  For adversarial imitation learning algorithms (AILs), no true rewards are
obtained from the environment for learning the strategy. However, the pseudo
rewards based on the output of the discriminator are still required. Given the
implicit reward bias problem in AILs, we design several representative reward
function shapes and compare their performances by large-scale experiments. To
ensure our results' reliability, we conduct the experiments on a series of
Mujoco and Box2D continuous control tasks based on four different AILs.
Besides, we also compare the performance of various reward function shapes
using varying numbers of expert trajectories. The empirical results reveal that
the positive logarithmic reward function works well in typical continuous
control tasks. In contrast, the so-called unbiased reward function is limited
to specific kinds of tasks. Furthermore, several designed reward functions
perform excellently in these environments as well.
