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：我们报告了理想哈密顿蒙特卡洛采样器中可变积分时间与部分速度刷新之间一个看似引人入胜的联系，这两种方法均可用于减少动力学的耗散行为。具体而言，我们证明在二次势能下，相较于经典的固定积分时间、完全刷新的HMC，通过上述方法可将效率在Wasserstein-2距离上提升$\sqrt{\kappa}$倍。此外，我们还探讨了在更高阶正则性条件下，随机积分器用于模拟哈密顿动力学的优势。