We report on what seems to be an intriguing connection between variable integration time and partial velocity refreshment of Ideal Hamiltonian Monte Carlo samplers, both of which can be used for reducing the dissipative behavior of the dynamics. More concretely, we show that on quadratic potentials, efficiency can be improved through these means by a $\sqrt{\kappa}$ factor in Wasserstein-2 distance, compared to classical constant integration time, fully refreshed HMC. We additionally explore the benefit of randomized integrators for simulating the Hamiltonian dynamics under higher order regularity conditions.

翻译：我们报道了理想哈密顿蒙特卡洛采样器中变量积分时间与部分速度更新之间似乎存在的有趣关联，两者均可用于降低动力学的耗散行为。具体而言，我们证明在二次势能场景下，相较于采用恒定积分时间与完全速度更新的经典HMC方法，通过上述手段可将Wasserstein-2距离下的效率提升$\sqrt{\kappa}$倍。此外，我们探讨了在更高阶正则条件下，随机积分器用于模拟哈密顿动力学的优势。