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

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 tha...

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Bibliographic Details
Published in:2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS) pp. 416 - 426
Main Authors: Gonczarowski, Yannai A., Weinberg, S. Matthew
Format: Conference Proceeding
Language:English
Published: IEEE 01.10.2018
Subjects:
Additives
algorithmic game theory
algorithmic mechanism design
approximate revenue maximization
auctions
Bayes methods
Complexity theory
Computational modeling
Cost accounting
Economics
generalization bounds
multi dimensional auctions
PAC learning
Resource management
sample complexity
ISSN:2575-8454
Online Access:Get full text
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Summary: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.
ISSN:2575-8454
DOI:10.1109/FOCS.2018.00047