  This paper addresses the end-to-end sample complexity bound for learning the
H2 optimal controller (the Linear Quadratic Gaussian (LQG) problem) with
unknown dynamics, for potentially unstable Linear Time Invariant (LTI) systems.
The robust LQG synthesis procedure is performed by considering bounded additive
model uncertainty on the coprime factors of the plant. The closed-loop
identification of the nominal model of the true plant is performed by
constructing a Hankel-like matrix from a single time-series of noisy finite
length input-output data, using the ordinary least squares algorithm from
Sarkar et al. (2020). Next, an H-infinity bound on the estimated model error is
provided and the robust controller is designed via convex optimization, much in
the spirit of Boczar et al. (2018) and Zheng et al. (2020a), while allowing for
bounded additive uncertainty on the coprime factors of the model. Our
conclusions are consistent with previous results on learning the LQG and LQR
controllers.
