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We revisit the problem of sampling from a target distribution that has asmooth strongly log-concave density everywhere in $\mathbb R^p$. In thiscontext, if no additional density information is available, the randomizedmidpoint discretization for the kinetic Langevin diffusion is known to be themost scalable method in high dimensions with large condition numbers. Our mainresult is a nonasymptotic and easy to compute upper bound on the Wasserstein-2error of this method. To provide a more thorough explanation of our method forestablishing the computable upper bound, we conduct an analysis of the midpointdiscretization for the vanilla Langevin process. This analysis helps to clarifythe underlying principles and provides valuable insights that we use toestablish an improved upper bound for the kinetic Langevin process with themidpoint discretization. Furthermore, by applying these techniques we establishnew guarantees for the kinetic Langevin process with Euler discretization,which have a better dependence on the condition number than existing upperbounds.

Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisited