# Contextual Linear Bandits under Noisy Features: Towards Bayesian Oracles

arXiv: https://arxiv.org/abs/1703.01347 · HTML: https://mlsanity.com/paper/1703.01347/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2017.

## Built on by (most cited first, 9 of 9)

- [Thompson Sampling in Partially Observable Contextual Bandits](https://mlsanity.com/paper/2402.10289/) (2024)
- [Linear Bandits with Partially Observable Features](https://mlsanity.com/paper/2502.06142/) (2025)
- [Distributed Multi-Task Learning for Stochastic Bandits with Context Distribution and Stage-wise Constraints](https://mlsanity.com/paper/2401.11563/) (2024)
- [Thompson Sampling for Stochastic Bandits with Noisy Contexts: An Information-Theoretic Regret Analysis](https://mlsanity.com/paper/2401.11565/) (2024)
- [Online Linear Regression with Paid Stochastic Features](https://mlsanity.com/paper/2511.08073/) (2025)
- [Learning with Incomplete Context: Linear Contextual Bandits with Pretrained Imputation](https://mlsanity.com/paper/2510.09908/) (2025)
- [Exploration via Feature Perturbation in Contextual Bandits](https://mlsanity.com/paper/2510.17390/) (2025)
- [Set Membership Estimation for Stochastic Linear Contextual Bandits](https://mlsanity.com/paper/2606.20022/) (2026)
- [Beyond Second-Order Information: Paid Logistic Regression with Noisy Features](https://mlsanity.com/paper/2610.12919/) (2026)

## Abstract (arXiv)

We study contextual linear bandit problems under feature uncertainty, where the features are noisy and have missing entries. To address the challenges posed by this noise, we analyze Bayesian oracles given the observed noisy features. Our Bayesian analysis reveals that the optimal hypothesis can significantly deviate from the underlying realizability function, depending on the noise characteristics. These deviations are highly non-intuitive and do not occur in classical noiseless setups. This implies that classical approaches cannot guarantee a non-trivial regret bound. Therefore, we propose an algorithm that aims to approximate the Bayesian oracle based on the observed information under this model, achieving tildeO(d√T) regret bound when there is a large number of arms. We demonstrate the proposed algorithm using synthetic and real-world datasets.