Controlled Sequential Monte Carlo

TL;DR

This paper introduces controlled sequential Monte Carlo algorithms that optimize proposal distributions via an approximate optimal control solution, improving performance in high-dimensional inference tasks.

Contribution

It generalizes existing algorithms by integrating optimal control techniques into sequential Monte Carlo methods for complex models.

Findings

Significant performance improvements over existing methods.

Theoretical analysis of fluctuation and stability.

Effective in high-dimensional and complex static models.

Abstract

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in statistics and related fields; e.g. for inference in non-linear non-Gaussian state space models, and in complex static models. Like many Monte Carlo sampling schemes, they rely on proposal distributions which crucially impact their performance. We introduce here a class of controlled sequential Monte Carlo algorithms, where the proposal distributions are determined by approximating the solution to an associated optimal control problem using an iterative scheme. This method builds upon a number of existing algorithms in econometrics, physics, and statistics for inference in state space models, and generalizes these methods so as to accommodate complex static models. We provide a theoretical analysis concerning the fluctuation and stability of this methodology that also provides insight into the properties of related algorithms. We demonstrate significant gains over state-of-the-art methods at a fixed computational complexity on a variety of applications.