论文标题
张量最佳运输，量度集和张量表之间的距离
Tensor optimal transport, distance between sets of measures and tensor scaling
论文作者
论文摘要
我们研究了$ d> 2 $离散措施的最佳运输问题。这是$ d $ tensors上的线性编程问题。它提供了一种计算两组离散度量之间的“距离”的方法。我们引入了一个熵正则化术语，该术语产生了张量的缩放。我们给出了著名的Sinkhorn缩放算法的变体。我们表明，该算法可以看作是严格凸功能的部分最小化算法。在适当的条件下，收敛速率是几何形状，我们估计速率。我们的结果是两种离散措施的经典情况下已知结果的概括。
We study the optimal transport problem for $d>2$ discrete measures. This is a linear programming problem on $d$-tensors. It gives a way to compute a "distance" between two sets of discrete measures. We introduce an entropic regularization term, which gives rise to a scaling of tensors. We give a variation of the celebrated Sinkhorn scaling algorithm. We show that this algorithm can be viewed as a partial minimization algorithm of a strictly convex function. Under appropriate conditions the rate of convergence is geometric and we estimate the rate. Our results are generalizations of known results for the classical case of two discrete measures.
