标题： 熵最优传输的样本复杂度与径向代价 显示英文标题

标题： Sample complexity for entropic optimal transport with radial cost

摘要： 我们证明了熵正则化最优传输的新样本复杂度结果。 我们的界限适用于$\mathbb R^d$上具有指数尾部衰减的概率测度以及满足局部 Lipschitz 条件的径向代价函数。 它在对数因子范围内是精确的，并通过其支撑集的广义覆盖数捕捉了边缘分布的内在维度。 适合我们框架的示例包括次指数和次高斯分布以及径向代价函数$c(x,y)=|x-y|^p$对$p\ge 2.$ 显示英文摘要

摘要： 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 $p\ge 2.$