# Linear Bandits with Feature Feedback

## TL;DR

This paper introduces a novel linear bandit model that incorporates feature feedback, enabling algorithms to identify relevant features and significantly reduce regret and computational complexity compared to traditional methods.

## Contribution

The paper develops new theory and algorithms for linear bandits with feature feedback, achieving regret bounds that depend on the number of relevant features without prior knowledge.

## Key findings

- Regret scales as k√T, improving over d√T when k ≪ d
- Algorithm complexity proportional to k, not d
- Effective on synthetic and real human-labeled data

## Abstract

This paper explores a new form of the linear bandit problem in which the algorithm receives the usual stochastic rewards as well as stochastic feedback about which features are relevant to the rewards, the latter feedback being the novel aspect. The focus of this paper is the development of new theory and algorithms for linear bandits with feature feedback. We show that linear bandits with feature feedback can achieve regret over time horizon $T$ that scales like $k\sqrt{T}$, without prior knowledge of which features are relevant nor the number $k$ of relevant features. In comparison, the regret of traditional linear bandits is $d\sqrt{T}$, where $d$ is the total number of (relevant and irrelevant) features, so the improvement can be dramatic if $k\ll d$. The computational complexity of the new algorithm is proportional to $k$ rather than $d$, making it much more suitable for real-world applications compared to traditional linear bandits. We demonstrate the performance of the new algorithm with synthetic and real human-labeled data.