Ensemble Kalman Filter (EnKF) for Reinforcement Learning (RL)

This paper is concerned with the problem of representing and learning the optimal control law for the linear quadratic Gaussian (LQG) optimal control problem. In recent years, there is a growing interest in re-visiting this classical problem, in part due to the successes of reinforcement learning (RL). The main question of this body of research (and also of our paper) is to approximate the optimal control law {\em without} explicitly solving the Riccati equation. For this purpose, a novel simulation-based algorithm, namely an ensemble Kalman filter (EnKF), is introduced in this paper. The algorithm is used to obtain formulae for optimal control, expressed entirely in terms of the EnKF particles. For the general partially observed LQG problem, the proposed EnKF is combined with a standard EnKF (for the estimation problem) to obtain the optimal control input based on the use of the separation principle. A nonlinear extension of the algorithm is also discussed which clarifies the duality roots of the proposed EnKF. The theoretical results and algorithms are illustrated with numerical experiments

The Hitchhiker's Guide to Nonlinear Filtering

Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We start our review of the theory on nonlinear filtering from the simplest `filtering' task we can think of, namely static Bayesian inference. From there we continue our journey through discrete-time models, which is usually encountered in machine learning, and generalize to and further emphasize continuous-time filtering theory. The idea of changing the probability measure connects and elucidates several aspects of the theory, such as the parallels between the discrete- and continuous-time problems and between different observation models. Furthermore, it gives insight into the construction of particle filtering algorithms. This tutorial is targeted at scientists and engineers and should serve as an introduction to the main ideas of nonlinear filtering, and as a segway to more advanced and specialized literature.Comment: 64 page