Reinforcement-learning- (RL-) based algorithms have recently emerged as a promising approach for adaptive optics (AO) control. In simulations and laboratory experiments, they have demonstrated robustness to real-world effects such as photon and detector noise, misregistration, vibrations, and rapid variations in seeing conditions. However, their performance has not been validated on sky yet. We report the first on-sky demonstration of a RL controller for AO, named Policy Optimization for AO (PO4AO). We further analyzed its on-sky behavior and identified directions for improving the algorithm and its implementation. PO4AO was implemented and deployed on the Papyrus AO system installed at the Coudé focus of the 1.52 m telescope (T152) at the Observatoire de Haute-Provence (OHP). A Python-based implementation was interfaced with the existing real-time controller (DAO RTC) via shared-memory buffers. The performance of PO4AO was compared to that of a standard integrator controller over several nights, covering a range of flux levels and atmospheric conditions. PO4AO consistently outperformed the standard integrator in all tested configurations. The controller successfully learned and compensated for vibration patterns and demonstrated strong robustness to measurement noise. Once tuned for Papyrus, PO4AO operated in a turnkey fashion, using a single set of hyperparameters across varying observing conditions and science targets. These performance gains were achieved despite a non-optimized Python implementation introducing approximately 720 s of additional latency, along with control jitter and occasional frame drops. When properly implemented and optimized, PO4AO constitutes a robust and high-performance turnkey controller for single-conjugate AO systems, paving the way for broader adoption of RL strategies in on-sky AO operations.