  This paper studies the sample complexity of the stochastic Linear Quadratic
Regulator when applied to systems with multiplicative noise. We assume that the
covariance of the noise is unknown and estimate it using the sample covariance,
which results in suboptimal behaviour. The main contribution of this paper is
then to bound the suboptimality of the methodology and prove that it decreases
with 1/N, where N denotes the amount of samples. The methodology easily
generalizes to the case where the mean is unknown and to the distributionally
robust case studied in a previous work of the authors. The analysis is mostly
based on results from matrix function perturbation analysis.
