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This paper considers the Linear Quadratic Regulator problem for linearsystems with unknown dynamics, a central problem in data-driven control andreinforcement learning. We propose a method that uses data to directly return acontroller without estimating a model of the system. Sufficient conditions aregiven under which this method returns a stabilizing controller with guaranteedrelative error when the data used to design the controller are affected bynoise. This method has low complexity as it only requires a finite number ofsamples of the system response to a sufficiently exciting input, and can beefficiently implemented as a semi-definite program. Further, the method doesnot require assumptions on the noise statistics, and the relative error nicelyscales with the noise magnitude.

Low-complexity Learning of Linear Quadratic Regulators from Noisy Data