Federated Wasserstein Distance

Alain Rakotomamonjy, Kimia Nadjahi, Liva Ralaivola

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Keywords: Wasserstein distance, Federated Learning ; Triangle inequality

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TL;DR: We propose a federated manner of computing Wasserstein distance by exploiting its metric property and its geodesics

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.

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Primary Area: general machine learning (i.e., none of the above)

Submission Number: 5765