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2020

Gradient descent algorithms for Bures-Wasserstein barycenters

Chewi, Sinho, Maunu, Tyler, Rigollet, Philippe et al.

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We study first order methods to compute the barycenter of a probability distribution $P$ over the space of probability measures with finite second moment.

We develop a framework to derive global rates of convergence for both gradient descent and stochastic gradient descent despite the fact that the barycenter functional is not geodesically convex.
Our analysis overcomes this technical hurdle by employing a Polyak-Lojasiewicz (PL) inequality and relies on tools from optimal transport and metric geometry.
In turn, we establish a PL inequality when $P$ is supported on the Bures-Wasserstein manifold of Gaussian probability measures.

Gradient descent algorithms for Bures-Wasserstein barycenters · Around

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