We prove a new sample complexity result for entropy regularized optimal transport. Our bound holds for probability measures on $\mathbb R^d$ with exponential tail decay and for radial cost functions that satisfy a local Lipschitz condition. It is sharp up to logarithmic factors, and captures the intrinsic dimension of the marginal distributions through a generalized covering number of their supports. Examples that fit into our framework include subexponential and subgaussian distributions and radial cost functions $c(x,y)=|x-y|^p$ for $p\ge 2.$

翻译：我们证明了熵正则化最优传输的一个新样本复杂度结果。该界限适用于具有指数尾部衰减的$\mathbb R^d$上的概率测度，以及满足局部Lipschitz条件的径向成本函数。该结果在对数因子范围内是尖锐的，并通过边际分布支撑集的一个广义覆盖数捕捉了其内在维度。符合我们框架的示例包括亚指数与亚高斯分布，以及对于$p\ge 2$的径向成本函数$c(x,y)=|x-y|^p$。