Recommender Systems meet Mechanism Design

TL;DR

This paper introduces a mechanism design framework for large-scale multi-item auctions that leverages topic models to reduce complexity and improve robustness against prior estimation errors.

Contribution

It extends a recent robustification framework to incorporate topic models, enabling scalable and less prior-sensitive multi-item mechanism design.

Findings

Reduces the effective dimensionality of the mechanism design problem.

Removes dependence of complexity on the number of items.

Enhances robustness to prior estimation errors.

Abstract

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.