  Many online companies sell advertisement space in second-price auctions with
reserve. In this paper, we develop a probabilistic method to learn a profitable
strategy to set the reserve price. We use historical auction data with features
to fit a predictor of the best reserve price. This problem is delicate - the
structure of the auction is such that a reserve price set too high is much
worse than a reserve price set too low. To address this we develop objective
variables, a new framework for combining probabilistic modeling with optimal
decision-making. Objective variables are "hallucinated observations" that
transform the revenue maximization task into a regularized maximum likelihood
estimation problem, which we solve with an EM algorithm. This framework enables
a variety of prediction mechanisms to set the reserve price. As examples, we
study objective variable methods with regression, kernelized regression, and
neural networks on simulated and real data. Our methods outperform previous
approaches both in terms of scalability and profit.
