Sequential Monte Carlo (SMC) methods are a set of simulation-based techniques used to approximate high- dimensional probability distributions and their normalizing constants. They have found numerous applications in statistics as they can be applied to perform state estimation for state-space models and inference for complex static models. Like many Monte Carlo sampling schemes, they rely on proposal distributions which have a crucial impact on their performance. We introduce here a class of controlled SMC algorithms where the proposal distributions are determined by approximating the solution of an associated optimal control problem using an iterative scheme. We provide theoretical analysis of our proposed methodology and demonstrate significant gains over state-of-the-art methods at a fixed computational complexity on a variety of applications.
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