Current and future high-contrast imaging instruments require extreme Adaptive Optics (XAO) systems to reach contrasts necessary to directly image exoplanets. Telescope vibrations and the temporal error induced by the latency of the control loop limit the performance of these systems. Optimization of the (predictive) control algorithm is crucial in reducing these effects. We describe how model-free Reinforcement Learning can be used to optimize a Recurrent Neural Network controller for closed-loop adaptive optics control. We verify our proposed approach for tip-tilt control in simulations and a lab setup. The results show that this algorithm can effectively learn to suppress a combination of tip-tilt vibrations. Furthermore, we report decreased residuals for power-law input turbulence compared to an optimal gain integrator. Finally, we demonstrate that the controller can learn to identify the parameters of a varying vibration without requiring online updating of the control law. We conclude that Reinforcement Learning is a promising approach towards data-driven predictive control; future research will apply this approach to the control of high-order deformable mirrors.