An Accelerated Stochastic Variance-Reduced Algorithm for Entropic Wasserstein Barycenters

Yiling Xie; Yiling Luo; Xiaoming Huo

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arXiv · 2203.00813

An Accelerated Stochastic Variance-Reduced Algorithm for Entropic Wasserstein Barycenters

Yiling Xie·Yiling Luo·Xiaoming Huo

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Abstract

Fixed-support Wasserstein barycenters average probability distributions while accounting for the geometry of the support. We study the entropically regularized Wasserstein barycenter problem with a fixed regularization parameter and propose an accelerated stochastic variance-reduced primal-dual algorithm. The proposed algorithm uses a semi-dual finite-sum structure in which each stochastic gradient requires only one softmax over the barycenter support. The resulting finite-sum components have dimension-free smoothness bounds, which lead to a complexity result showing that the method improves the support-size dependence of deterministic accelerated gradient by a square-root factor while preserving accelerated dependence on the target accuracy. Experiments on synthetic data, DOTmark images, shape aggregation, and digit-averaging instances are consistent with the theoretical dependence on support size and accuracy and show lower arithmetic costs than the tested first-order baselines.

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BibTeX RIS

Yiling Xie, Yiling Luo, Xiaoming Huo. 2022-03-02. An Accelerated Stochastic Variance-Reduced Algorithm for Entropic Wasserstein Barycenters. https://arxiv.org/abs/2203.00813

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