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.
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