Airborne wind energy systems are built to exploit the stronger and more consistent wind available at high altitudes that conventional wind turbines cannot reach. This however requires a reliable controller design that can keep the airborne system flying for long durations in varying environmental conditions, while respecting all operational constraints. A frequent design for such a system includes a flying airfoil tethered to a ground station. We demonstrate an on-line data based method that optimizes the towing force of such a system in the presence of altitude constraints and varying wind. We actively learn Gaussian Process models, mapping relevant measurements to the objective, constraint and state dynamic functions of the system. We then formulate a chance - constrained optimization problem that takes into consideration uncertainty in the learned functions and finds feasible directions for improvement. Simulation studies show that we can find near optimal set points for the controller without the use of significant assumptions on model dynamics while respecting the unknown constraint function. The results also show an improved performance over our previous work which was restricted to steady state processes.