Learning When to Stop Searching

In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned through experience. To investigate learning in such settings, we conduct a large-scale behavioral experiment in which people search repeatedly from fixed distributions in a "repeated secretary problem." In contrast to prior investigations that find no evidence for learning in the classical scenario, in the repeated setting we observe substantial learning resulting in near-optimal stopping behavior. We conduct a Bayesian comparison of multiple behavioral models, which shows that participants' behavior is best described by a class of threshold-based models that contains the theoretically optimal strategy. Fitting such a threshold-based model to data reveals players' estimated thresholds to be close to the optimal thresholds after only a small number of games.