  This paper presents an inverse reinforcement learning~(IRL) framework for
Bayesian stopping time problems. By observing the actions of a Bayesian
decision maker, we provide a necessary and sufficient condition to identify if
these actions are consistent with optimizing a cost function. In a Bayesian
(partially observed) setting, the inverse learner can at best identify
optimality wrt the observed strategies. Our IRL algorithm identifies optimality
and then constructs set-valued estimates of the cost function.To achieve this
IRL objective, we use novel ideas from Bayesian revealed preferences stemming
from microeconomics. We illustrate the proposed IRL scheme using two important
examples of stopping time problems, namely, sequential hypothesis testing and
Bayesian search. As a real-world example, we illustrate using a YouTube dataset
comprising metadata from 190000 videos how the proposed IRL method predicts
user engagement in online multimedia platforms with high accuracy. Finally, for
finite datasets, we propose an IRL detection algorithm and give finite sample
bounds on its error probabilities.
