A Permutation-Equivariant Neural Network Architecture For Auction Design

TL;DR

This paper introduces a permutation-equivariant neural network architecture for auction design that outperforms previous models by leveraging symmetry, enabling perfect recovery of optimal mechanisms and improved generalization.

Contribution

The paper presents a novel permutation-equivariant neural network architecture tailored for auction design, overcoming limitations of previous general-purpose models.

Findings

The architecture can perfectly recover permutation-equivariant optimal mechanisms.

Permutation-equivariant models demonstrate better generalization.

Previous architectures cannot achieve perfect recovery of such mechanisms.

Abstract

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.