Fourier Analysis-based Iterative Combinatorial Auctions

by   Jakob Weissteiner, et al.

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 iterative combinatorial auctions. The key idea is to approximate the 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 real-world auctions, we propose a novel hybrid auction design: we first use neural networks to learn bidders' values and then apply Fourier analysis to those 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 mechanism that asks Fourier-based queries. Our experimental evaluation shows that our hybrid auction leads to a fairer distribution of social welfare among bidders and significantly reduces runtime, while matching the economic efficiency of state-of-the-art auction designs. With this paper, we are the first to leverage Fourier analysis in combinatorial auction design and lay the foundation for future work in this area.



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