Listwise learning-to-rank methods form a powerful class of ranking algorithms that are widely adopted in applications such as information retrieval. These algorithms learn to rank a set of items by optimizing a loss that is a function of the entire set—as a surrogate to a typically non-differentiable ranking metric. Despite their empirical success, existing listwise methods are based on heuristics and remain theoretically ill-understood. In particular, none of the empirically-successful loss functions are related to ranking metrics. In this work, we propose a cross entropy-based learning-to-rank loss function that is theoretically sound, is a convex bound on NDCG—a popular ranking metric—and is consistent with NDCG under learning scenarios common in information retrieval. Furthermore, empirical evaluation of an implementation of the proposed method with gradient boosting machines on benchmark learning-to-rank datasets demonstrates the superiority of our proposed formulation over existing algorithms in quality and robustness.

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