Procurement Auctions via Approximately Optimal Submodular Optimization

Yuan Deng, Amin Karbasi, Vahab Mirrokni, Renato Paes Leme, Grigoris Velegkas, Song Zuo
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:13152-13180, 2025.

Abstract

We study the problem of procurement auctions, in which an auctioneer seeks to acquire services from a group of strategic sellers with private costs. The quality of the services is measured through some submodular function that is known to the auctioneer. Our goal is to design computationally efficient procurement auctions that (approximately) maximize the difference between the quality of the acquired services and the total cost of the sellers, in a way that is incentive compatible (IC) and individual rational (IR) for the sellers, and generates non-negative surplus (NAS) for the auctioneer. Our contribution is twofold: i) we provide an improved analysis of existing algorithms for non-positive submodular function maximization and ii) we design computationally efficient frameworks that transform submodular function optimization algorithms to mechanisms that are IC and IR for the sellers, NAS for the auctioneer, and approximation-preserving. Our frameworks are general and work both in the offline setting where the auctioneer can observe the bids and the services of all the sellers simultaneously, and in the online setting where the sellers arrive in an adversarial order and the auctioneer has to make an irrevocable decision whether to purchase their service or not. We further investigate whether it is possible to convert state-of-art submodular optimization algorithms into descending auctions. We focus on the adversarial setting, meaning that the schedule of the descending prices is determined by an adversary. We show that a submodular optimization algorithm satisfying bi-criteria $(1/2,1)$-approximation in welfare can be effectively converted to a descending auction in this setting. We further establish a connection between descending auctions and online submodular optimization. Finally, we demonstrate the practical applications of our frameworks by instantiating them with different state-of-the-art submodular optimization algorithms and comparing their welfare performance through empirical experiments on publicly available datasets that consist of thousands of sellers.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-deng25e, title = {Procurement Auctions via Approximately Optimal Submodular Optimization}, author = {Deng, Yuan and Karbasi, Amin and Mirrokni, Vahab and Paes Leme, Renato and Velegkas, Grigoris and Zuo, Song}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {13152--13180}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/deng25e/deng25e.pdf}, url = {https://proceedings.mlr.press/v267/deng25e.html}, abstract = {We study the problem of procurement auctions, in which an auctioneer seeks to acquire services from a group of strategic sellers with private costs. The quality of the services is measured through some submodular function that is known to the auctioneer. Our goal is to design computationally efficient procurement auctions that (approximately) maximize the difference between the quality of the acquired services and the total cost of the sellers, in a way that is incentive compatible (IC) and individual rational (IR) for the sellers, and generates non-negative surplus (NAS) for the auctioneer. Our contribution is twofold: i) we provide an improved analysis of existing algorithms for non-positive submodular function maximization and ii) we design computationally efficient frameworks that transform submodular function optimization algorithms to mechanisms that are IC and IR for the sellers, NAS for the auctioneer, and approximation-preserving. Our frameworks are general and work both in the offline setting where the auctioneer can observe the bids and the services of all the sellers simultaneously, and in the online setting where the sellers arrive in an adversarial order and the auctioneer has to make an irrevocable decision whether to purchase their service or not. We further investigate whether it is possible to convert state-of-art submodular optimization algorithms into descending auctions. We focus on the adversarial setting, meaning that the schedule of the descending prices is determined by an adversary. We show that a submodular optimization algorithm satisfying bi-criteria $(1/2,1)$-approximation in welfare can be effectively converted to a descending auction in this setting. We further establish a connection between descending auctions and online submodular optimization. Finally, we demonstrate the practical applications of our frameworks by instantiating them with different state-of-the-art submodular optimization algorithms and comparing their welfare performance through empirical experiments on publicly available datasets that consist of thousands of sellers.} }
Endnote
%0 Conference Paper %T Procurement Auctions via Approximately Optimal Submodular Optimization %A Yuan Deng %A Amin Karbasi %A Vahab Mirrokni %A Renato Paes Leme %A Grigoris Velegkas %A Song Zuo %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-deng25e %I PMLR %P 13152--13180 %U https://proceedings.mlr.press/v267/deng25e.html %V 267 %X We study the problem of procurement auctions, in which an auctioneer seeks to acquire services from a group of strategic sellers with private costs. The quality of the services is measured through some submodular function that is known to the auctioneer. Our goal is to design computationally efficient procurement auctions that (approximately) maximize the difference between the quality of the acquired services and the total cost of the sellers, in a way that is incentive compatible (IC) and individual rational (IR) for the sellers, and generates non-negative surplus (NAS) for the auctioneer. Our contribution is twofold: i) we provide an improved analysis of existing algorithms for non-positive submodular function maximization and ii) we design computationally efficient frameworks that transform submodular function optimization algorithms to mechanisms that are IC and IR for the sellers, NAS for the auctioneer, and approximation-preserving. Our frameworks are general and work both in the offline setting where the auctioneer can observe the bids and the services of all the sellers simultaneously, and in the online setting where the sellers arrive in an adversarial order and the auctioneer has to make an irrevocable decision whether to purchase their service or not. We further investigate whether it is possible to convert state-of-art submodular optimization algorithms into descending auctions. We focus on the adversarial setting, meaning that the schedule of the descending prices is determined by an adversary. We show that a submodular optimization algorithm satisfying bi-criteria $(1/2,1)$-approximation in welfare can be effectively converted to a descending auction in this setting. We further establish a connection between descending auctions and online submodular optimization. Finally, we demonstrate the practical applications of our frameworks by instantiating them with different state-of-the-art submodular optimization algorithms and comparing their welfare performance through empirical experiments on publicly available datasets that consist of thousands of sellers.
APA
Deng, Y., Karbasi, A., Mirrokni, V., Paes Leme, R., Velegkas, G. & Zuo, S.. (2025). Procurement Auctions via Approximately Optimal Submodular Optimization. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:13152-13180 Available from https://proceedings.mlr.press/v267/deng25e.html.

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