Contraction in Wasserstein 1-distance with explicit rates is established for generalized Hamiltonian Monte Carlo with stochastic gradients under possibly nonconvex conditions. The algorithms considered include splitting schemes of kinetic Langevin diffusion commonly used in molecular dynamics simulations. To accommodate the degenerate noise structure corresponding to inertia existing in the chain, a characteristically discrete-in-time coupling and contraction proof is devised. As consequence, quantitative Gaussian concentration bounds are provided for empirical averages. Convergence in Wasserstein 2-distance and total variation are also given, together with numerical bias estimates.

翻译：本文针对可能非凸条件下的随机梯度广义哈密顿蒙特卡洛方法，建立了具有显式收敛速率的Wasserstein 1-距离收缩性结果。所考虑的算法包括分子动力学模拟中常用的动能朗之万扩散分裂格式。为适应马尔可夫链中惯性对应的退化噪声结构，我们设计了一种特征性的离散时间耦合与收缩证明方法。由此，我们为经验平均值提供了定量的高斯集中界。同时给出了Wasserstein 2-距离和全变差收敛性结果，并附有数值偏差估计。