  In this work we introduce an alternative model for the design and analysis of
strategyproof mechanisms that is motivated by the recent surge of work in
"learning-augmented algorithms". Aiming to complement the traditional approach
in computer science, which analyzes the performance of algorithms based on
worst-case instances, this line of work has focused on the design and analysis
of algorithms that are enhanced with machine-learned predictions regarding the
optimal solution. The algorithms can use the predictions as a guide to inform
their decisions, and the goal is to achieve much stronger performance
guarantees when these predictions are accurate (consistency), while also
maintaining near-optimal worst-case guarantees, even if these predictions are
very inaccurate (robustness). So far, these results have been limited to
algorithms, but in this work we argue that another fertile ground for this
framework is in mechanism design.
  We initiate the design and analysis of strategyproof mechanisms that are
augmented with predictions regarding the private information of the
participating agents. To exhibit the important benefits of this approach, we
revisit the canonical problem of facility location with strategic agents in the
two-dimensional Euclidean space. We study both the egalitarian and utilitarian
social cost functions, and we propose new strategyproof mechanisms that
leverage predictions to guarantee an optimal trade-off between consistency and
robustness guarantees. This provides the designer with a menu of mechanism
options to choose from, depending on her confidence regarding the prediction
accuracy. Furthermore, we also prove parameterized approximation results as a
function of the prediction error, showing that our mechanisms perform well even
when the predictions are not fully accurate.
