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We present an extensive analysis of the key problem of learning optimalreserve prices for generalized second price auctions. We describe twoalgorithms for this task: one based on density estimation, and a novelalgorithm benefiting from solid theoretical guarantees and with a veryfavorable running-time complexity of $O(n S \log (n S))$, where $n$ is thesample size and $S$ the number of slots. Our theoretical guarantees are morefavorable than those previously presented in the literature. Additionally, weshow that even if bidders do not play at an equilibrium, our second algorithmis still well defined and minimizes a quantity of interest. To our knowledge,this is the first attempt to apply learning algorithms to the problem ofreserve price optimization in GSP auctions. Finally, we present the firstconvergence analysis of empirical equilibrium bidding functions to the uniquesymmetric Bayesian-Nash equilibrium of a GSP.

Non-parametric Revenue Optimization for Generalized Second Price Auctions