# Multiple-Play Bandits in the Position-Based Model

arXiv: https://arxiv.org/abs/1606.02448 · HTML: https://mlsanity.com/paper/1606.02448/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2016.

## Built on by (most cited first, 28 of 28)

- [Doubly-Robust Estimation for Correcting Position-Bias in Click Feedback for Unbiased Learning to Rank](https://mlsanity.com/paper/2203.17118/) (2022)
- [A Survey on LLM-based Conversational User Simulation](https://mlsanity.com/paper/2604.24977/) (2026)
- [Optimal Design for Human Preference Elicitation](https://mlsanity.com/paper/2404.13895/) (2024)
- [Multi-Armed Bandits with Interference](https://mlsanity.com/paper/2402.01845/) (2024)
- [Active Learning for Direct Preference Optimization](https://mlsanity.com/paper/2503.01076/) (2025)
- [Online Experimental Design With Estimation-Regret Trade-off Under Network Interference](https://mlsanity.com/paper/2412.03727/) (2024)
- [Robust Generalization and Safe Query-Specialization in Counterfactual Learning to Rank](https://mlsanity.com/paper/2102.05990/) (2021)
- [Multiple-Play Stochastic Bandits with Shareable Finite-Capacity Arms](https://mlsanity.com/paper/2206.08776/) (2022)
- [Adversarial Attacks on Online Learning to Rank with Click Feedback](https://mlsanity.com/paper/2305.17071/) (2023)
- [Adversarial Attacks on Online Learning to Rank with Stochastic Click Models](https://mlsanity.com/paper/2305.19218/) (2023)
- [Graph-Dependent Regret Bounds in Multi-Armed Bandits with Interference](https://mlsanity.com/paper/2503.07555/) (2025)
- [Probabilistic Permutation Graph Search: Black-Box Optimization for Fairness in Ranking](https://mlsanity.com/paper/2204.13765/) (2022)
- [Cascading Reinforcement Learning](https://mlsanity.com/paper/2401.08961/) (2024)
- [Simultaneously Learning Stochastic and Adversarial Bandits under the Position-Based Model](https://mlsanity.com/paper/2207.05437/) (2022)
- [Contextual bandits with concave rewards, and an application to fair ranking](https://mlsanity.com/paper/2210.09957/) (2022)
- [Bandit Learning to Rank with Position-Based Click Models: Personalized and Equal Treatments](https://mlsanity.com/paper/2311.04528/) (2023)
- [Ranking In Generalized Linear Bandits](https://mlsanity.com/paper/2207.00109/) (2022)
- [Overcoming Prior Misspecification in Online Learning to Rank](https://mlsanity.com/paper/2301.10651/) (2023)
- [Misalignment, Learning, and Ranking: Harnessing Users Limited Attention](https://mlsanity.com/paper/2402.14013/) (2024)
- [Design-Based Bandits Under Network Interference: Trade-Off Between Regret and Statistical Inference](https://mlsanity.com/paper/2510.07646/) (2025)
- [UniRank: Unimodal Bandit Algorithm for Online Ranking](https://mlsanity.com/paper/2208.01515/) (2022)
- [Exploration of Unranked Items in Safe Online Learning to Re-Rank](https://mlsanity.com/paper/2305.01202/) (2023)
- [Adaptively Learning to Select-Rank in Online Platforms](https://mlsanity.com/paper/2406.05017/) (2024)
- [Observation-Free Attacks on Online Learning to Rank](https://mlsanity.com/paper/2509.22855/) (2025)
- [Online Learning to Rank under Corruption: A Robust Cascading Bandits Approach](https://mlsanity.com/paper/2511.03074/) (2025)
- [Multiple-play Stochastic Bandits with Prioritized Arm Capacity Sharing](https://mlsanity.com/paper/2512.21626/) (2025)
- [Contextual Slate GLM Bandits with Limited Adaptivity](https://mlsanity.com/paper/2606.31449/) (2026)
- [Ranking Bandits for Carousel Interfaces with Observable Browsing Depth](https://mlsanity.com/paper/2610.05220/) (2026)

## Abstract (arXiv)

Sequentially learning to place items in multi-position displays or lists is a task that can be cast into the multiple-play semi-bandit setting. However, a major concern in this context is when the system cannot decide whether the user feedback for each item is actually exploitable. Indeed, much of the content may have been simply ignored by the user. The present work proposes to exploit available information regarding the display position bias under the so-called Position-based click model (PBM). We first discuss how this model differs from the Cascade model and its variants considered in several recent works on multiple-play bandits. We then provide a novel regret lower bound for this model as well as computationally efficient algorithms that display good empirical and theoretical performance.