Federated Wasserstein Distance
This work addresses the challenge of privacy-preserving distribution comparison in federated learning, offering a novel method for a specific bottleneck.
The paper tackles the problem of computing the Wasserstein distance between distributions in a federated setting, where data is stored on different devices without central access, and introduces FedWad, an algorithm that achieves this by leveraging geometric properties, with empirical results showing applications in federated coresets and boosting federated learning performance.
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.