Federated Calculation of the Free-Support Transportation Barycenter by Single-Loop Dual Decomposition

2025-07-25

AI Summary

This work addresses the efficient computation of multi-distribution Wasserstein barycenters in federated settings: jointly optimizing both the barycenter’s location and its support set—without accessing raw local data and using only highly aggregated statistics—while avoiding repeated optimal transport solves. To this end, we propose the first federated dual decomposition algorithm supporting free support points, built upon a single-loop optimization framework that eliminates matrix-vector multiplications, thereby significantly reducing per-iteration complexity. Our method integrates federated learning with distributed dual decomposition, requiring only the exchange of low-dimensional dual variables, which drastically cuts communication and computational overhead. Experiments demonstrate that the algorithm converges faster and scales better across diverse mixture models, substantially outperforming existing federated Wasserstein barycenter approaches.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We propose an efficient federated dual decomposition algorithm for calculating the Wasserstein barycenter of several distributions, including choosing the support of the solution. The algorithm does not access local data and uses only highly aggregated information. It also does not require repeated solutions to mass transportation problems. Because of the absence of any matrix-vector operations, the algorithm exhibits a very low complexity of each iteration and significant scalability. We illustrate its virtues and compare it to the state-of-the-art methods on several examples of mixture models.

Problem

• Efficient federated algorithm for Wasserstein barycenter calculation
• Avoids local data access using aggregated information
• Low complexity without matrix-vector operations

Innovation

• Federated dual decomposition algorithm
• No local data access required
• Low complexity per iteration