Collision-based Dynamics for Multi-Marginal Optimal Transport

• URL: http://arxiv.org/abs/2412.16385v1
• Date: Fri, 20 Dec 2024 22:41:16 GMT
• Title: Collision-based Dynamics for Multi-Marginal Optimal Transport
• Authors: Mohsen Sadr, Hossein Gorji,
• Abstract summary: We propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample indices. The computational complexity and memory usage of the proposed method scale linearly with the number of samples, making it highly attractive for high-dimensional settings.
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• Abstract: Inspired by the Boltzmann kinetics, we propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample indices. The computational complexity and memory usage of the proposed method scale linearly with the number of samples, making it highly attractive for high-dimensional settings. In several examples, we demonstrate the efficiency of the proposed method compared to the state-of-the-art methods.

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