We consider (approximate) revenue maximization in auctions where the distribution on input valuations is given via "black box" access to samples from the distribution. We observe that the number of samples required -the sample complexity -is tightly related to the representation complexity of an approximately revenue-maximizing auction. Our main results are upper bounds and an exponential lower bound on these complexities.
Of these, Dughmi et al. REF consider general, correlated valuation distributions, and prove bounds on sample complexity based on the representation complexity of an auction.
Sampling and Representation Complexity of Revenue Maximization
ArXiv
ArXiv
Mathematics Computer Science