  Counterfactual Learning to Rank (LTR) methods optimize ranking systems using
logged user interactions that contain interaction biases. Existing methods are
only unbiased if users are presented with all relevant items in every ranking.
There is currently no existing counterfactual unbiased LTR method for top-k
rankings. We introduce a novel policy-aware counterfactual estimator for LTR
metrics that can account for the effect of a stochastic logging policy. We
prove that the policy-aware estimator is unbiased if every relevant item has a
non-zero probability to appear in the top-k ranking. Our experimental results
show that the performance of our estimator is not affected by the size of k:
for any k, the policy-aware estimator reaches the same retrieval performance
while learning from top-k feedback as when learning from feedback on the full
ranking. Lastly, we introduce novel extensions of traditional LTR methods to
perform counterfactual LTR and to optimize top-k metrics. Together, our
contributions introduce the first policy-aware unbiased LTR approach that
learns from top-k feedback and optimizes top-k metrics. As a result,
counterfactual LTR is now applicable to the very prevalent top-k ranking
setting in search and recommendation.
