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arXiv · 2504.02067

A Truncated Newton Method for Optimal Transport

Mete Kemertas·Amir-massoud Farahmand·Allan D. Jepson
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Abstract

Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical performance in terms of precision versus runtime, and numerical stability in practice. With these challenges in mind, we introduce a specialized truncated Newton algorithm for entropic-regularized OT. In addition to proving that locally quadratic convergence is possible without assuming a Lipschitz Hessian, we provide strategies to maximally exploit the high rate of local convergence in practice. Our GPU-parallel algorithm exhibits exceptionally favorable runtime performance, achieving high precision orders of magnitude faster than many existing alternatives. This is evidenced by wall-clock time experiments on 24 problem sets (12 datasets $\times$ 2 cost functions). The scalability of the algorithm is showcased on an extremely large OT problem with $n \approx 10^6$, solved approximately under weak entopric regularization.

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Mete Kemertas, Amir-massoud Farahmand, Allan D. Jepson. 2025-04-02. A Truncated Newton Method for Optimal Transport. https://arxiv.org/abs/2504.02067

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