An Asynchronous Decentralized Algorithm for Wasserstein Barycenter Problem
This work addresses the computational bottleneck in decentralized optimization for AI applications, though it appears incremental as it builds on existing synchronous approaches.
The paper tackled the Wasserstein Barycenter Problem in a decentralized setting by proposing an asynchronous algorithm (A$^2$DWB) that uses stale neighbor information to reduce waiting overhead, resulting in improved time efficiency compared to synchronous methods.
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.