  We present a polynomial-time algorithm that, given samples from the unknown
valuation distribution of each bidder, learns an auction that approximately
maximizes the auctioneer's revenue in a variety of single-parameter auction
environments including matroid environments, position environments, and the
public project environment. The valuation distributions may be arbitrary
bounded distributions (in particular, they may be irregular, and may differ for
the various bidders), thus resolving a problem left open by previous papers.
The analysis uses basic tools, is performed in its entirety in value-space, and
simplifies the analysis of previously known results for special cases.
Furthermore, the analysis extends to certain single-parameter auction
environments where precise revenue maximization is known to be intractable,
such as knapsack environments.
