薛定谔势的稳定性与Sinkhorn算法的收敛性
Stability of Schrödinger Potentials and Convergence of Sinkhorn's Algorithm
摘要：
研究了熵正则化最优输运关于边界的稳定性。由于边缘收敛弱，我们建立了一个强收敛的薛定谔电位描述的密度的最佳耦合。当边缘值以全变差收敛时，最优耦合也以全变差收敛。这用于表明，当成本为二次且边缘为亚高斯时，或者更一般地，对于满足可积性条件的所有连续成本，辛霍恩算法在全变差中收敛。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
