This work approaches the problem of controlling quadrupedal running and jumping motions with a parametrized, model-based, state-feedback controller. Inspired by the motor learning principles observed in nature, our method automatically fine tunes the parameters of our controller by repeatedly executing slight variations of the same motion task. This learn-through-practice process is performed in simulation in order to best exploit computational resources and to prevent the robot from damaging itself. In order to ensure that the simulation results match the behavior of the hardware platform sufficiently well, we introduce and validate an accurate model of the compliant actuation system. The proposed method is experimentally verified on the torque-controllable quadruped robot StarlETH by executing squat jumps and dynamic gaits such as a running trot, pronk and a bounding gait.