The direct imaging of potentially habitable Exoplanets is one prime science case for the next generation of high contrast imaging instruments on ground-based extremely large telescopes. To reach this demanding science goal, the instruments are equipped with eXtreme Adaptive Optics (XAO) systems which will control thousands of actuators at a framerate of kilohertz to several kilohertz. Most of the habitable exoplanets are located at small angular separations from their host stars, where the current XAO systems' control laws leave strong residuals.Current AO control strategies like static matrix-based wavefront reconstruction and integrator control suffer from temporal delay error and are sensitive to mis-registration, i.e., to dynamic variations of the control system geometry. We aim to produce control methods that cope with these limitations, provide a significantly improved AO correction and, therefore, reduce the residual flux in the coronagraphic point spread function. We extend previous work in Reinforcement Learning for AO. The improved method, called PO4AO, learns a dynamics model and optimizes a control neural network, called a policy. We introduce the method and study it through numerical simulations of XAO with Pyramid wavefront sensing for the 8-m and 40-m telescope aperture cases. We further implemented PO4AO and carried out experiments in a laboratory environment using MagAO-X at the Steward laboratory. PO4AO provides the desired performance by improving the coronagraphic contrast in numerical simulations by factors 3-5 within the control region of DM and Pyramid WFS, in simulation and in the laboratory. The presented method is also quick to train, i.e., on timescales of typically 5-10 seconds, and the inference time is sufficiently small (