Federated Learning for Discrete Optimal Transport with Large Population under Incomplete Information

TL;DR

This paper introduces a federated learning approach for discrete optimal transport in large, heterogeneous populations, enabling efficient resource allocation while preserving privacy, applicable when target type distributions are known or unknown.

Contribution

It presents a novel federated learning framework for large-scale discrete optimal transport with unknown target distributions, including a distributed algorithm for known distributions.

Findings

The federated approach effectively computes optimal transport schemes.

The algorithms scale to large populations with heterogeneity.

Case studies demonstrate practical performance and privacy preservation.

Abstract

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.