Time optimal output transition for input constrained systems is a frequent requirement in many actuation systems. In the case of known and/or linear systems, techniques exist to determine the corresponding control input either analytically and/or experimentally. In other cases however, is a sufficiently precise model is available. Against this background this paper proposes a learning algorithmic approach to solve the issue for unknown nonlinear saturated systems. The proposed approach searches the fastest transition by setting a time optimal but unfeasible trajectory and using learning techniques to recover the nearest feasible one in some sense. To achieve this goal, the proposed approach performs twice a learning process. On one side, it determines by iterative learning control for each suggested trajectory either the optimal input if the trajectory is feasible or an error information if this is not the case. On the other side, a model free learning model generator is used to determine the best feasible reference trajectory.