论文标题
瓦斯尔斯坦重中心问题改善复杂性界限
Improved Complexity Bounds in Wasserstein Barycenter Problem
论文作者
论文摘要
在本文中，我们着重于Wasserstein Barycenter问题的计算方面。我们提出了两种算法，以计算$ m $ $ $ n $ $ n $的Wasserstein Barycenters，并具有准确的$ \ e $。第一种基于具有特定规范的镜像代理的第一种算法达到了著名的加速迭代迭代式Bregman预测（IBP）的复杂性，即$ \ widetilde o（Mn^2 \ sqrt n/\ e）$，但是与（加速度不正常的IBP）相反，ibp bigralsimate n n s vimne n is n s n is n s vimne nemerations Insimable nise Insealise INSERABLE INSERABLE INSERIDES毫无疑问。第二种算法基于面积 - 凸性和双重外推，提高了wasserstein barycenter问题的先前最著名的收敛速度，享受$ \ widetilde o（Mn^2/\ e）$复杂性。
In this paper, we focus on computational aspects of the Wasserstein barycenter problem. We propose two algorithms to compute Wasserstein barycenters of $m$ discrete measures of size $n$ with accuracy $\e$. The first algorithm, based on mirror prox with a specific norm, meets the complexity of celebrated accelerated iterative Bregman projections (IBP), namely $\widetilde O(mn^2\sqrt n/\e)$, however, with no limitations in contrast to the (accelerated) IBP, which is numerically unstable under small regularization parameter. The second algorithm, based on area-convexity and dual extrapolation, improves the previously best-known convergence rates for the Wasserstein barycenter problem enjoying $\widetilde O(mn^2/\e)$ complexity.
