# An Asynchronous Decentralized Algorithm for Wasserstein Barycenter Problem

arXiv: https://arxiv.org/abs/2304.11653 · HTML: https://mlsanity.com/paper/2304.11653/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 23 Apr 2023.

## Builds on (most cited first, 20 of 20)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Asynchronous Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1710.06952/) (2017)
- [Scalable Bayes via Barycenter in Wasserstein Space](https://mlsanity.com/paper/1508.05880/) (2015)
- [Fast Discrete Distribution Clustering Using Wasserstein Barycenter with Sparse Support](https://mlsanity.com/paper/1510.00012/) (2015)
- [Fast Convergence Rates for Distributed Non-Bayesian Learning](https://mlsanity.com/paper/1508.05161/) (2015)
- [Accelerated, Parallel and Proximal Coordinate Descent](https://mlsanity.com/paper/1312.5799/) (2013)
- [Stochastic Wasserstein Barycenters](https://mlsanity.com/paper/1802.05757/) (2018)
- [Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters](https://mlsanity.com/paper/1806.03915/) (2018)
- [Parallel Streaming Wasserstein Barycenters](https://mlsanity.com/paper/1705.07443/) (2017)
- [Accelerated Decentralized Optimization with Local Updates for Smooth and Strongly Convex Objectives](https://mlsanity.com/paper/1810.02660/) (2018)
- [A Fast Globally Linearly Convergent Algorithm for the Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1809.04249/) (2018)
- [AsySPA: An Exact Asynchronous Algorithm for Convex Optimization Over Digraphs](https://mlsanity.com/paper/1808.04118/) (2018)
- [Distributed Learning for Cooperative Inference](https://mlsanity.com/paper/1704.02718/) (2017)
- [Accelerating Asynchronous Algorithms for Convex Optimization by Momentum Compensation](https://mlsanity.com/paper/1802.09747/) (2018)
- [Improved Linear Programs for Discrete Barycenters](https://mlsanity.com/paper/1803.11313/) (2018)
- [Asynchronous decentralized accelerated stochastic gradient descent](https://mlsanity.com/paper/1809.09258/) (2018)
- [A2BCD: An Asynchronous Accelerated Block Coordinate Descent Algorithm With Optimal Complexity](https://mlsanity.com/paper/1803.05578/) (2018)
- [Asynchronous Accelerated Proximal Stochastic Gradient for Strongly Convex Distributed Finite Sums](https://mlsanity.com/paper/1901.09865/) (2019)

## Abstract (arXiv)

Wasserstein Barycenter Problem (WBP) has recently received much attention in the field of artificial intelligence. In this paper, we focus on the decentralized setting for WBP and propose an asynchronous decentralized algorithm (A2DWB). A2DWB is induced by a novel stochastic block coordinate descent method to optimize the dual of entropy regularized WBP. To our knowledge, A2DWB is the first asynchronous decentralized algorithm for WBP. Unlike its synchronous counterpart, it updates local variables in a manner that only relies on the stale neighbor information, which effectively alleviate the waiting overhead, and thus substantially improve the time efficiency. Empirical results validate its superior performance compared to the latest synchronous algorithm.