  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. One way to reduce these
effects is to use predictive control. We describe how model-free Reinforcement
Learning can be used to optimize a Recurrent Neural Network controller for
closed-loop predictive control. First, 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 mitigate vibrations and reduce the residuals
for power-law input turbulence as compared to an optimal gain integrator. We
also show that the controller can learn to minimize random vibrations without
requiring online updating of the control law. Next, we show in simulations that
our algorithm can also be applied to the control of a high-order deformable
mirror. We demonstrate that our controller can provide two orders of magnitude
improvement in contrast at small separations under stationary turbulence.
Furthermore, we show more than an order of magnitude improvement in contrast
for different wind velocities and directions without requiring online updating
of the control law.
