Title: Learning in the Repeated Secretary Problem,
Abstract: 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 a repeated
secretary problem we conduct a large-scale behavioral experiment in which
people search repeatedly from fixed distributions. 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 surprisingly close to the optimal thresholds after only a
small number of games.