# An Alternative Cross Entropy Loss for Learning-to-Rank

arXiv: https://arxiv.org/abs/1911.09798 · HTML: https://mlsanity.com/paper/1911.09798/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2019.

## Built on by (most cited first, 17 of 17)

- [MSTRIQ: No Reference Image Quality Assessment Based on Swin Transformer with Multi-Stage Fusion](https://mlsanity.com/paper/2205.10101/) (2022)
- [Multi-Label Learning to Rank through Multi-Objective Optimization](https://mlsanity.com/paper/2207.03060/) (2022)
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- [Applications of Entropy in Data Analysis and Machine Learning: A Review](https://mlsanity.com/paper/2503.02921/) (2025)
- [QAMRO: Quality-aware Adaptive Margin Ranking Optimization for Human-aligned Assessment of Audio Generation Systems](https://mlsanity.com/paper/2508.08957/) (2025)
- [Differentiable Fast Top-K Selection for Large-Scale Recommendation](https://mlsanity.com/paper/2510.11472/) (2025)
- [LFQ: Logit-aware Final-block Quantization for Boosting the Generation Quality of Low-Bit Quantized LLMs](https://mlsanity.com/paper/2605.29756/) (2026)
- [Composing Efficient, Robust Tests for Policy Selection](https://mlsanity.com/paper/2306.07372/) (2023)
- [Attribute-Enhanced Similarity Ranking for Sparse Link Prediction](https://mlsanity.com/paper/2412.00261/) (2024)
- [Relative-Based Scaling Law for Neural Language Models](https://mlsanity.com/paper/2510.20387/) (2025)
- [Distributionally Robust Multi-Output Regression Ranking](https://mlsanity.com/paper/2109.12803/) (2021)
- [An IPW-based Unbiased Ranking Metric in Two-sided Markets](https://mlsanity.com/paper/2307.10204/) (2023)
- [NDCG-Consistent Softmax Approximation with Accelerated Convergence](https://mlsanity.com/paper/2506.09454/) (2025)
- [Explanation Quality Assessment as Ranking with Listwise Rewards](https://mlsanity.com/paper/2604.24176/) (2026)

## Abstract (arXiv)

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.