  We consider the problem of performing inverse reinforcement learning when the
trajectory of the expert is not perfectly observed by the learner. Instead, a
noisy continuous-time observation of the trajectory is provided to the learner.
This problem exhibits wide-ranging applications and the specific application we
consider here is the scenario in which the learner seeks to penetrate a
perimeter patrolled by a robot. The learner's field of view is limited due to
which it cannot observe the patroller's complete trajectory. Instead, we allow
the learner to listen to the expert's movement sound, which it can also use to
estimate the expert's state and action using an observation model. We treat the
expert's state and action as hidden data and present an algorithm based on
expectation maximization and maximum entropy principle to solve the non-linear,
non-convex problem. Related work considers discrete-time observations and an
observation model that does not include actions. In contrast, our technique
takes expectations over both state and action of the expert, enabling learning
even in the presence of extreme noise and broader applications.
