We study three kinetic Langevin samplers including the Euler discretization, the BU and the UBU splitting scheme. We provide contraction results in $L^1$-Wasserstein distance for non-convex potentials. These results are based on a carefully tailored distance function and an appropriate coupling construction. Additionally, the error in the $L^1$-Wasserstein distance between the true target measure and the invariant measure of the discretization scheme is bounded. To get an $\varepsilon$-accuracy in $L^1$-Wasserstein distance, we show complexity guarantees of order $\mathcal{O}(\sqrt{d}/\varepsilon)$ for the Euler scheme and $\mathcal{O}(d^{1/4}/\sqrt{\varepsilon})$ for the UBU scheme under appropriate regularity assumptions on the target measure. The results are applicable to interacting particle systems and provide bounds for sampling probability measures of mean-field type.

翻译：我们研究了三种动力学朗之万采样器，包括欧拉离散化方法、BU和UBU分裂格式。针对非凸势函数，我们提供了在$L^1$-Wasserstein距离下的收缩结果。这些结果基于精心设计的距离函数和适当的耦合构造。此外，我们界定了真实目标测度与离散化方案不变测度之间$L^1$-Wasserstein距离的误差。为达到$L^1$-Wasserstein距离下的$\varepsilon$精度，在目标测度满足适当正则性假设的条件下，我们证明欧拉方案的复杂度保证为$\mathcal{O}(\sqrt{d}/\varepsilon)$，UBU方案为$\mathcal{O}(d^{1/4}/\sqrt{\varepsilon})$。这些结果适用于相互作用粒子系统，并为平均场类型概率测度的采样提供了界。