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 is a numerical approximation of entropic mirror descent applied to the 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 used as an alternative to Langevin-based algorithms to minimize the KL divergence. We exploit the connection between tempering and mirror descent iterates to justify common practices in SMC and propose improvements to algorithms in literature.

翻译：本文探讨了温度调整（用于顺序蒙特卡洛方法；SMC）与熵镜像下降之间的联系，以从未知归一化密度但已知非归一化密度的目标概率分布中采样。我们证明温度调整SMC是熵镜像下降应用于Kullback-Leibler（KL）散度的一种数值近似方法，并获得了温度调整迭代的收敛速率。我们的研究结果从优化角度为温度调整迭代提供了理论依据，表明温度调整可作为基于Langevin算法的KL散度最小化替代方法。我们利用温度调整与镜像下降迭代之间的联系，为SMC中的常见实践提供了理论支撑，并提出了对现有文献中算法的改进方案。