论文标题
哈密顿蒙特卡洛的熵方法：理想化的案例
An entropic approach for Hamiltonian Monte Carlo: the idealized case
论文作者
论文摘要
为理想化的哈密顿蒙特卡洛链建立了定量的长期熵收敛和短期正则化，或者在固定时间内遵循哈密顿动力学，然后通过自动登记高斯步骤部分或完全刷新其速度。这些结果在离散的时间内是连续时动力学扩散的相似结果的类似结果，而后者可以从我们的边界中以适当的极限制度获得。靶标度量的对数 - 核心恒定的依赖性很清晰，并在平均场情况和低温方向上进行了说明，并应用于模拟退火算法。简要讨论了实用的未调整算法。
Quantitative long-time entropic convergence and short-time regularization are established for an idealized Hamiltonian Monte Carlo chain which alternatively follows an Hamiltonian dynamics for a fixed time and then partially or totally refreshes its velocity with an auto-regressive Gaussian step. These results, in discrete time, are the analogous of similar results for the continuous-time kinetic Langevin diffusion, and the latter can be obtained from our bounds in a suitable limit regime. The dependency in the log-Sobolev constant of the target measure is sharp and is illustrated on a mean-field case and on a low-temperature regime, with an application to the simulated annealing algorithm. The practical unadjusted algorithm is briefly discussed.
