research-article

Public Access

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

Authors:

Yannai A. Gonczarowski,

S. Matthew WeinbergAuthors Info & Claims

Journal of the ACM (JACM), Volume 68, Issue 3

Article No.: 15, Pages 1 - 28

https://doi.org/10.1145/3439722

Published: 22 March 2021 Publication History

All formats PDF

Abstract

We consider the sample complexity of revenue maximization for multiple bidders in unrestricted multi-dimensional settings. Specifically, we study the standard model of

additive bidders whose values for

heterogeneous items are drawn independently. For any such instance and any

, we show that it is possible to learn an

-Bayesian Incentive Compatible auction whose expected revenue is within

of the optimal

-BIC auction from only polynomially many samples.

Our fully nonparametric 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 are not 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.

References

[1]

Moshe Babaioff, Yannai A. Gonczarowski, and Noam Nisan. 2017. The menu-size complexity of revenue approximation. In Proceedings of the 49th Annual ACM Symposium on Theory of Computing (STOC’17). 869–877.

Digital Library

[2]

Moshe Babaioff, Nicole Immorlica, Brendan Lucier, and S. Matthew Weinberg. 2014. A simple and approximately optimal mechanism for an additive buyer. In Proceedings of the 55th Annual IEEE Symposium on Foundations of Computer Science (FOCS’14). 21–30.

Digital Library

[3]

Yakov Babichenko, Siddharth Barman, and Ron Peretz. 2017. Empirical distribution of equilibrium play and its testing application. Math. Operat. Res. 42, 1 (2017), 15–29. Preliminary version (“Simple approximate equilibria in large games”) in Proceedings of the 15th ACM Conference on Economics and Computation (EC). 2014.

Digital Library

[4]

Maria-Florina Balcan, Avrim Blum, Jason D. Hartline, and Yishay Mansour. 2005. Mechanism design via machine learning. In Proceedings of the 46th Annual IEEE Symposium on the Foundations of Computer Science (FOCS’05). 426–439. Full version: Technical Report CMU-CS-05-143.

Digital Library

[5]

Maria-Florina Balcan, Tuomas Sandholm, and Ellen Vitercik. 2016. Sample complexity of automated mechanism design. In Proceedings of the 30th Conference on Neural Information Processing Systems (NIPS’16). 2083–2091.

Digital Library

[6]

Maria-Florina Balcan, Tuomas Sandholm, and Ellen Vitercik. 2018. A general theory of sample complexity for multi-item profit maximization. In Proceedings of the 19th ACM Conference on Economics and Computation (EC’18). 173–174.

Digital Library

[7]

Xiaohui Bei and Zhiyi Huang. 2011. Bayesian incentive compatibility via fractional assignments. In Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’11). 720–733.

Digital Library

[8]

Yang Cai and Constantinos Daskalakis. 2017. Learning multi-item auctions with (or without) samples. In Proceedings of the 58th IEEE Annual Symposium on Foundations of Computer Science (FOCS’17). 516–527.

[9]

Yang Cai, Constantinos Daskalakis, and S. Matthew Weinberg. 2012. Optimal multi-dimensional mechanism design: Reducing revenue to welfare maximization. In Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science (FOCS’12). 130–139.

Digital Library

[10]

Yang Cai, Nikhil Devanur, and S. Matthew Weinberg. 2016. A duality based unified approach to Bayesian mechanism design. In Proceedings of the 48th Annual ACM Symposium on Theory of Computing (STOC’16). 926–939.

Digital Library

[11]

Yang Cai and Mingfei Zhao. 2017. Simple mechanisms for subadditive buyers via duality. In Proceedings of the 49th Annual ACM Symposium on Theory of Computing (STOC’17). 170–183.

Digital Library

[12]

Shuchi Chawla, Jason D. Hartline, and Robert Kleinberg. 2007. Algorithmic pricing via virtual valuations. In Proceedings of the 8th ACM Conference on Electronic Commerce (EC’07). 243–251.

Digital Library

[13]

Shuchi Chawla, Jason D. Hartline, David L. Malec, and Balasubramanian Sivan. 2010. Multi-parameter mechanism design and sequential posted pricing. In Proceedings of the 42nd Annual ACM Symposium on Theory of Computing (STOC’10). 311–320.

Digital Library

[14]

Shuchi Chawla, David L. Malec, and Balasubramanian Sivan. 2015. The power of randomness in Bayesian optimal mechanism design. Games Econ. Behav. 91 (2015), 297–317. Preliminary version in Proceedings of the 11th ACM Conference on Electronic Commerce (EC). 2010.

Digital Library

[15]

Shuchi Chawla and J. Benjamin Miller. 2016. Mechanism design for subadditive agents via an ex ante relaxation. In Proceedings of the 17th ACM Conference on Economics and Computation (EC’16). 579–596.

Digital Library

[16]

Richard Cole and Tim Roughgarden. 2014. The sample complexity of revenue maximization. In Proceedings of the 46th Annual ACM Symposium on Theory of Computing (STOC’14). 243–252.

Digital Library

[17]

Constantinos Daskalakis, Alan Deckelbaum, and Christos Tzamos. 2013. Mechanism design via optimal transport. In Proceedings of the 14th ACM Conference on Electronic Commerce (EC’13). 269–286.

Digital Library

[18]

Constantinos Daskalakis and S. Matthew Weinberg. 2012. Symmetries and optimal multi-dimensional mechanism design. In Proceedings of the 13th ACM Conference on Electronic Commerce (EC’12). 370–387.

Digital Library

[19]

Nikhil R. Devanur, Zhiyi Huang, and Christos-Alexandros Psomas. 2016. The sample complexity of auctions with side information. In Proceedings of the 48th Annual ACM Symposium on Theory of Computing (STOC’16). 426–439.

Digital Library

[20]

Peerapong Dhangwatnotai, Tim Roughgarden, and Qiqi Yan. 2015. Revenue maximization with a single sample. Games Econ. Behav. 91 (2015), 318–333.

[21]

Shaddin Dughmi, Li Han, and Noam Nisan. 2014. Sampling and representation complexity of revenue maximization. In Proceedings of the 10th Conference on Web and Internet Economics (WINE’14). 277–291.

[22]

Shaddin Dughmi, Jason D. Hartline, Robert Kleinberg, and Rad Niazadeh. 2017. Bernoulli factories and black-box reductions in mechanism design. In Proceedings of the 49th Annual ACM Symposium on Theory of Computing (STOC’17). 158–169.

Digital Library

[23]

Edith Elkind. 2007. Designing and learning optimal finite support auctions. In Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’07). 736–745.

Digital Library

[24]

Evangelia Gergatsouli, Brendan Lucier, and Christos Tzamos. 2019. The complexity of black-box mechanism design with priors. In Proceedings of the 20th ACM Conference on Economics and Computation (EC’19). 869–883.

Digital Library

[25]

Yannai A. Gonczarowski. 2018. Bounding the menu-size of approximately optimal auctions via optimal-transport duality. In Proceedings of the 50th Annual ACM Symposium on Theory of Computing (STOC’18). 123–131.

Digital Library

[26]

Yannai A. Gonczarowski and Noam Nisan. 2017. Efficient empirical revenue maximization in single-parameter auction environments. In Proceedings of the 49th Annual ACM Symposium on Theory of Computing (STOC’17). 856–868.

Digital Library

[27]

Yannai A. Gonczarowski and S. Matthew Weinberg. 2018. The sample complexity of up-to-

multi-dimensional revenue maximization. In Proceedings of the 59th Annual IEEE Symposium on Foundations of Computer Science (FOCS’18). 416–426.

[28]

Chenghao Guo, Zhiyi Huang, Zhihao Gavin Tang, and Xinzhi Zhang. 2019. Generalizing Complex Hypotheses on Product Distributions: Auctions, Prophet Inequalities, and Pandora’s Problem. arXiv:1911.11936. Retrieved from https://arxiv.org/abs/1911.11936.

[29]

Sergiu Hart and Noam Nisan. 2012. Approximate revenue maximization with multiple items. In Proceedings of the 13th ACM Conference on Electronic Commerce (EC’12). 656.

Digital Library

[30]

Sergiu Hart and Noam Nisan. 2013. The menu-size complexity of auctions. In Proceedings of the 14th ACM Conference on Electronic Commerce (EC’12). 565.

Digital Library

[31]

Sergiu Hart and Philip J. Reny. 2015. Maximal revenue with multiple goods: Nonmonotonicity and other observations. Theor. Econ. 10, 3 (2015), 893–922.

[32]

Jason Hartline and Samuel Taggart. 2019. Sample complexity for non-truthful mechanisms. In Proceedings of the 20th ACM Conference on Economics and Computation (EC’19). 399–416.

Digital Library

[33]

Jason D. Hartline, Robert Kleinberg, and Azarakhsh Malekian. 2011. Bayesian incentive compatibility via matchings. In Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’11). 734–747.

Digital Library

[34]

Zhiyi Huang, Yishay Mansour, and Tim Roughgarden. 2015. Making the most of your samples. In Proceedings of the 16th ACM Conference on Economics and Computation (EC’15). 45–60.

Digital Library

[35]

Pravesh Kothari, Divyarthi Mohan, Ariel Schvartzman, Sahil Singla, and S. Matthew Weinberg. 2019. Approximation schemes for a buyer with independent items via symmetries. In Proceedings of the 60th Annual IEEE Symposium on Foundations of Computer Science (FOCS’19).

[36]

Kristóf Madarász and Andrea Prat. 2017. Sellers with misspecified models. The Review of Economic Studies 84, 2 (2017), 790--815.

Digital Library

[37]

Jamie Morgenstern and Tim Roughgarden. 2015. On the pseudo-dimension of nearly optimal auctions. In Proceedings of the 29th Annual Conference on Neural Information Processing Systems (NIPS’15). 136–144.

[38]

Jamie Morgenstern and Tim Roughgarden. 2016. Learning simple auctions. In Proceedings of the 29th Annual Conference on Learning Theory (COLT’16). 1298–1318.

Digital Library

[39]

Roger Myerson. 1981. Optimal auction design. Math. Oper. Res. 6, 1 (1981), 58–73.

Digital Library

[40]

Tim Roughgarden and Okke Schrijvers. 2016. Ironing in the dark. In Proceedings of the 17th ACM Conference on Economics and Computation (EC’16). 1–18.

Digital Library

[41]

Aviad Rubinstein and S. Matthew Weinberg. 2015. Simple mechanisms for a combinatorial buyer and applications to revenue monotonicity. In Proceedings of the 16th ACM Conference on Economics and Computation (EC’15). 377–394.

Digital Library

[42]

Vasilis Syrgkanis. 2017. A sample complexity measure with applications to learning optimal auctions. In Proceedings of the 31th Annual Conference on Neural Information Processing Systems (NIPS’17). 5352–5359.

[43]

John Thanassoulis. 2004. Haggling over substitutes. J. Econ. Theory 117, 2 (2004), 217–245.

Digital Library

[44]

Andrew Chi-Chih Yao. 2015. An

-to-1 bidder reduction for multi-item auctions and its applications. In Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’15). 92–109.

Digital Library

[45]

Andrew Chi-Chih Yao. 2017. Dominant-strategy versus Bayesian multi-item auctions: Maximum revenue determination and comparison. In Proceedings of the 18th ACM Conference on Economics and Computation (EC’17). 3–20.

Cited By

Wang TDütting PIvanov DTalgam-Cohen IParkes DOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Deep contract design via discontinuous networksProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3668995(65818-65836)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3668995
Lin TChen YOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Sample complexity of forecast aggregationProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667686(36053-36093)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3667686
Chen ZHuang ZMajdi DYan ZLeyton-Brown KSamuelson LHartline J(2023)Strong Revenue (Non-)Monotonicity of Single-parameter AuctionsProceedings of the 24th ACM Conference on Economics and Computation10.1145/3580507.3597745(452-471)Online publication date: 9-Jul-2023
https://dl.acm.org/doi/10.1145/3580507.3597745
Show More Cited By

Index Terms

The Sample Complexity of Up-to-ε Multi-dimensional Revenue Maximization
1. Theory of computation
  1. Design and analysis of algorithms
  2. Theory and algorithms for application domains
    1. Algorithmic game theory and mechanism design
    2. Machine learning theory
      1. Sample complexity and generalization bounds

Recommendations

The sample complexity of revenue maximization
STOC '14: Proceedings of the forty-sixth annual ACM symposium on Theory of computing

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 ...
Revenue maximization with a single sample
EC '10: Proceedings of the 11th ACM conference on Electronic commerce

We design and analyze approximately revenue-maximizing auctions in general single-parameter settings. Bidders have publicly observable attributes, and we assume that the valuations of indistinguishable bidders are independent draws from a common ...
Dynamic and Nonuniform Pricing Strategies for Revenue Maximization
^† Special Section on the Fiftieth Annual IEEE Symposium on Foundations of Computer Science (FOCS 2009)

We consider the item pricing problem for revenue maximization, where a single seller with multiple distinct items caters to multiple buyers with unknown subadditive valuation functions who arrive in a sequence. The seller sets the prices on individual items, ...

Comments

Information & Contributors

Information

Published In

cover image Journal of the ACM

Journal of the ACM Volume 68, Issue 3

June 2021

244 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/3456663

Editor:
Éva Tardos
Cornell University, United States

Issue’s Table of Contents

Copyright © 2021 Copyright held by the owner/author(s). Publication rights licensed to ACM.

Permission to make digital or hard copies of all or part 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 components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 22 March 2021

Accepted: 01 November 2020

Revised: 01 September 2020

Received: 01 December 2019

Published in JACM Volume 68, Issue 3

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Refereed

Funding Sources

ISF
Israel-USA Binational Science Foundation (BSF)
European Union's Horizon 2020 research and innovation programme
NSF
NSF CAREER

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

8
Total Citations
View Citations
503
Total Downloads

Downloads (Last 12 months)126
Downloads (Last 6 weeks)25

Reflects downloads up to 30 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

Wang TDütting PIvanov DTalgam-Cohen IParkes DOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Deep contract design via discontinuous networksProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3668995(65818-65836)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3668995
Lin TChen YOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Sample complexity of forecast aggregationProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3667686(36053-36093)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3667686
Chen ZHuang ZMajdi DYan ZLeyton-Brown KSamuelson LHartline J(2023)Strong Revenue (Non-)Monotonicity of Single-parameter AuctionsProceedings of the 24th ACM Conference on Economics and Computation10.1145/3580507.3597745(452-471)Online publication date: 9-Jul-2023
https://dl.acm.org/doi/10.1145/3580507.3597745
Cai YWu JSaha BServedio R(2023)On the Optimal Fixed-Price Mechanism in Bilateral TradeProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585171(737-750)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585171
Cai LWeinberg SWildenhain EZhang S(2023)Selling to Multiple No-Regret BuyersWeb and Internet Economics10.1007/978-3-031-48974-7_7(113-129)Online publication date: 4-Dec-2023
https://dl.acm.org/doi/10.1007/978-3-031-48974-7_7
Giannakopoulos YPoças DTsigonias-Dimitriadis A(2022)Robust Revenue Maximization Under Minimal Statistical InformationACM Transactions on Economics and Computation10.1145/354660610:3(1-34)Online publication date: 2-Sep-2022
https://dl.acm.org/doi/10.1145/3546606
Chawla SRezvan RTeng YTzamos CLeonardi SGupta A(2022)Pricing ordered itemsProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3520065(722-735)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3520065
Guo WJordan MZampetakis MRanzato MBeygelzimer ADauphin YLiang PVaughan J(2021)Robust learning of optimal auctionsProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3541888(21273-21284)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.5555/3540261.3541888
Balcan MDeBlasio DDick TKingsford CSandholm TVitercik E(undefined)How Much Data Is Sufficient to Learn High-Performing Algorithms?Journal of the ACM10.1145/3676278
https://dl.acm.org/doi/10.1145/3676278

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

HTML Format

View this article in HTML Format.

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Media

Figures

Other

Tables

View Issue’s Table of Contents