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Annealed Importance Sampling (AIS) synthesizes weighted samples from anintractable distribution given its unnormalized density function. Thisalgorithm relies on a sequence of interpolating distributions bridging thetarget to an initial tractable distribution such as the well-known geometricmean path of unnormalized distributions which is assumed to be suboptimal ingeneral. In this paper, we prove that the geometric annealing corresponds tothe distribution path that minimizes the KL divergence between the currentparticle distribution and the desired target when the feasible change in theparticle distribution is constrained. Following this observation, we derive theconstant rate discretization schedule for this annealing sequence, whichadjusts the schedule to the difficulty of moving samples between the initialand the target distributions. We further extend our results to $f$-divergencesand present the respective dynamics of annealing sequences based on which wepropose the Constant Rate AIS (CR-AIS) algorithm and its efficientimplementation for $\alpha$-divergences. We empirically show that CR-AISperforms well on multiple benchmark distributions while avoiding thecomputationally expensive tuning loop in existing Adaptive AIS.

Adaptive Annealed Importance Sampling with Constant Rate Progress