2021
DOI: 10.48550/arxiv.2106.08502
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Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descent

Abstract: We study first-order optimization algorithms for computing the barycenter of Gaussian distributions with respect to the optimal transport metric. Although the objective is geodesically non-convex, Riemannian GD empirically converges rapidly, in fact faster than off-theshelf methods such as Euclidean GD and SDP solvers. This stands in stark contrast to the best-known theoretical results for Riemannian GD, which depend exponentially on the dimension. In this work, we prove new geodesic convexity results which pr… Show more

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