A Permutation-Equivariant Neural Network Architecture For Auction Design
This work addresses auction design for economists and AI researchers by introducing a specialized neural architecture that improves upon existing computational approaches, though it is incremental in focusing on permutation-equivariant cases.
The authors tackled the problem of designing revenue-maximizing incentive-compatible auctions by proposing a permutation-equivariant neural network architecture that leverages symmetries in the problem, achieving perfect recovery of the optimal mechanism and better generalization compared to previous general-purpose neural methods.
Designing an incentive compatible auction that maximizes expected revenue is a central problem in Auction Design. Theoretical approaches to the problem have hit some limits in the past decades and analytical solutions are known for only a few simple settings. Computational approaches to the problem through the use of LPs have their own set of limitations. Building on the success of deep learning, a new approach was recently proposed by Duetting et al. (2019) in which the auction is modeled by a feed-forward neural network and the design problem is framed as a learning problem. The neural architectures used in that work are general purpose and do not take advantage of any of the symmetries the problem could present, such as permutation equivariance. In this work, we consider auction design problems that have permutation-equivariant symmetry and construct a neural architecture that is capable of perfectly recovering the permutation-equivariant optimal mechanism, which we show is not possible with the previous architecture. We demonstrate that permutation-equivariant architectures are not only capable of recovering previous results, they also have better generalization properties.