  Imitation learning from observation (LfO) is more preferable than imitation
learning from demonstration (LfD) due to the nonnecessity of expert actions
when reconstructing the expert policy from the expert data. However, previous
studies imply that the performance of LfO is inferior to LfD by a tremendous
gap, which makes it challenging to employ LfO in practice. By contrast, this
paper proves that LfO is almost equivalent to LfD in the deterministic robot
environment, and more generally even in the robot environment with bounded
randomness. In the deterministic robot environment, from the perspective of the
control theory, we show that the inverse dynamics disagreement between LfO and
LfD approaches zero, meaning that LfO is almost equivalent to LfD. To further
relax the deterministic constraint and better adapt to the practical
environment, we consider bounded randomness in the robot environment and prove
that the optimizing targets for both LfD and LfO remain almost same in the more
generalized setting. Extensive experiments for multiple robot tasks are
conducted to empirically demonstrate that LfO achieves comparable performance
to LfD. In fact, most common robot systems in reality are the robot environment
with bounded randomness (i.e., the environment this paper considered). Hence,
our findings greatly extend the potential of LfO and suggest that we can safely
apply LfO without sacrificing the performance compared to LfD in practice.
