  This paper introduces a probabilistic framework to estimate parameters of an
acquisition function given observed human behavior that can be modeled as a
collection of sample paths from a Bayesian optimization procedure. The
methodology involves defining a likelihood on observed human behavior from an
optimization task, where the likelihood is parameterized by a Bayesian
optimization subroutine governed by an unknown acquisition function. This
structure enables us to make inference on a subject's acquisition function
while allowing their behavior to deviate around the solution to the Bayesian
optimization subroutine. To test our methods, we designed a sequential
optimization task which forced subjects to balance exploration and exploitation
in search of an invisible target location. Applying our proposed methods to the
resulting data, we find that many subjects tend to exhibit exploration
preferences beyond that of standard acquisition functions to capture. Guided by
the model discrepancies, we augment the candidate acquisition functions to
yield a superior fit to the human behavior in this task.
