ON THE INFINITE SWAPPING LIMIT FOR PARALLEL TEMPERING
ON THE INFINITE SWAPPING LIMIT FOR PARALLEL TEMPERING
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DOI：
10.1137/110853145
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发表时间：
2012-01-01
影响因子：
1.6
通讯作者：
Doll, J. D.
中科院分区：
文献类型：
--
作者：
Dupuis, Paul;Liu, Yufei;Doll, J. D.
平行回火，也称为副本交换采样，是模拟复杂系统的一种重要方法。在该算法中，模拟在一系列温度下并行进行，并且该算法的关键特征是以给定速率在并行模拟之间交换配置的交换机制。该机制被设计为允许感兴趣的低温系统从深局部能量最小值中逃逸，否则它可能通过与较高温度组件的交换而被捕获。在本文中，我们介绍了这样的计划的大偏差理论的基础上的性能标准，并认为收敛速度是一个单调递增的函数的交换率。这激发了对互换利率趋于无穷大时的极限过程的研究。我们构造一个计划，这是相当于这个限制在分配意义上，但不涉及交换。相反，交换的效果是通过影响动态和经验测量的权重集合来捕获的。虽然理论上是最佳的，但当温度的数量很大时，这个限制在计算上是不可行的，因此也开发了易于实现和接近最佳的变化。
Parallel tempering, also known as replica exchange sampling, is an important method for simulating complex systems. In this algorithm simulations are conducted in parallel at a series of temperatures, and the key feature of the algorithm is a swap mechanism that exchanges configurations between the parallel simulations at a given rate. The mechanism is designed to allow the low temperature system of interest to escape from deep local energy minima where it might otherwise be trapped via those swaps with the higher temperature components. In this paper we introduce a performance criterion for such schemes based on large deviation theory and argue that the rate of convergence is a monotone increasing function of the swap rate. This motivates the study of the limit process as the swap rate goes to infinity. We construct a scheme which is equivalent to this limit in a distributional sense but which involves no swapping at all. Instead, the effect of the swapping is captured by a collection of weights that influence both the dynamics and the empirical measure. While theoretically optimal, this limit is not computationally feasible when the number of temperatures is large, and so variations that are easy to implement and nearly optimal are also developed.