  Many web systems rank and present a list of items to users, from recommender
systems to search and advertising. An important problem in practice is to
evaluate new ranking policies offline and optimize them before they are
deployed. We address this problem by proposing evaluation algorithms for
estimating the expected number of clicks on ranked lists from historical logged
data. The existing algorithms are not guaranteed to be statistically efficient
in our problem because the number of recommended lists can grow exponentially
with their length. To overcome this challenge, we use models of user
interaction with the list of items, the so-called click models, to construct
estimators that learn statistically efficiently. We analyze our estimators and
prove that they are more efficient than the estimators that do not use the
structure of the click model, under the assumption that the click model holds.
We evaluate our estimators in a series of experiments on a real-world dataset
and show that they consistently outperform prior estimators.
