The sample complexity of up-to-ϵ multi-dimensional revenue maximization

Yannai A. Gonczarowski, S. Matthew Weinberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

Abstract

We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multidimensional 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.

Original languageEnglish (US)
Title of host publicationProceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
EditorsMikkel Thorup
PublisherIEEE Computer Society
Pages416-426
Number of pages11
ISBN (Electronic)9781538642306
DOIs
StatePublished - Nov 30 2018
Event59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 - Paris, France
Duration: Oct 7 2018Oct 9 2018

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2018-October
ISSN (Print)0272-5428

Other

Other59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018
CountryFrance
CityParis
Period10/7/1810/9/18

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

Keywords

  • Algorithmic game theory
  • Algorithmic mechanism design
  • Approximate revenue maximization
  • Auctions
  • Generalization bounds
  • Multidimensional auctions
  • PAC learning
  • Sample complexity

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  • Cite this

    Gonczarowski, Y. A., & Weinberg, S. M. (2018). The sample complexity of up-to-ϵ multi-dimensional revenue maximization. In M. Thorup (Ed.), Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018 (pp. 416-426). [8555125] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 2018-October). IEEE Computer Society. https://doi.org/10.1109/FOCS.2018.00047