# Robust Contextual Linear Bandits

arXiv: https://arxiv.org/abs/2210.14483 · HTML: https://mlsanity.com/paper/2210.14483/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 26 Oct 2022.

## Builds on (most cited first, 12 of 12)

- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Adapting to Misspecification in Contextual Bandits](https://mlsanity.com/paper/2107.05745/) (2021)
- [Stochastic Linear Bandits Robust to Adversarial Attacks](https://mlsanity.com/paper/2007.03285/) (2020)
- [Meta-Thompson Sampling](https://mlsanity.com/paper/2102.06129/) (2021)
- [Misspecified Linear Bandits](https://mlsanity.com/paper/1704.06880/) (2017)
- [Hierarchical Bayesian Bandits](https://mlsanity.com/paper/2111.06929/) (2021)
- [Robust Stochastic Linear Contextual Bandits Under Adversarial Attacks](https://mlsanity.com/paper/2106.02978/) (2021)
- [No Regrets for Learning the Prior in Bandits](https://mlsanity.com/paper/2107.06196/) (2021)
- [Metadata-based Multi-Task Bandits with Bayesian Hierarchical Models](https://mlsanity.com/paper/2108.06422/) (2021)
- [Adapting to Misspecification in Contextual Bandits with Offline Regression Oracles](https://mlsanity.com/paper/2102.13240/) (2021)
- [Towards Scalable and Robust Structured Bandits: A Meta-Learning Framework](https://mlsanity.com/paper/2202.13227/) (2022)
- [Random Effect Bandits](https://mlsanity.com/paper/2106.12200/) (2021)

## Built on by (most cited first, 4 of 4)

- [reBandit: Random Effects based Online RL algorithm for Reducing Cannabis Use](https://mlsanity.com/paper/2402.17739/) (2024)
- [Follow-ups Also Matter: Improving Contextual Bandits via Post-serving Contexts](https://mlsanity.com/paper/2309.13896/) (2023)
- [UCB Exploration for Fixed-Budget Bayesian Best Arm Identification](https://mlsanity.com/paper/2408.04869/) (2024)
- [Robust Linear Dueling Bandits with Post-serving Context under Unknown Delays and Adversarial Corruptions](https://mlsanity.com/paper/2605.01752/) (2026)

## Abstract (arXiv)

Model misspecification is a major consideration in applications of statistical methods and machine learning. However, it is often neglected in contextual bandits. This paper studies a common form of misspecification, an inter-arm heterogeneity that is not captured by context. To address this issue, we assume that the heterogeneity arises due to arm-specific random variables, which can be learned. We call this setting a robust contextual bandit. The arm-specific variables explain the unknown inter-arm heterogeneity, and we incorporate them in the robust contextual estimator of the mean reward and its uncertainty. We develop two efficient bandit algorithms for our setting: a UCB algorithm called RoLinUCB and a posterior-sampling algorithm called RoLinTS. We analyze both algorithms and bound their n-round Bayes regret. Our experiments show that RoLinTS is comparably statistically efficient to the classic methods when the misspecification is low, more robust when the misspecification is high, and significantly more computationally efficient than its naive implementation.