As the systems we control become more complex, first-principle modeling\nbecomes either impossible or intractable, motivating the use of machine\nlearning techniques for the control of systems with continuous action spaces.\nAs impressive as the empirical success of these methods have been, strong\ntheoretical guarantees of performance, safety, or robustness are few and far\nbetween. This paper takes a step towards such providing such guarantees by\nestablishing finite-data performance guarantees for the robust output-feedback\ncontrol of an unknown FIR SISO system. In particular, we introduce the\n"Coarse-ID control" pipeline, which is composed of a system identification step\nfollowed by a robust controller synthesis procedure, and analyze its end-to-end\nperformance, providing quantitative bounds on the performance degradation\nsuffered due to model uncertainty as a function of the number of experiments\nrun to identify the system. We conclude with numerical examples demonstrating\nthe effectiveness of our method.\n