The sample complexity of revenue maximization

Richard Cole, Tim Roughgarden

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

Abstract

In the design and analysis of revenue-maximizing auctions, auction performance is typically measured with respect to a prior distribution over inputs. The most obvious source for such a distribution is past data. The goal of this paper is to understand how much data is necessary and sufficient to guarantee near-optimal expected revenue. Our basic model is a single-item auction in which bidders' valuations are drawn independently from unknown and nonidentical distributions. The seller is given m samples from each of these distributions "for free" and chooses an auction to run on a fresh sample. How large does m need to be, as a function of the number k of bidders and ε > 0, so that a (1 - ε)-approximation of the optimal revenue is achievable? We prove that, under standard tail conditions on the underlying distributions, m = poly(k, 1/ε) samples are necessary and sufficient. Our lower bound stands in contrast to many recent results on simple and prior-independent auctions and fundamentally involves the interplay between bidder competition, non-identical distributions, and a very close (but still constant) approximation of the optimal revenue. It effectively shows that the only way to achieve a sufficiently good constant approximation of the optimal revenue is through a detailed understanding of bidders' valuation distributions. Our upper bound is constructive and applies in particular to a variant of the empirical Myerson auction, the natural auction that runs the revenue-maximizing auction with respect to the empirical distributions of the samples. To capture how our sample complexity upper bound depends on the set of allowable distributions, we introduce α-strongly regular distributions, which interpolate between the well-studied classes of regular (α = 0) and MHR (α = 1) distributions. We give evidence that this definition is of independent interest.

Original languageEnglish (US)
Title of host publicationSTOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Pages243-252
Number of pages10
ISBN (Print)9781450327107
DOIs
StatePublished - 2014
Event4th Annual ACM Symposium on Theory of Computing, STOC 2014 - New York, NY, United States
Duration: May 31 2014Jun 3 2014

Other

Other4th Annual ACM Symposium on Theory of Computing, STOC 2014
CountryUnited States
CityNew York, NY
Period5/31/146/3/14

Keywords

  • Myerson's auction
  • Sample complexity

ASJC Scopus subject areas

  • Software

Cite this

Cole, R., & Roughgarden, T. (2014). The sample complexity of revenue maximization. In STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing (pp. 243-252). Association for Computing Machinery. https://doi.org/10.1145/2591796.2591867

The sample complexity of revenue maximization. / Cole, Richard; Roughgarden, Tim.

STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing. Association for Computing Machinery, 2014. p. 243-252.

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

Cole, R & Roughgarden, T 2014, The sample complexity of revenue maximization. in STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing. Association for Computing Machinery, pp. 243-252, 4th Annual ACM Symposium on Theory of Computing, STOC 2014, New York, NY, United States, 5/31/14. https://doi.org/10.1145/2591796.2591867
Cole R, Roughgarden T. The sample complexity of revenue maximization. In STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing. Association for Computing Machinery. 2014. p. 243-252 https://doi.org/10.1145/2591796.2591867
Cole, Richard ; Roughgarden, Tim. / The sample complexity of revenue maximization. STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing. Association for Computing Machinery, 2014. pp. 243-252
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