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.

翻译：傅里叶分析的最新进展为高效表示和学习集合函数带来了新工具。本文首次将傅里叶分析引入组合拍卖（CAs）的设计中。核心思想是利用傅里叶稀疏集函数近似竞拍者的价值函数，该函数可通过相对少量的查询计算得出。由于该查询数量对实际CA而言仍然过大，我们提出了一种新的混合设计：首先使用神经网络（NNs）学习竞拍者的价值，然后将傅里叶分析应用于学习到的表示。在技术层面，我们构建了基于傅里叶变换的胜者确定问题，并推导出相应的混合整数规划公式。基于此，我们设计了一种提出傅里叶型查询的迭代CA。实验表明，我们的混合ICA相比先前的拍卖设计实现了更高的效率，带来了更公平的社会福利分配，并显著缩短了运行时间。本文首次在CA设计中利用傅里叶分析，为该领域的未来研究奠定了基础。我们的代码已发布于GitHub：https://github.com/marketdesignresearch/FA-based-ICAs。