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The Sample Complexity of Up-to- 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 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 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