Optimal transport is a powerful framework for the efficient allocation of resources between sources and targets. However, traditional models often struggle to scale effectively in the presence of large and heterogeneous populations. In this work, we introduce a discrete optimal transport framework designed to handle large-scale, heterogeneous target populations, characterized by type distributions. We address two scenarios: one where the type distribution of targets is known, and one where it is unknown. For the known distribution, we propose a fully distributed algorithm to achieve optimal resource allocation. In the case of unknown distribution, we develop a federated learning-based approach that enables efficient computation of the optimal transport scheme while preserving privacy. Case studies are provided to evaluate the performance of our learning algorithm.

翻译：最优传输是资源在源与目标之间高效分配的有力框架。然而，传统模型在面对大规模异质群体时往往难以有效扩展。本文提出一种离散最优传输框架，旨在处理以类型分布为特征的大规模、异质目标群体。我们针对两种情形展开研究：一种是目标类型分布已知的情形，另一种是分布未知的情形。对于已知分布的情形，我们提出一种完全分布式算法以实现最优资源分配。对于分布未知的情形，我们开发了一种基于联邦学习的方法，该方法能够在保护隐私的同时高效计算最优传输方案。本文通过案例研究评估了我们所提出学习算法的性能。