  Machine learning has developed a variety of tools for learning and
representing high-dimensional distributions with structure. Recent years have
also seen big advances in designing multi-item mechanisms. Akin to overfitting,
however, these mechanisms can be extremely sensitive to the Bayesian prior that
they target, which becomes problematic when that prior is only approximately
known. At the same time, even if access to the exact Bayesian prior is given,
it is known that optimal or even approximately optimal multi-item mechanisms
run into sample, computational, representation and communication intractability
barriers.
  We consider a natural class of multi-item mechanism design problems with very
large numbers of items, but where the bidders' value distributions can be
well-approximated by a topic model akin to those used in recommendation systems
with very large numbers of possible recommendations. We propose a mechanism
design framework for this setting, building on a recent robustification
framework by Brustle et al., which disentangles the statistical challenge of
estimating a multi-dimensional prior from the task of designing a good
mechanism for it, and robustifies the performance of the latter against the
estimation error of the former. We provide an extension of this framework
appropriate for our setting, which allows us to exploit the expressive power of
topic models to reduce the effective dimensionality of the mechanism design
problem and remove the dependence of its computational, communication and
representation complexity on the number of items.
