论文标题
Schrödinger电位的稳定性和Sinkhorn算法的收敛性
Stability of Schrödinger Potentials and Convergence of Sinkhorn's Algorithm
论文作者
论文摘要
我们研究了相对于边缘的熵正则最佳运输的稳定性。给定边缘弱收敛，我们为描述最佳耦合的密度的schrödinger电位建立了强大的收敛性。当边际分散总变化时，最佳耦合也会在总变化中收敛。这用于表明，当成本是二次，边缘是subgaussian或更一般的所有连续成本满足可集成性条件的所有连续成本时，Sinkhorn的算法总差异会融合。
We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Schrödinger potentials describing the density of the optimal couplings. When the marginals converge in total variation, the optimal couplings also converge in total variation. This is applied to show that Sinkhorn's algorithm converges in total variation when costs are quadratic and marginals are subgaussian, or more generally for all continuous costs satisfying an integrability condition.
