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. As consequence, quantitative Gaussian concentration bounds are provided for empirical averages. Convergence in Wasserstein 2-distance, total variation and relative entropy are also given, together with numerical bias estimates.

翻译：在可能非凸的条件下，建立了带有随机梯度的广义哈密顿蒙特卡洛方法在Wasserstein 1-距离中具有显式速率的收缩性质。所考虑的算法包括动力学朗之万扩散的分裂格式。作为推论，给出了经验平均值的定量高斯集中界。此外，还给出了Wasserstein 2-距离、总变差和相对熵的收敛结果，以及数值偏差估计。