Variational Optimization of Annealing Schedules

TL;DR

This paper introduces a novel algorithm for optimizing annealing schedules in annealed importance sampling, leading to more accurate partition function estimates by minimizing estimation error.

Contribution

It proposes a functional-based approach to derive and numerically minimize an optimal annealing schedule, improving over heuristic or linear methods.

Findings

The proposed algorithm outperforms conventional schedules in experiments.

Optimized schedules reduce AIS estimation error.

Large quantization numbers benefit more from the optimized approach.

Abstract

Annealed importance sampling (AIS) is a common algorithm to estimate partition functions of useful stochastic models. One important problem for obtaining accurate AIS estimates is the selection of an annealing schedule. Conventionally, an annealing schedule is often determined heuristically or is simply set as a linearly increasing sequence. In this paper, we propose an algorithm for the optimal schedule by deriving a functional that dominates the AIS estimation error and by numerically minimizing this functional. We experimentally demonstrate that the proposed algorithm mostly outperforms conventional scheduling schemes with large quantization numbers.