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arXiv · 2504.16890

Computing Optimal Transport Plans via Min-Max Gradient Flows

Lauren Conger·Franca Hoffmann·Ricardo Baptista·Eric Mazumdar
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Abstract

We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the timescale-separated gradient descent dynamics to the optimal transport plan, and implement the gradient descent algorithm with a particle method, where the marginal constraints are enforced weakly using the KL divergence, automatically selecting a dynamical adaptation of the regularizer. The numerical results highlight the different advantages of using the standard Kullback-Leibler (KL) divergence versus the reverse KL divergence with this approach, opening the door for new methodologies.

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Lauren Conger, Franca Hoffmann, Ricardo Baptista, Eric Mazumdar. 2025-04-23. Computing Optimal Transport Plans via Min-Max Gradient Flows. https://arxiv.org/abs/2504.16890

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