Learning Optimal Auctions with Correlated Valuations from Samples

In single-item auction design, it is well known due to Cremer and McLean that when bidders' valuations are drawn from a correlated prior distribution, the auctioneer can extract full social surplus as revenue. However, in most real-world applications, the prior is usually unknown and can only be learned from historical data. In this work, we investigate the robustness of the optimal auction with correlated valuations via sample complexity analysis. We prove upper and lower bounds on the number of samples from the unknown prior required to learn a (1 - epsilon)-approximately optimal auction. Our results reinforce the common belief that optimal correlated auctions are sensitive to the distribution parameters and hard to learn unless the prior distribution is well-behaved.