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

Navpreet Kaur, Juntao Chen, Yingdong Lu

TL;DR

This work introduces a discrete optimal transport framework designed to handle large-scale, heterogeneous target populations, characterized by type distributions, and develops a federated learning-based approach that enables efficient computation of the optimal transport scheme while preserving privacy.

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.

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

TL;DR

This work introduces a discrete optimal transport framework designed to handle large-scale, heterogeneous target populations, characterized by type distributions, and develops a federated learning-based approach that enables efficient computation of the optimal transport scheme while preserving privacy.

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.

Paper Structure

This paper contains 18 sections, 6 theorems, 62 equations, 2 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Federated Learning with Heterogeneous Data
  4. Optimal Transport and Federated Learning
  5. Large-Scale Discrete Optimal Transport
  6. Framework
  7. Nodes: sources and targets
  8. Network Topology
  9. Problem Formulation
  10. Distributed Optimal Transport with Known Target's Type Distribution
  11. Federated Learning under Unknown Type Distribution
  12. Convergence Proof of Algorithm \ref{['algorithm_prox']}
  13. Case Studies
  14. Distributed Resource Allocation Efficiency
  15. Resilience in the Federated Learning Algorithm
  16. ...and 3 more sections

Key Result

Proposition 1

The iterative steps of ADMM to OT2:eqn are summarized as follows: where $\Pi_{\tilde{x},t}:=\{\pi_{xy}^t\}_{y\in\mathcal{Y}_x,x=\tilde{x}}$ represents the solution at target node $\tilde{x}\in\mathcal{X}$, and $\Pi_{\tilde{y},s}:=\{\pi_{xy}^s\}_{x\in\mathcal{X}_y,y=\tilde{y}}$ represents the proposed solution at source node $\tilde{y}\in\mathcal{Y}$. In addition,

Figures (2)

  • Figure 1: (a): Distribution of the sampled targets' type data; (b): Transport plan; (c): Transport utility given by the federated learning algorithm; (d): Resource received by each type of target node.
  • Figure 2: (a): Distribution of the sampled targets' type data incorporating the new distribution; (b): Transport plan before and after the update; (c): Transport utility given by the federated learning algorithm; (d): Resource received by each type of target node before and after the update.

Theorems & Definitions (14)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Remark 1
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1
  • ...and 4 more