  We propose and validate a novel car following model based on deep
reinforcement learning. Our model is trained to maximize externally given
reward functions for the free and car-following regimes rather than reproducing
existing follower trajectories. The parameters of these reward functions such
as desired speed, time gap, or accelerations resemble that of traditional
models such as the Intelligent Driver Model (IDM) and allow for explicitly
implementing different driving styles. Moreover, they partially lift the
black-box nature of conventional neural network models. The model is trained on
leading speed profiles governed by a truncated Ornstein-Uhlenbeck process
reflecting a realistic leader's kinematics.
  This allows for arbitrary driving situations and an infinite supply of
training data. For various parameterizations of the reward functions, and for a
wide variety of artificial and real leader data, the model turned out to be
unconditionally string stable, comfortable, and crash-free. String stability
has been tested with a platoon of five followers following an artificial and a
real leading trajectory. A cross-comparison with the IDM calibrated to the
goodness-of-fit of the relative gaps showed a higher reward compared to the
traditional model and a better goodness-of-fit.
