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Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm
Giulia Luise · Saverio Salzo · Massimiliano Pontil · Carlo Ciliberto

Tue Dec 10 05:20 PM -- 05:25 PM (PST) @ West Exhibition Hall A
in Track 2 Session 2 »

We present a novel algorithm to estimate the barycenter of arbitrary probability distributions with respect to the Sinkhorn divergence. Based on a Frank-Wolfe optimization strategy, our approach proceeds by populating the support of the barycenter incrementally, without requiring any pre-allocation. We consider discrete as well as continuous distributions, proving convergence rates of the proposed algorithm in both settings. Key elements of our analysis are a new result showing that the Sinkhorn divergence on compact domains has Lipschitz continuous gradient with respect to the Total Variation and a characterization of the sample complexity of Sinkhorn potentials. Experiments validate the effectiveness of our method in practice.

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Author Information

Giulia Luise (University College London)
Saverio Salzo (Istituto Italiano di Tecnologia)
Massimiliano Pontil (IIT & UCL)
Carlo Ciliberto (Imperial College London)

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