A Permutation-Equivariant Neural Network Architecture For Auction Design

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 Dütting et al. (2017) 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 permutationequivariant 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.

Sampling usingSU(N)gauge equivariant flows

“…Permutation equivariance is required to ensure that the kernel acts only based on the spectrum, not the particular order of eigenvalues produced during diagonalization. Normalizing flows that are permutation equivariant have previously been investigated in the machinelearning community to learn densities over sets (such as point-clouds, objects in a 3D scene, particles in molecular dynamics, and particle tracks in collider events) [41][42][43][45][46][47][48][49][50][51][52]. Such approaches are directly applicable to kernels for U(N ) variables, because the eigenvalues can be transformed independently.…”

Learning Revenue-Maximizing Auctions With Differentiable Matching

“…Further work has built directly on both RochetNet and RegretNet [30,10,43,44]. Others have taken a similar approach but applied to different mechanism design problems, including finding welfare-maximizing auctions [49] and facility location [21].…”

“…Our architecture works for both single-agent and multi-agent auctions. Following previous work [14,44,43], we use these single-agent experiments as a test case to make sure it recovers some known optimal mechanisms, before continuing on to multi-agent settings where optimal auctions are not known and where RochetNet or [48] cannot work.…”

“…Following previous work that uses neural networks to approximate optimal auctions (including but not limited to [14,48,44,43]), we train on synthetic data. While in principle deep-learning-based methods could be used to train on truthful bids from real-world bidders, and doing so would be extremely interesting, such data is hard to come by.…”

“…This learning approach to auction design can replicate some known-optimal auctions, and can learn good auctions in settings where the optimal auction is not known. It has been extended in a variety of ways [10,49,21,30,18,43,44,41].…”