Fourier Analysis-based Iterative Combinatorial Auctions

TL;DR

This paper introduces a novel combinatorial auction method that combines Fourier analysis and neural networks to efficiently approximate bidders' value functions, improving efficiency, fairness, and runtime.

Contribution

It is the first to apply Fourier analysis to combinatorial auction design and proposes a hybrid approach with neural networks for practical implementation.

Findings

Achieves higher efficiency than prior auction designs.

Leads to a fairer distribution of social welfare.

Significantly reduces runtime.

Abstract

Recent advances in Fourier analysis have brought new tools to efficiently represent and learn set functions. In this paper, we bring the power of Fourier analysis to the design of combinatorial auctions (CAs). The key idea is to approximate bidders' value functions using Fourier-sparse set functions, which can be computed using a relatively small number of queries. Since this number is still too large for practical CAs, we propose a new hybrid design: we first use neural networks (NNs) to learn bidders' values and then apply Fourier analysis to the learned representations. On a technical level, we formulate a Fourier transform-based winner determination problem and derive its mixed integer program formulation. Based on this, we devise an iterative CA that asks Fourier-based queries. We experimentally show that our hybrid ICA achieves higher efficiency than prior auction designs, leads to a fairer distribution of social welfare, and significantly reduces runtime. With this paper, we are the first to leverage Fourier analysis in CA design and lay the foundation for future work in this area. Our code is available on GitHub: https://github.com/marketdesignresearch/FA-based-ICAs.