  Clicks on rankings suffer from position-bias: generally items on lower ranks
are less likely to be examined - and thus clicked - by users, in spite of their
actual preferences between items. The prevalent approach to unbiased
click-based learning-to-rank (LTR) is based on counterfactual
inverse-propensity-scoring (IPS) estimation. In contrast with general
reinforcement learning, counterfactual doubly-robust (DR) estimation has not
been applied to click-based LTR in previous literature. In this paper, we
introduce a novel DR estimator that is the first DR approach specifically
designed for position-bias. The difficulty with position-bias is that the
treatment - user examination - is not directly observable in click data. As a
solution, our estimator uses the expected treatment per rank, instead of the
actual treatment that existing DR estimators use. Our novel DR estimator has
more robust unbiasedness conditions than the existing IPS approach, and in
addition, provides enormous decreases in variance: our experimental results
indicate it requires several orders of magnitude fewer datapoints to converge
at optimal performance. For the unbiased LTR field, our DR estimator
contributes both increases in state-of-the-art performance and the most robust
theoretical guarantees of all known LTR estimators.
