# Preselection Bandits

## TL;DR

This paper introduces the Preselection Bandit problem where a learner preselects subsets of options to a user, learns preferences from stochastic choices modeled by Plackett-Luce, and develops algorithms with near-optimal regret bounds.

## Contribution

It formalizes the Preselection Bandit problem, introduces a regret measure, derives lower bounds, and proposes algorithms with matching upper bounds up to logarithmic factors.

## Key findings

- Derived lower bounds on expected regret.
- Proposed algorithms achieve near-optimal regret bounds.
- Modeling user choices with Plackett-Luce enhances learning efficiency.

## Abstract

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.