论文标题
关于理想的哈密顿蒙特卡洛采样器的耗散
On the Dissipation of Ideal Hamiltonian Monte Carlo Sampler
论文作者
论文摘要
我们报告了理想的汉密尔顿蒙特卡洛采样器的可变积分时间与部分速度茶点之间的有趣联系，这两种都可用于减少动力学的耗散行为。更具体地说，我们表明，在二次电势时，与经典的恒定整合时间相比，在Wasserstein-2距离中，可以通过这些手段通过$ \sqrtκ$因素提高效率，完全刷新了HMC。我们还探讨了随机集成剂在高阶规则条件下模拟汉密尔顿动态的好处。
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 $\sqrtκ$ 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.
