论文标题
通过量化正规化最佳运输的收敛速率
Convergence Rates for Regularized Optimal Transport via Quantization
论文作者
论文摘要
我们研究了随着正则化参数的消失，差异性最佳转运的收敛性消失。一般差异的尖锐费率包括相对熵或$ l^{p} $正则化，一般运输成本和多边界问题。使用量化和Martingale耦合的新方法适用于非紧密的边缘和实现，特别是对于所有有限$（2+δ）$ - 时刻的边际距离的熵正规化2-wasserstein距离的尖锐前阶项。
We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. Sharp rates for general divergences including relative entropy or $L^{p}$ regularization, general transport costs and multi-marginal problems are obtained. A novel methodology using quantization and martingale couplings is suitable for non-compact marginals and achieves, in particular, the sharp leading-order term of entropically regularized 2-Wasserstein distance for all marginals with finite $(2+δ)$-moment.
