Learning-to-Rank (LTR) is a supervised machine learning approach that constructs models specifically designed to order a set of items or documents based on their relevance or importance to a given query or context. Despite significant success in real-world information retrieval systems, current LTR methods rely on one prefix ranking metric (e.g., such as Normalized Discounted Cumulative Gain (NDCG) or Mean Average Precision (MAP)) for optimizing the ranking objective function. Such metric-dependent setting limits LTR methods from two perspectives: (1) non-differentiable problem: directly optimizing ranking functions over a given ranking metric is inherently non-smooth, making the training process unstable and inefficient; (2) limited ranking utility: optimizing over one single metric makes it difficult to generalize well to other ranking metrics of interest. To address the above issues, we propose a novel listwise LTR framework for efficient and generalizable ranking purpose. Specifically, we propose a new differentiable ranking loss that combines a smooth approximation to the ranking operator with the average mean square loss per query. Then, we adapt gradient-boosting machines to minimize our proposed loss with respect to each list, a novel contribution. Finally, extensive experimental results confirm that our method outperforms the current state-of-the-art in information retrieval measures with similar efficiency.

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