Convergence of kinetic Langevin samplers for non-convex potentials

We study three kinetic Langevin samplers including the Euler discretization, the BU and the UBU splitting scheme. We provide contraction results in L¹-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 L¹-Wasserstein distance between the true target measure and the invariant measure of the discretization scheme is bounded. To get an ε-accuracy in L¹-Wasserstein distance, we show complexity guarantees of order O(√d/ε) for the Euler scheme and O(d1/4/√ε) 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.