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A General Theory of Sample Complexity for Multi-Item Profit Maximization

Published: 11 June 2018 Publication History

Abstract

One of the most tantalizing and long-standing open problems in mechanism design is profit maximization in multi-item, multi-buyer settings. Much of the literature surrounding this problem rests on the strong assumption that the mechanism designer knows the distribution over buyers' values. In reality, this information is rarely available. The support of the distribution alone is often doubly exponential, so obtaining and storing the distribution is impractical. We relax this assumption and instead assume that the mechanism designer only has a set of samples from the distribution. We develop learning-theoretic foundations of sample-based mechanism design. In particular, we provide generalization guarantees which bound the difference between the empirical profit of a mechanism over a set of samples and its expected profit on the unknown distribution.
In this paper, we present a general theory for deriving worst-case generalization bounds in multi-item settings, as well as data-dependent guarantees when the distribution over buyers' values is well-behaved. We analyze mechanism classes that have not yet been studied in the sample-based mechanism design literature and match or improve over the best-known guarantees for many of the special classes that have been studied. The classes we study include randomized mechanisms, pricing mechanisms, multi-part tariffs, and generalized VCG auctions such as affine maximizer auctions.

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Cited By

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  • (2024)Nash incentive-compatible online mechanism learning via weakly differentially private online learningProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692898(20643-20659)Online publication date: 21-Jul-2024
  • (2024)Applying Opponent Modeling for Automatic Bidding in Online Repeated AuctionsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662938(843-851)Online publication date: 6-May-2024
  • (2024)Bandit Sequential Posted Pricing via Half-ConcavityProceedings of the 25th ACM Conference on Economics and Computation10.1145/3670865.3673495(922-939)Online publication date: 8-Jul-2024
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cover image ACM Conferences
EC '18: Proceedings of the 2018 ACM Conference on Economics and Computation
June 2018
713 pages
ISBN:9781450358293
DOI:10.1145/3219166
Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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New York, NY, United States

Publication History

Published: 11 June 2018

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Author Tags

  1. combinatorial auctions
  2. learning theory
  3. machine learning
  4. profit maximization
  5. revenue maximization

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EC '18
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EC '18 Paper Acceptance Rate 70 of 269 submissions, 26%;
Overall Acceptance Rate 664 of 2,389 submissions, 28%

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The 25th ACM Conference on Economics and Computation
July 7 - 11, 2025
Stanford , CA , USA

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Cited By

View all
  • (2024)Nash incentive-compatible online mechanism learning via weakly differentially private online learningProceedings of the 41st International Conference on Machine Learning10.5555/3692070.3692898(20643-20659)Online publication date: 21-Jul-2024
  • (2024)Applying Opponent Modeling for Automatic Bidding in Online Repeated AuctionsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662938(843-851)Online publication date: 6-May-2024
  • (2024)Bandit Sequential Posted Pricing via Half-ConcavityProceedings of the 25th ACM Conference on Economics and Computation10.1145/3670865.3673495(922-939)Online publication date: 8-Jul-2024
  • (2024)Online Combinatorial Allocations and Auctions with Few Samples2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS61266.2024.00081(1231-1250)Online publication date: 27-Oct-2024
  • (2023)Bicriteria multidimensional mechanism design with side informationProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667901(40832-40852)Online publication date: 10-Dec-2023
  • (2023)Private Data Manipulation in Sponsored Search AuctionsCAAI Artificial Intelligence Research10.26599/AIR.2023.9150024(9150024)Online publication date: Dec-2023
  • (2023)Differentiable economics for randomized affine maximizer auctionsProceedings of the Thirty-Second International Joint Conference on Artificial Intelligence10.24963/ijcai.2023/293(2633-2641)Online publication date: 19-Aug-2023
  • (2023)A Learning Framework for Distribution-Based Game-Theoretic Solution ConceptsACM Transactions on Economics and Computation10.1145/358037411:1-2(1-23)Online publication date: 24-Jun-2023
  • (2023)On the Sample Complexity of Storage ControlIEEE Transactions on Smart Grid10.1109/TSG.2023.326386214:6(4398-4408)Online publication date: Nov-2023
  • (2022)Maximizing revenue under market shrinkage and market uncertaintyProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3600390(1643-1655)Online publication date: 28-Nov-2022
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