Many online companies sell advertisement space in second-price auctions withreserve. In this paper, we develop a probabilistic method to learn a profitablestrategy to set the reserve price. We use historical auction data with featuresto fit a predictor of the best reserve price. This problem is delicate - thestructure of the auction is such that a reserve price set too high is muchworse than a reserve price set too low. To address this we develop objectivevariables, a new framework for combining probabilistic modeling with optimaldecision-making. Objective variables are "hallucinated observations" thattransform the revenue maximization task into a regularized maximum likelihoodestimation problem, which we solve with an EM algorithm. This framework enablesa variety of prediction mechanisms to set the reserve price. As examples, westudy objective variable methods with regression, kernelized regression, andneural networks on simulated and real data. Our methods outperform previousapproaches both in terms of scalability and profit.
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