# Active Bipartite Ranking with Smooth Posterior Distributions

arXiv: https://arxiv.org/abs/2602.24263 · HTML: https://mlsanity.com/paper/2602.24263/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 11 of 11)

- [Global optimization of Lipschitz functions](https://mlsanity.com/paper/1703.02628/) (2017)
- [The True Sample Complexity of Identifying Good Arms](https://mlsanity.com/paper/1906.06594/) (2019)
- [A simple parameter-free and adaptive approach to optimization under a minimal local smoothness assumption](https://mlsanity.com/paper/1810.00997/) (2018)
- [Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandits](https://mlsanity.com/paper/2006.07862/) (2020)
- [Bandits with many optimal arms](https://mlsanity.com/paper/2103.12452/) (2021)
- [Pure Exploration in Infinitely-Armed Bandit Models with Fixed-Confidence](https://mlsanity.com/paper/1803.04665/) (2018)
- [On the Complexity of A/B Testing](https://mlsanity.com/paper/1405.3224/) (2014)
- [Global Continuous Optimization with Error Bound and Fast Convergence](https://mlsanity.com/paper/1607.04817/) (2016)
- [Active Ranking of Experts Based on their Performances in Many Tasks](https://mlsanity.com/paper/2306.02628/) (2023)
- [Mass Volume Curves and Anomaly Ranking](https://mlsanity.com/paper/1705.01305/) (2017)
- [Ranking Data with Continuous Labels through Oriented Recursive Partitions](https://mlsanity.com/paper/1801.05772/) (2018)

## Built on by (most cited first, 1 of 1)

- [Active Seriation: Efficient Ordering Recovery with Statistical Guarantees](https://mlsanity.com/paper/2603.15336/) (2026)

## Abstract (arXiv)

In this article, bipartite ranking, a statistical learning problem involved in many applications and widely studied in the passive context, is approached in a much more general textitactive setting than the discrete one previously considered in the literature. While the latter assumes that the conditional distribution is piece wise constant, the framework we develop permits in contrast to deal with continuous conditional distributions, provided that they fulfill a H"older smoothness constraint. We first show that a naive approach based on discretisation at a uniform level, fixed textita priori and consisting in applying next the active strategy designed for the discrete setting generally fails. Instead, we propose a novel algorithm, referred to as smooth-rank and designed for the continuous setting, which aims to minimise the distance between the ROC curve of the estimated ranking rule and the optimal one w.r.t. the sup norm. We show that, for a fixed confidence level ε>0 and probability δ∈ (0,1), smooth-rank is PAC(ε,δ). In addition, we provide a problem dependent upper bound on the expected sampling time of smooth-rank and establish a problem dependent lower bound on the expected sampling time of any PAC(ε,δ) algorithm. Beyond the theoretical analysis carried out, numerical results are presented, providing solid empirical evidence of the performance of the algorithm proposed, which compares favorably with alternative approaches.