Annealed Sequential Monte Carlo (SMC) samplers are special cases of SMC samplers where the sequence of distributions can be embedded in a smooth path of distributions. Using this underlying path of distributions and a performance model based on the variance of the normalisation constant estimator, we systematically study dense schedule and large particle limits. From our theory and adaptive methods emerges a notion of global barrier capturing the inherent complexity of normalisation constant approximation under our performance model. We then turn the resulting approximations into surrogate objective functions of algorithm performance, and use them for methodology development. We obtain novel adaptive methodologies, Sequential SMC (SSMC) and Sequential AIS (SAIS) samplers, which address practical difficulties inherent in previous adaptive SMC methods. First, our SSMC algorithms are predictable: they produce a sequence of increasingly precise estimates at deterministic and known times. Second, SAIS, a special case of SSMC, enables schedule adaptation at a memory cost constant in the number of particles and require much less communication. Finally, these characteristics make SAIS highly efficient on GPUs. We develop an open-source, high-performance GPU implementation based on our methodology and demonstrate up to a hundred-fold speed improvement compared to state-of-the-art adaptive AIS methods.

翻译：退火序列蒙特卡洛（SMC）采样器是SMC采样器的一种特例，其分布序列可嵌入一个平滑的分布路径中。利用这一基础分布路径以及基于归一化常数估计量方差的性能模型，我们系统研究了密集调度和大粒子极限。从我们的理论和自适应方法中，浮现出一个全局障碍的概念，该概念捕捉了在我们的性能模型下归一化常数近似所固有的复杂性。随后，我们将所得近似转化为算法性能的代理目标函数，并将其用于方法学开发。我们获得了新颖的自适应方法——序列SMC（SSMC）和序列AIS（SAIS）采样器，这些方法解决了先前自适应SMC方法中固有的实际困难。首先，我们的SSMC算法具有可预测性：它们在确定且已知的时间点产生一系列精度逐步提升的估计。其次，作为SSMC特例的SAIS，能够在内存成本与粒子数量无关的情况下实现调度自适应，并且所需通信量大幅减少。最后，这些特性使得SAIS在GPU上具有极高的效率。我们基于所提方法开发了一个开源的高性能GPU实现，并展示了相比最先进的自适应AIS方法高达百倍的加速效果。