An Asynchronous Decentralized Algorithm for Wasserstein Barycenter Problem

TL;DR

This paper introduces A$^2$DWB, the first asynchronous decentralized algorithm for the Wasserstein Barycenter Problem, improving efficiency by using stale neighbor information and demonstrating superior empirical performance.

Contribution

It presents a novel asynchronous decentralized algorithm for WBP based on a stochastic block coordinate descent method, addressing efficiency issues in previous synchronous approaches.

Findings

A$^2$DWB outperforms synchronous algorithms in empirical tests.

The algorithm effectively uses stale neighbor information to reduce waiting times.

It is the first asynchronous decentralized solution for WBP.

Abstract

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 (A$^2$DWB). A$^2$DWB is induced by a novel stochastic block coordinate descent method to optimize the dual of entropy regularized WBP. To our knowledge, A$^2$DWB 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.