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.
From: Yiling Xie [view email]
[v1]
Wed, 2 Mar 2022 01:16:10 UTC (105 KB)
[v2]
Tue, 22 Mar 2022 21:01:28 UTC (106 KB)
[v3]
Tue, 30 May 2023 00:15:35 UTC (82 KB)
[v4]
Fri, 3 Jul 2026 09:56:12 UTC (533 KB)
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