Federated Wasserstein Distance
Authors: Alain Rakotomamonjy,Kimia Nadjahi,Liva Ralaivola
Presentation: ICLR 2024,Poster

Abstract: We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner.
Namely, we show how to estimate the Wasserstein distance between two samples stored and
 kept on different devices/clients whilst a central entity/server orchestrates the computations 
 (again, without having access to the samples). To achieve this feat, we take advantage of the geometric 
properties of the Wasserstein distance -- in particular, the triangle inequality -- 
 and that of the associated {\em geodesics}: our algorithm, FedWad (for Federated Wasserstein Distance), iteratively approximates 
 the Wasserstein distance by manipulating and exchanging distributions from the
  space of geodesics in lieu of the input samples. 
  In addition to establishing the convergence properties of FedWad,
   we provide empirical results on federated coresets and federate 
   optimal transport dataset distance, that we respectively exploit for
   building a novel federated model and for boosting performance of popular federated learning algorithms.