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.

翻译：我们提出了一种基于特定分裂方案的新型动力学朗之万采样器，该方案采用精确调和朗之万积分器。针对强对数凹目标测度，该采样器利用强凸势能分解为二次部分与具有利普希茨连续梯度的凸扰动的特性。对于该分裂方案对应的一阶和二阶格式，我们建立了$L^2$-瓦瑟斯坦距离下的收敛速率以及非渐近误差界。特别地，其收缩率与底层连续动力学的收缩率同阶。为实现$\varepsilon$精度，二阶格式所需的步长与机器学习及分子动力学中广泛使用的OBABO或UBU等经典分裂方案相当。