# PairRank: Online Pairwise Learning to Rank by Divide-and-Conquer

arXiv: https://arxiv.org/abs/2103.00368 · HTML: https://mlsanity.com/paper/2103.00368/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 28 Feb 2021.

## Builds on (most cited first, 13 of 13)

- [Unbiased Learning-to-Rank with Biased Feedback](https://mlsanity.com/paper/1608.04468/) (2016)
- [Introducing LETOR 4.0 Datasets](https://mlsanity.com/paper/1306.2597/) (2013)
- [Cascading Bandits: Learning to Rank in the Cascade Model](https://mlsanity.com/paper/1502.02763/) (2015)
- [Combinatorial Cascading Bandits](https://mlsanity.com/paper/1507.04208/) (2015)
- [TopRank: A practical algorithm for online stochastic ranking](https://mlsanity.com/paper/1806.02248/) (2018)
- [Online Learning to Rank in Stochastic Click Models](https://mlsanity.com/paper/1703.02527/) (2017)
- [Differentiable Unbiased Online Learning to Rank](https://mlsanity.com/paper/1809.08415/) (2018)
- [Online Learning to Rank with Features](https://mlsanity.com/paper/1810.02567/) (2018)
- [DCM Bandits: Learning to Rank with Multiple Clicks](https://mlsanity.com/paper/1602.03146/) (2016)
- [Efficient Exploration of Gradient Space for Online Learning to Rank](https://mlsanity.com/paper/1805.07317/) (2018)
- [Variance Reduction in Gradient Exploration for Online Learning to Rank](https://mlsanity.com/paper/1906.03766/) (2019)
- [Balancing Speed and Quality in Online Learning to Rank for Information Retrieval](https://mlsanity.com/paper/1711.09446/) (2017)
- [BubbleRank: Safe Online Learning to Re-Rank via Implicit Click Feedback](https://mlsanity.com/paper/1806.05819/) (2018)

## Built on by (most cited first, 6 of 6)

- [GeoRanker: Distance-Aware Ranking for Worldwide Image Geolocalization](https://mlsanity.com/paper/2505.13731/) (2025)
- [Rankify: A Comprehensive Python Toolkit for Retrieval, Re-Ranking, and Retrieval-Augmented Generation](https://mlsanity.com/paper/2502.02464/) (2025)
- [Adversarial Attacks on Online Learning to Rank with Stochastic Click Models](https://mlsanity.com/paper/2305.19218/) (2023)
- [Unlearning for Federated Online Learning to Rank: A Reproducibility Study](https://mlsanity.com/paper/2505.12791/) (2025)
- [Calibrating Explore-Exploit Trade-off for Fair Online Learning to Rank](https://mlsanity.com/paper/2111.00735/) (2021)
- [Learning Neural Ranking Models Online from Implicit User Feedback](https://mlsanity.com/paper/2201.06658/) (2022)

## Abstract (arXiv)

Online Learning to Rank (OL2R) eliminates the need of explicit relevance annotation by directly optimizing the rankers from their interactions with users. However, the required exploration drives it away from successful practices in offline learning to rank, which limits OL2R's empirical performance and practical applicability. In this work, we propose to estimate a pairwise learning to rank model online. In each round, candidate documents are partitioned and ranked according to the model's confidence on the estimated pairwise rank order, and exploration is only performed on the uncertain pairs of documents, i.e., divide-and-conquer. Regret directly defined on the number of mis-ordered pairs is proven, which connects the online solution's theoretical convergence with its expected ranking performance. Comparisons against an extensive list of OL2R baselines on two public learning to rank benchmark datasets demonstrate the effectiveness of the proposed solution.