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This paper presents an inverse reinforcement learning~(IRL) framework forBayesian stopping time problems. By observing the actions of a Bayesiandecision maker, we provide a necessary and sufficient condition to identify ifthese actions are consistent with optimizing a cost function. In a Bayesian(partially observed) setting, the inverse learner can at best identifyoptimality wrt the observed strategies. Our IRL algorithm identifies optimalityand then constructs set-valued estimates of the cost function.To achieve thisIRL objective, we use novel ideas from Bayesian revealed preferences stemmingfrom microeconomics. We illustrate the proposed IRL scheme using two importantexamples of stopping time problems, namely, sequential hypothesis testing andBayesian search. As a real-world example, we illustrate using a YouTube datasetcomprising metadata from 190000 videos how the proposed IRL method predictsuser engagement in online multimedia platforms with high accuracy. Finally, forfinite datasets, we propose an IRL detection algorithm and give finite samplebounds on its error probabilities.

Necessary and Sufficient Conditions for Inverse Reinforcement Learning of Bayesian Stopping Time Problems