  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.
