{"type":"ScholarlyArticle","title":"Fourier Analysis-based Iterative Combinatorial Auctions","authors":[{"name":"Jakob Weissteiner","slug":"jakob-weissteiner","given":"Jakob","family":"Weissteiner","affiliation":"University of Zurich; ETH AI Center"},{"name":"Chris Wendler","slug":"chris-wendler","given":"Chris","family":"Wendler","affiliation":"ETH Zurich"},{"name":"Sven Seuken","slug":"sven-seuken","given":"Sven","family":"Seuken","affiliation":"University of Zurich; ETH AI Center"},{"name":"Ben Lubin","slug":"ben-lubin","given":"Ben","family":"Lubin","affiliation":"Boston University"},{"name":"Markus Püschel","slug":"markus-puschel","given":"Markus","family":"Püschel","affiliation":"ETH Zurich"}],"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.","doi":"10.24963/ijcai.2022/78","url":"https://ijcai.org/proceedings/2022/78","pdf":"https://ijcai.org/proceedings/2022/0078.pdf","markdown":"https://ijcai.org/proceedings/2022/78.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/78","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":78,"pages":{"first":549,"last":556},"keywords":["Machine Learning: Regression","Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems","Machine Learning: Feature Extraction, Selection and Dimensionality Reduction","Machine Learning: Learning Sparse Models"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986533","length_sec":88,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984676","length_sec":351,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Abraham et al., 2012] I. Abraham, M. Babaioff, S. Dughmi, and T. Roughgarden. Combinatorial auctions with re- stricted complements. In Proceedings of the 13th ACM Conference on Electronic Commerce, 2012.","title":"Combinatorial auctions with restricted complements","authors":"Abraham","year":"2012","venue":"Proceedings of the 13th ACM Conference on Electronic Commerce","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Amrollahi et al., 2019] A. Amrollahi, A. Zandieh, M. Kapralov, and A. Krause. Efficiently learning Fourier sparse set functions. In Advances in Neural Information Processing Systems, 2019.","title":"Efficiently learning Fourier sparse set functions","authors":"A Amrollahi, A Zandieh, M Kapralov, A Krause","year":"2019","venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Ausubel and Baranov, 2017] L. M. Ausubel and O. Bara- nov. A practical guide to the combinatorial clock auction. Economic Journal, 127(605):F334-F350, 2017.","title":"A practical guide to the combinatorial clock auction","authors":"L M Ausubel, O Baranov","year":"2017","venue":"Economic Journal","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Ausubel and Cramton, 2011] L. Ausubel and P. Cramton. Auction design for wind rights. Report to Bureau of Ocean Energy Management, Regulation and Enforcement, 2011.","title":"Auction design for wind rights","authors":"L Ausubel, P Cramton","year":"2011","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Ausubel et al., 2006] L. Ausubel, P. Cramton, and P. Mil- grom. The clock-proxy auction: A practical combinatorial auction design. In Combinatorial Auctions, pages 115- 138. MIT Press, 2006.","title":"The clock-proxy auction: A practical combinatorial auction design","authors":"L Ausubel, P Cramton, P Milgrom","year":"2006","venue":"Combinatorial Auctions","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bernasconi et al., 1996] A. Bernasconi, B. Codenotti, and J. Simon. On the Fourier analysis of Boolean functions. preprint, pages 1-24, 1996.","title":"On the Fourier analysis of Boolean functions","authors":"A Bernasconi, B Codenotti, J Simon","year":"1996","venue":null,"doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Blum et al., 2004] A. Blum, J. Jackson, T. Sandholm, and M. Zinkevich. Preference elicitation and query learning. Journal of Machine Learning Research, 5:649-667, 2004.","title":"Preference elicitation and query learning","authors":"A Blum, J Jackson, T Sandholm, M Zinkevich","year":"2004","venue":"Journal of Machine Learning Research","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Brero et al., 2018] G. Brero, B. Lubin, and S. Seuken. Com- binatorial auctions via machine learning-based preference elicitation. In Proceedings of the 27th International Joint Conference on Artificial Intelligence, 2018.","title":"Combinatorial auctions via machine learning-based preference elicitation","authors":"G Brero, B Lubin, S Seuken","year":"2018","venue":"Proceedings of the 27th International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2018/18"},{"position":9,"raw":"[Brero et al., 2019] G. Brero, S. Lahaie, and S. Seuken. Fast iterative combinatorial auctions via bayesian learning. In Proceedings of the 33rd AAAI Conference of Artificial In- telligence, 2019.","title":"Fast iterative combinatorial auctions via bayesian learning","authors":"G Brero, S Lahaie, S Seuken","year":"2019","venue":"Proceedings of the 33rd AAAI Conference of Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Brero et al., 2021] G. Brero, B. Lubin, and S. Seuken. Ma- chine learning-powered iterative combinatorial auctions. arXiv:1911.08042, Jan 2021.","title":"Machine learning-powered iterative combinatorial auctions","authors":"G Brero, B Lubin, S Seuken","year":"2021","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Cramton, 2013] P. Cramton. Spectrum auction design. Re- view of Industrial Organization, 42(2):161-190, 2013.","title":"Spectrum auction design","authors":"P Cramton","year":"2013","venue":"Review of Industrial Organization","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Dütting et al., 2019] P. Dütting, Z. Feng, H. Narasimhan, D. Parkes, and S. Ravindranath. Optimal auctions through deep learning. In Proceedings of the 36th International Conference on Machine Learning, 2019.","title":"Optimal auctions through deep learning","authors":"P Dütting, Z Feng, H Narasimhan, D Parkes, S Ravindranath","year":"2019","venue":"Proceedings of the 36th International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Goeree and Holt, 2010] J. K. Goeree and C. A. Holt. Hier- archical package bidding: A paper & pencil combinatorial auction. Games and Economic Behavior, 2010.","title":"Hierarchical package bidding: A paper & pencil combinatorial auction","authors":"J K Goeree, C A Holt","year":"2010","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Hudson and Sandholm, 2003] B. Hudson and T. Sandholm. Using value queries in combinatorial auctions. In Proceed- ings of the 4th ACM Conference on Electronic commerce, pages 226-227, 2003.","title":"Using value queries in combinatorial auctions","authors":"B Hudson, T Sandholm","year":"2003","venue":"Proceedings of the 4th ACM Conference on Electronic commerce","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Lahaie and Parkes, 2004] S. Lahaie and C. Parkes. Apply- ing learning algorithms to preference elicitation. In Pro- ceedings of the 5th ACM Conference on Electronic Com- merce, 2004.","title":"Applying learning algorithms to preference elicitation","authors":"S Lahaie, C Parkes","year":"2004","venue":"Proceedings of the 5th ACM Conference on Electronic Commerce","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Lahaie, 2010] S. Lahaie. Kernel methods for revealed pref- erence analysis. In ECAI, pages 439-444, 2010.","title":"Kernel methods for revealed preference analysis","authors":"S Lahaie","year":"2010","venue":"ECAI","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Milgrom, 2007] P. Milgrom. Package auctions and ex- changes. Econometrica, 75(4):935-965, 2007.","title":"Package auctions and exchanges","authors":"P Milgrom","year":"2007","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Nisan and Segal, 2006] N. Nisan and I. Segal. The commu- nication requirements of efficient allocations and support- ing prices. Journal of Economic Theory, 2006.","title":"The communication requirements of efficient allocations and supporting prices","authors":"N Nisan, I Segal","year":"2006","venue":"Journal of Economic Theory","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[O'Donnell, 2014] R. O'Donnell. Analysis of boolean func- tions. Cambridge University Press, 2014.","title":"Analysis of boolean functions","authors":"R O Donnell","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Püschel and Wendler, 2020] M. Püschel and C. Wendler. Discrete signal processing with set functions. IEEE Trans- actions on Signal Processing, 69:1039-1053, 2020.","title":"Discrete signal processing with set functions","authors":"M Püschel, C Wendler","year":"2020","venue":"IEEE Transactions on Signal Processing","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Rahaman et al., 2019] N. Rahaman, A. Baratin, D. Arpit, F. Draxler, M. Lin, F. Hamprecht, Y. Bengio, and A. Courville. On the spectral bias of neural networks. In International Conference on Machine Learning, 2019.","title":"On the spectral bias of neural networks","authors":"N Rahaman, A Baratin, D Arpit, F Draxler, M Lin, F Hamprecht, Y Bengio, A Courville","year":"2019","venue":"International Conference on Machine Learning","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Rahme et al., 2021] J. Rahme, S. Jelassi, J. Bruna, and M. Weinberg. A permutation-equivariant neural network architecture for auction design. In Proceedings of the 35th AAAI Conference on Artificial Intelligence, 2021.","title":"A permutation-equivariant neural network architecture for auction design","authors":"J Rahme, S Jelassi, J Bruna, M Weinberg","year":"2021","venue":"Proceedings of the 35th AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Scheffel et al., 2012] T. Scheffel, G. Ziegler, and M. Bich- ler. On the impact of package selection in combinatorial auctions: an experimental study in the context of spectrum auction design. Experimental Economics, 2012.","title":"On the impact of package selection in combinatorial auctions: an experimental study in the context of spectrum auction design","authors":"T Scheffel, G Ziegler, M Bichler","year":"2012","venue":"Experimental Economics","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Shen et al., 2019] W. Shen, P. Tang, and S. Zuo. Automated mechanism design via neural networks. In Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems, 2019.","title":"Automated mechanism design via neural networks","authors":"W Shen, P Tang, S Zuo","year":"2019","venue":"Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Shen et al., 2020] W. Shen, B. Peng, H. Liu, M. Zhang, R. Qian, Y. Hong, Z. Guo, Z. Ding, P. Lu, and P. Tang. Reinforcement mechanism design: With applications to dynamic pricing in sponsored search auctions. In Proceed- ings of the 34th AAAI Conference, 2020.","title":"Reinforcement mechanism design: With applications to dynamic pricing in sponsored search auctions","authors":"W Shen, B Peng, H Liu, M Zhang, R Qian, Y Hong, Z Guo, Z Ding, P Lu, P Tang","year":"2020","venue":"Proceedings of the 34th AAAI Conference","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Stobbe and Krause, 2012] P. Stobbe and A. Krause. Learn- ing Fourier sparse set functions. In Artificial Intelligence and Statistics, 2012.","title":"Learning Fourier sparse set functions","authors":"P Stobbe, A Krause","year":"2012","venue":"Artificial Intelligence and Statistics","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Weiss et al., 2017] M. Weiss, B. Lubin, and S. Seuken. Sats: A universal spectrum auction test suite. In Proceedings of the 16th Conference on Autonomous Agents and Multi- Agent Systems, 2017.","title":"Sats: A universal spectrum auction test suite","authors":"M Weiss, B Lubin, S Seuken","year":"2017","venue":"Proceedings of the 16th Conference on Autonomous Agents and Multi-Agent Systems","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Weissteiner and Seuken, 2020] Jakob Weissteiner and Sven Seuken. Deep learning-powered iterative combinatorial auctions. In Proceedings of the 34th AAAI Conference of Artificial Intelligence, 2020.","title":"Deep learning-powered iterative combinatorial auctions","authors":"Seuken Weissteiner, Jakob Weissteiner, Sven Seuken","year":"2020","venue":"Proceedings of the 34th AAAI Conference of Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Weissteiner et al., 2022] Jakob Weissteiner, Jakob Heiss, Julien Siems, and Sven Seuken. Monotone-value neural networks: Exploiting preference monotonicity in combi- natorial assignment. In Proceedings of the 31st Interna- tional Joint Conference on Artificial Intelligence, 2022.","title":"Monotone-value neural networks: Exploiting preference monotonicity in combinatorial assignment","authors":"Jakob Weissteiner, Jakob Heiss, Julien Siems, Sven Seuken","year":"2022","venue":"Proceedings of the 31st International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/2022/77"},{"position":30,"raw":"[Wendler et al., 2021] C. Wendler, A. Amrollahi, B. Seifert, A. Krause, and M. Püschel. Learning set functions that are sparse in non-orthogonal Fourier bases. In Proceedings of the 35th AAAI Conference on Artificial Intelligence, 2021.","title":"Learning set functions that are sparse in non-orthogonal Fourier bases","authors":"C Wendler, A Amrollahi, B Seifert, A Krause, M Püschel","year":"2021","venue":"Proceedings of the 35th AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}