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.

翻译：传统上，贝叶斯最优拍卖设计问题要么在投标人价值独立同分布的情况下考虑，要么在每位投标人可通过其价值分布单独识别的情况下考虑。后一方法在投标人可划分为少数类别时较为合理，但存在许多投标人分类为连续体的情况。例如，投标人的分类可能基于其年收入、根据过往行为的购买倾向，或在广告拍卖中基于其广告的点击率。我们引入了一个捕捉这一特性的替代模型，其中投标人事先相同，但可（仅）基于拍卖人在拍卖时获得的某些辅助信息进行区分。我们将Dhangwatnotai、Roughgarden和Yan（2014）以及Cole和Roughgarden（2014）的样本复杂度方法扩展到该模型，并得到了几乎匹配的上下界。此外，我们推导出一个可能具有独立意义的收益单调性引理。我们还展示了如何利用经验风险最小化技术来改进Cole和Roughgarden（2014）针对非恒同但独立价值分布情况的样本复杂度界。