In this paper, we present a novel, efficient approach to improve the acceleration commands computed by the popular social force model (SFM) for navigation through pedestrian crowds. Our method consists of two stages. In the first phase, we collect training data with a simulated approach. In this step, we modify the steering acceleration commands from the SFM according to a set of discrete alterations and simulate the motion of the robot as well as the pedestrians into the future for each alteration. We rate each resulting trajectory based on a cost function and apply the best steering command to the robot. While controlling the robot in such way, we collect for every time step the input and output training data. In the second stage, we then learn a neural network given the collected training data. We use the best acceleration values experienced in the first phase as target values for the neural network and define simple input features describing the local surrounding of the robot. In extensive simulation experiments using different pedestrian densities, we demonstrate that the controls generated by the learned neural network lead to a significantly reduced number of collisions with pedestrians compared to the results of the basic SFM controller, while achieving similar or even shorter completion times.