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October 20, 2025Open Access

Faster Computation of Entropic Optimal Transport via Stable Low Frequency Modes

Key Points

The new method achieves faster convergence than the traditional Sinkhorn algorithm for entropic optimal transport.
Numerical experiments show that the spectral warm-start strategy effectively addresses convergence slowdown as regularization weakens.
Spectral insights into the Hessian behavior provide a foundation for the accelerated solution to optimal transport problems.
Improving efficiency in optimal transport computations can have broader implications in machine learning and data analysis.

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 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.

Faster Computation of Entropic Optimal Transport via Stable Low Frequency Modes

Key Points

Abstract

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