  Sponsored search is an important monetization channel for search engines, in
which an auction mechanism is used to select the ads shown to users and
determine the prices charged from advertisers. There have been several pieces
of work in the literature that investigate how to design an auction mechanism
in order to optimize the revenue of the search engine. However, due to some
unrealistic assumptions used, the practical values of these studies are not
very clear. In this paper, we propose a novel \emph{game-theoretic machine
learning} approach, which naturally combines machine learning and game theory,
and learns the auction mechanism using a bilevel optimization framework. In
particular, we first learn a Markov model from historical data to describe how
advertisers change their bids in response to an auction mechanism, and then for
any given auction mechanism, we use the learnt model to predict its
corresponding future bid sequences. Next we learn the auction mechanism through
empirical revenue maximization on the predicted bid sequences. We show that the
empirical revenue will converge when the prediction period approaches infinity,
and a Genetic Programming algorithm can effectively optimize this empirical
revenue. Our experiments indicate that the proposed approach is able to produce
a much more effective auction mechanism than several baselines.
