Abstract

In this talk we study three kinetic Langevin samplers including the Euler discretization, the BU and the UBU splitting scheme. We are interested in how efficiently they sample a given probability distribution with non-convex potential. We show contraction results in L^{1 -Wasserstein distance for all three samplers. These results are based on a carefully tailored distance function and an appropriate coupling construction. Additionally, we analyse the error in the L}1 -Wasserstein distance between the target measure and the invariant measure of the discretization scheme. To get an ε-accuracyin L^{1-Wasserstein distance, we show complexity guarantees of order O( d}{1/2}/ε) for the Euler scheme and O(d^{1/4} / ε) for the UBU scheme under appropriate regularity assumptions on the target measure. The results can also be applied to interacting particle systems and provide bounds for sampling probability measures of mean-field type. The talk is based on a joint work with Peter A. Whalley.