  This paper considers the Linear Quadratic Regulator problem for linear
systems with unknown dynamics, a central problem in data-driven control and
reinforcement learning. We propose a method that uses data to directly return a
controller without estimating a model of the system. Sufficient conditions are
given under which this method returns a stabilizing controller with guaranteed
relative error when the data used to design the controller are affected by
noise. This method has low complexity as it only requires a finite number of
samples of the system response to a sufficiently exciting input, and can be
efficiently implemented as a semi-definite program. Further, the method does
not require assumptions on the noise statistics, and the relative error nicely
scales with the noise magnitude.
