Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterations

Understand

We study the computation of doubly regularized Wasserstein barycenters, a recently introduced family of entropic barycenters governed by inner and outer regularization strengths.

• Previous research has demonstrated that various regularization parameter choices unify several notions of entropy-penalized barycenters while also revealing new ones, including a special case of debiased barycenters.
• In this paper, we propose and analyze an algorithm for computing doubly regularized Wasserstein barycenters.
• Our procedure builds on damped Sinkhorn iterations followed by exact maximization/minimization steps and guarantees convergence for any choice of regularization parameters.