  We present an extensive analysis of the key problem of learning optimal
reserve prices for generalized second price auctions. We describe two
algorithms for this task: one based on density estimation, and a novel
algorithm benefiting from solid theoretical guarantees and with a very
favorable running-time complexity of $O(n S \log (n S))$, where $n$ is the
sample size and $S$ the number of slots. Our theoretical guarantees are more
favorable than those previously presented in the literature. Additionally, we
show that even if bidders do not play at an equilibrium, our second algorithm
is still well defined and minimizes a quantity of interest. To our knowledge,
this is the first attempt to apply learning algorithms to the problem of
reserve price optimization in GSP auctions. Finally, we present the first
convergence analysis of empirical equilibrium bidding functions to the unique
symmetric Bayesian-Nash equilibrium of a GSP.
