Imitation and Transfer Learning for LQG Control

In this paper we study an imitation and transfer learning setting for Linear Quadratic Gaussian (LQG) control, where (i) the system dynamics, noise statistics cost function are unknown expert data is provided (that is, sequences of optimal inputs outputs) to learn LQG controller, (ii) multiple control tasks performed same but with different costs. We show that controller can be learned from a set trajectories length $n(l+2)-1$, $n$ $l$ dimension state output, respectively. Further, decomposed as product estimation matrix, which depends only on cost. This data-based separation principle allows us matrix across tasks, reduce needed to~$2n+m-1$ $m$ (for single-input systems $l=2$, yields approximately $50\%$ reduction required data).