Reviews: Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters

This paper presents a distributed algorithm for computing Wasserstein barycenters. The basic setup is that each agent in the decentralized system has access to one probability distribution; similar to "gossip" based optimization techniques in the classical case (e.g. It seems this paper missed the closest related work, "Stochastic Wasserstein Barycenters" (Claici et al., ArXiv/ICML), which proposes a nonconvex semidiscrete barycenter optimization algorithm. Certainly any final version of this paper needs to compare to that work carefully. It may also be worth noting that the Wasserstein propagation algorithm in "Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains" (2015) could be implemented easily on a network in a similar fashion to what is proposed in this paper; see their Algorithm 4. Like lots of previous work in OT, this technique uses entropic regularization to make transport tractable; they solve the smoothed dual.