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The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization

Author(s): Gonczarowski, Yannai A; Weinberg, S Matthew

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Abstract: We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of n additive bidders whose values for m heterogeneous items are drawn independently. For any such instance and any ε>0, we show that it is possible to learn an ε-Bayesian Incentive Compatible auction whose expected revenue is within ε of the optimal ε-BIC auction from only polynomially many samples. Our approach is based on ideas that hold quite generally, and completely sidestep the difficulty of characterizing optimal (or near-optimal) auctions for these settings. Therefore, our results easily extend to general multi-dimensional settings, including valuations that aren't necessarily even subadditive, and arbitrary allocation constraints. For the cases of a single bidder and many goods, or a single parameter (good) and many bidders, our analysis yields exact incentive compatibility (and for the latter also computational efficiency). Although the single-parameter case is already well-understood, our corollary for this case extends slightly the state-of-the-art.
Publication Date: 2018
Citation: Gonczarowski, Yannai A., and S. Matthew Weinberg. "The Sample Complexity of Up-to-ε Multi-Dimensional Revenue Maximization." In Annual Symposium on Foundations of Computer Science (FOCS) (2018): pp. 416-426. doi:10.1109/FOCS.2018.00047
DOI: 10.1109/FOCS.2018.00047
ISSN: 1523-8288
EISSN: 2575-8454
Pages: 416 - 426
Type of Material: Conference Article
Journal/Proceeding Title: Annual Symposium on Foundations of Computer Science
Version: Author's manuscript

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