# Fourier Analysis-based Iterative Combinatorial Auctions

arXiv: https://arxiv.org/abs/2009.10749 · HTML: https://mlsanity.com/paper/2009.10749/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2020.

## Built on by (most cited first, 7 of 7)

- [Differentiable Economics for Randomized Affine Maximizer Auctions](https://mlsanity.com/paper/2202.02872/) (2022)
- [Learning to Understand: Identifying Interactions via the M"obius Transform](https://mlsanity.com/paper/2402.02631/) (2024)
- [Bayesian Optimization-based Combinatorial Assignment](https://mlsanity.com/paper/2208.14698/) (2022)
- [LLM-Powered Preference Elicitation in Combinatorial Assignment](https://mlsanity.com/paper/2502.10308/) (2025)
- [Machine Learning-Powered Combinatorial Clock Auction](https://mlsanity.com/paper/2308.10226/) (2023)
- [Machine Learning-Powered Course Allocation](https://mlsanity.com/paper/2210.00954/) (2022)
- [Prices, Bids, Values: One ML-Powered Combinatorial Auction to Rule Them All](https://mlsanity.com/paper/2411.09355/) (2024)

## Abstract (arXiv)

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.