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 $(2+\delta)$-moment.

翻译：随着正规化参数的消失,我们研究了分化-正规化最佳运输的趋同情况,获得了包括相对的正辛或美元正规化、一般运输成本和多边缘问题在内的一般差价的急剧率,一种使用量化和马丁基联结的新方法适用于非常规边缘,特别是实现所有边际(以(2 ⁇ delta)美元-时速有限的)极强的原型固定化2-Wasserstein距离,特别是实现非常规化2-Wasser-Wasser-ser-ser-ser-ser-ser-ser-ser-serm-servement。