Convergence and non-asymptotic error analysis for kinetic Langevin samplers using the exact harmonic Langevin integrator
It provides theoretical guarantees for a new splitting scheme in sampling, relevant for machine learning and molecular dynamics, but the improvement over existing methods is incremental.
The paper proposes a kinetic Langevin sampler using an exact harmonic Langevin integrator, achieving convergence rates in $L^2$-Wasserstein distance for strongly log-concave targets, with step size requirements comparable to existing schemes like OBABO or UBU.
We propose a novel kinetic Langevin sampler based on a specific splitting scheme using the exact harmonic Langevin integrator. For strongly log-concave target measures, the sampler exploits a decomposition of the strongly convex potential into a quadratic part and a convex perturbation with Lipschitz continuous gradient. For the resulting first- and second-order schemes associated with this splitting we establish convergence rates in $L^2$-Wasserstein distance as well as non-asymptotic error bounds. In particular, the contraction rate is of the same order as that of the underlying continuous dynamics. To achieve $\varepsilon$-accuracy, the required step size for the second-order scheme is comparable to that of established splitting schemes such as OBABO or UBU, which are widely used in machine learning and molecular dynamics.