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.

本研究解决了在大规模和异质性人群中，传统最优运输模型难以有效扩展的问题。我们提出了一种离散最优运输框架，分别针对已知和未知目标类型分布提出全分布式算法和基于联邦学习的方法，显著提高了资源分配的效率和隐私保护。结果表明，该方法在实施中表现出优良的性能，具有重要的实际应用价值。

面对不完全信息的大规模人群离散最优运输的联邦学习