The Sample Complexity of Auctions with Side Information

TL;DR

This paper studies the sample complexity of designing Bayesian optimal auctions when bidders are indistinguishable a priori but can be differentiated using side information, extending previous models to more realistic scenarios.

Contribution

It introduces a new model for auction design with side information and extends existing sample complexity bounds to this setting, including a revenue monotonicity lemma.

Findings

Derived almost matching upper and lower bounds for sample complexity.

Extended the sample complexity approach to auctions with side information.

Improved bounds using Empirical Risk Minimization techniques.

Abstract

Traditionally, the Bayesian optimal auction design problem has been considered either when the bidder values are i.i.d., or when each bidder is individually identifiable via her value distribution. The latter is a reasonable approach when the bidders can be classified into a few categories, but there are many instances where the classification of bidders is a continuum. For example, the classification of the bidders may be based on their annual income, their propensity to buy an item based on past behavior, or in the case of ad auctions, the click through rate of their ads. We introduce an alternate model that captures this aspect, where bidders are \emph{a priori} identical, but can be distinguished based (only) on some side information the auctioneer obtains at the time of the auction. We extend the sample complexity approach of Dhangwatnotai, Roughgarden, and Yan (2014) and Cole and Roughgarden (2014) to this model and obtain almost matching upper and lower bounds. As an aside, we obtain a revenue monotonicity lemma which may be of independent interest. We also show how to use Empirical Risk Minimization techniques to improve the sample complexity bound of Cole and Roughgarden (2014) for the non-identical but independent value distribution case.