

In this paper, we propose an accelerated version for the Sinkhorn algorithm, which is the reference method for computing the solution to Entropic Optimal Transport. Its main draw-back is the exponential slow-down of convergence as the regularization weakens $\varepsilon \rightarrow 0$. Thanks to spectral insights on the behavior of the Hessian, we propose to mitigate the problem via an original spectral warm-start strategy. This leads to faster convergence compared to the reference method, as also demonstrated in our numerical experiments.