发表机构
University of Toronto（多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从Wasserstein距离推广到重心代价的弱最优传输，提出多边际公式及其对偶，其中边际在凸序下受约束，为质心计算提供新框架。
AI 中文摘要
我们将Wasserstein重心理论从Wasserstein距离推广到具有重心代价的弱最优传输问题。我们找到了一个多边际公式及其对偶问题。该多边际问题本身是新颖的；与经典多边际最优传输问题相反，其竞争者的前M个边际不是固定的，而只需在凸序意义下支配前M个给定测度，而其竞争者的后N-M个边际在凸序意义下被后N-M个给定测度所支配。
英文摘要
We generalize the theory of Wasserstein barycenters between N given measures from the Wasserstein distance to the weak optimal transport problem with barycentric cost. We find a multi-marginal formulation and its dual problem. The multi-marginal problem is new in itself; contrary to the classical multi-marginal optimal transport problem, the first M marginals of its competitors are not fixed but instead only need dominate the first M given measures in convex order, while the last N-M marginals of its competitors are dominated in convex order by the last N-M given measures.
