标题： 广义散度正则化最优传输：样本复杂度和中心极限定理 显示英文标题

标题： General Divergence Regularized Optimal Transport: Sample Complexity and Central Limit Theorems

摘要： 最优运输近年来已成为一种基础方法，其应用跨越了多个研究领域。 然而，经验估计量与其总体对应量的收敛速率受到维度灾难的影响，这阻碍了其在高维空间中的应用。 虽然熵正则化已被证明可以有效缓解维度灾难，并在温和条件下实现参数收敛速率，但这些统计保证尚未扩展到一般的正则化方法。 我们的工作通过为更广泛的正则化家族建立类似的结果来弥补这一差距。 具体而言，在有界性约束下，我们证明了相对于样本大小n的收敛速率为\$ n^{-1/2}\$。 此外，我们推导了发散正则化最优运输的几个中心极限定理。 显示英文摘要

摘要： Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of dimensionality, which prevents its application in high-dimensional spaces. While entropic regularization has been proven to effectively mitigate the curse of dimensionality and achieve a parametric convergence rate under mild conditions, these statistical guarantees have not been extended to general regularizers. Our work bridges this gap by establishing analogous results for a broader family of regularizers. Specifically, under boundedness constraints, we prove a convergence rate of order $n^{-1/2} with respect to sample size n. Furthermore, we derive several central limit theorems for divergence regularized optimal transport.