  Providing users with alternatives to choose from is an essential component in
many online platforms, making the accurate prediction of choice vital to their
success. A renewed interest in learning choice models has led to significant
progress in modeling power, but most current methods are either limited in the
types of choice behavior they capture, cannot be applied to large-scale data,
or both.
  Here we propose a learning framework for predicting choice that is accurate,
versatile, theoretically grounded, and scales well. Our key modeling point is
that to account for how humans choose, predictive models must capture certain
set-related invariances. Building on recent results in economics, we derive a
class of models that can express any behavioral choice pattern, enjoy favorable
sample complexity guarantees, and can be efficiently trained end-to-end.
Experiments on three large choice datasets demonstrate the utility of our
approach.
