# Preselection Bandits

arXiv: https://arxiv.org/abs/1907.06123 · HTML: https://mlsanity.com/paper/1907.06123/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2019.

## Built on by (most cited first, 5 of 5)

- [Stochastic Contextual Dueling Bandits under Linear Stochastic Transitivity Models](https://mlsanity.com/paper/2202.04593/) (2022)
- [A Survey of Methods for Automated Algorithm Configuration](https://mlsanity.com/paper/2202.01651/) (2022)
- [Finding Optimal Arms in Non-stochastic Combinatorial Bandits with Semi-bandit Feedback and Finite Budget](https://mlsanity.com/paper/2202.04487/) (2022)
- [Narrowing Action Choices with AI Improves Human Sequential Decisions](https://mlsanity.com/paper/2510.16097/) (2025)
- [Prescriptive Machine Learning for Automated Decision Making: Challenges and Opportunities](https://mlsanity.com/paper/2112.08268/) (2021)

## Abstract (arXiv)

In this paper, we introduce the Preselection Bandit problem, in which the learner preselects a subset of arms (choice alternatives) for a user, which then chooses the final arm from this subset. The learner is not aware of the user's preferences, but can learn them from observed choices. In our concrete setting, we allow these choices to be stochastic and model the user's actions by means of the Plackett-Luce model. The learner's main task is to preselect subsets that eventually lead to highly preferred choices. To formalize this goal, we introduce a reasonable notion of regret and derive lower bounds on the expected regret. Moreover, we propose algorithms for which the upper bound on expected regret matches the lower bound up to a logarithmic term of the time horizon.