  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.
