This paper explores the connections between tempering (for Sequential Monte Carlo; SMC) and entropic mirror descent to sample from a target probability distribution whose unnormalized density is known. We establish that tempering SMC corresponds to entropic mirror descent applied to the reverse Kullback-Leibler (KL) divergence and obtain convergence rates for the tempering iterates. Our result motivates the tempering iterates from an optimization point of view, showing that tempering can be seen as a descent scheme of the KL divergence with respect to the Fisher-Rao geometry, in contrast to Langevin dynamics that perform descent of the KL with respect to the Wasserstein-2 geometry. We exploit the connection between tempering and mirror descent iterates to justify common practices in SMC and derive adaptive tempering rules that improve over other alternative benchmarks in the literature.

翻译：本文探讨了退火（用于序贯蒙特卡洛方法；SMC）与熵镜像下降之间的联系，以从未知归一化密度的目标概率分布中进行采样。我们证明退火SMC等价于应用于逆向Kullback-Leibler（KL）散度的熵镜像下降，并获得了退火迭代的收敛率。我们的结果从优化角度为退火迭代提供了理论依据，表明退火可视为KL散度关于Fisher-Rao几何的下降方案，这与兰之万动力学中KL散度关于Wasserstein-2几何的下降形成对比。我们利用退火与镜像下降迭代之间的联系，为SMC中的常见做法提供了合理性证明，并推导出了自适应退火规则，这些规则在文献中优于其他备选基准方法。