A Truncated Newton Method for Optimal Transport
Keywords: Computational optimal transport, numerical optimization, numerical linear algebra
TL;DR: A high-performing, high-precision, GPU-parallel optimal transport solver based on truncated Newton methods.
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 4096-dimensional MNIST and color transfer problems. The scalability of the algorithm is showcased on an extremely large OT problem with $n \approx 10^6$, solved approximately under weak entopric regularization.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 2216
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