Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution given its unnormalized density function. This algorithm relies on a sequence of interpolating distributions bridging the target to an initial tractable distribution such as the well-known geometric mean path of unnormalized distributions which is assumed to be suboptimal in general. In this paper, we prove that the geometric annealing corresponds to the distribution path that minimizes the KL divergence between the current particle distribution and the desired target when the feasible change in the particle distribution is constrained. Following this observation, we derive the constant rate discretization schedule for this annealing sequence, which adjusts the schedule to the difficulty of moving samples between the initial and the target distributions. We further extend our results to $f$-divergences and present the respective dynamics of annealing sequences based on which we propose the Constant Rate AIS (CR-AIS) algorithm and its efficient implementation for $\alpha$-divergences. We empirically show that CR-AIS performs well on multiple benchmark distributions while avoiding the computationally expensive tuning loop in existing Adaptive AIS.

翻译：退火重要性采样（Annealed Importance Sampling, AIS）通过非归一化密度函数从未知分布中合成带权样本。该算法依赖于一组插值分布序列，将目标分布与初始易处理分布（如广泛使用的非归一化分布几何均值路径）连接起来，而该路径通常被认为是次优的。本文证明，当粒子分布可行的变化受到约束时，几何退火对应于最小化当前粒子分布与期望目标之间KL散度的分布路径。基于这一发现，我们推导出该退火序列的恒定速率离散化调度方案，该方案可根据初始分布与目标分布之间传输样本的难度自适应调整调度参数。我们进一步将研究结果推广至$f$-散度，并给出相应的退火序列动力学过程，据此提出恒定速率退火重要性采样（CR-AIS）算法及其对$\alpha$-散度的高效实现。实验表明，CR-AIS在多个基准分布上表现优异，同时避免了现有自适应AIS中计算成本高昂的参数调优循环。