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

arXiv: https://arxiv.org/abs/2507.19627 · HTML: https://mlsanity.com/paper/2507.19627/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 51 references that are in the map.
- First posted on arXiv 25 Jul 2025.

## Builds on (most cited first, 24 of 24)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [An Improved Analysis of Stochastic Gradient Descent with Momentum](https://mlsanity.com/paper/2007.07989/) (2020)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [A Wasserstein-type distance in the space of Gaussian Mixture Models](https://mlsanity.com/paper/1907.05254/) (2019)
- [On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms](https://mlsanity.com/paper/1901.06482/) (2019)
- [Sliced Wasserstein Distance for Learning Gaussian Mixture Models](https://mlsanity.com/paper/1711.05376/) (2017)
- [A Unified Analysis of Stochastic Momentum Methods for Deep Learning](https://mlsanity.com/paper/1808.10396/) (2018)
- [Multilevel Clustering via Wasserstein Means](https://mlsanity.com/paper/1706.03883/) (2017)
- [A Smoothed Dual Approach for Variational Wasserstein Problems](https://mlsanity.com/paper/1503.02533/) (2015)
- [Semi-dual Regularized Optimal Transport](https://mlsanity.com/paper/1811.05527/) (2018)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters](https://mlsanity.com/paper/1806.03915/) (2018)
- [An Integrated Transportation Distance Between Kernels and Approximate Dynamic Risk Evaluation in Markov Systems](https://mlsanity.com/paper/2311.06645/) (2023)
- [Randomised Wasserstein Barycenter Computation: Resampling with Statistical Guarantees](https://mlsanity.com/paper/2012.06397/) (2020)
- [Mitigating Discrimination in Insurance with Wasserstein Barycenters](https://mlsanity.com/paper/2306.12912/) (2023)

## Built on by (most cited first, 1 of 1)

- [Spec-LLaVA: Accelerating Vision-Language Models with Dynamic Tree-Based Speculative Decoding](https://mlsanity.com/paper/2509.11961/) (2025)

## Abstract (arXiv)

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.