Recent advances in unbiased learning to rank (LTR) count on Inverse Propensity Scoring (IPS) to eliminate bias in implicit feedback. Though theoretically sound in correcting the bias introduced by treating clicked documents as relevant, IPS ignores the bias caused by (implicitly) treating non-clicked ones as irrelevant. In this work, we first rigorously prove that such use of click data leads to unnecessary pairwise comparisons between relevant documents, which prevent unbiased ranker optimization. Based on the proof, we derive a simple yet well justified new weighting scheme, called Propensity Ratio Scoring (PRS), which provides treatments on both clicks and non-clicks. Besides correcting the bias in clicks, PRS avoids relevant-relevant document comparisons in LTR training and enjoys a lower variability. Our extensive empirical evaluations confirm that PRS ensures a more effective use of click data and improved performance in both synthetic data from a set of LTR benchmarks, as well as in the real-world large-scale data from GMail search.
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