Papers › A Truncated Newton Method for Optimal Transport
A Truncated Newton Method for Optimal Transport
Mete Kemertas, Amir-Massoud Farahmand, Allan D. Jepson
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 × 2 cost functions). The scalability of the algorithm is showcased on an extremely large OT problem with n ≈10⁶, solved approximately under weak entopric regularization.
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