  We consider the problem of recovering an expert's reward function with
inverse reinforcement learning (IRL) when there are missing/incomplete
state-action pairs or observations in the demonstrated trajectories. This issue
of missing trajectory data or information occurs in many situations, e.g., GPS
signals from vehicles moving on a road network are intermittent. In this paper,
we propose a tractable approach to directly compute the log-likelihood of
demonstrated trajectories with incomplete/missing data. Our algorithm is
efficient in handling a large number of missing segments in the demonstrated
trajectories, as it performs the training with incomplete data by solving a
sequence of systems of linear equations, and the number of such systems to be
solved does not depend on the number of missing segments. Empirical evaluation
on a real-world dataset shows that our training algorithm outperforms other
conventional techniques.
