# Linear Bandits with Partially Observable Features

arXiv: https://arxiv.org/abs/2502.06142 · HTML: https://mlsanity.com/paper/2502.06142/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 23 of 23)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Learning with Good Feature Representations in Bandits and in RL with a Generative Model](https://mlsanity.com/paper/1911.07676/) (2019)
- [Best-Arm Identification in Linear Bandits](https://mlsanity.com/paper/1409.6110/) (2014)
- [Stochastic Linear Bandits Robust to Adversarial Attacks](https://mlsanity.com/paper/2007.03285/) (2020)
- [High-Dimensional Sparse Linear Bandits](https://mlsanity.com/paper/2011.04020/) (2020)
- [Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2205.06811/) (2022)
- [Doubly-Robust Lasso Bandit](https://mlsanity.com/paper/1907.11362/) (2019)
- [Sparsity-Agnostic Lasso Bandit](https://mlsanity.com/paper/2007.08477/) (2020)
- [Misspecified Linear Bandits](https://mlsanity.com/paper/1704.06880/) (2017)
- [Balanced Linear Contextual Bandits](https://mlsanity.com/paper/1812.06227/) (2018)
- [Bandits with Partially Observable Confounded Data](https://mlsanity.com/paper/2006.06731/) (2020)
- [Doubly robust Thompson sampling for linear payoffs](https://mlsanity.com/paper/2102.01229/) (2021)
- [Thresholded Lasso Bandit](https://mlsanity.com/paper/2010.11994/) (2020)
- [Thompson Sampling for High-Dimensional Sparse Linear Contextual Bandits](https://mlsanity.com/paper/2211.05964/) (2022)
- [Double Doubly Robust Thompson Sampling for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/2209.06983/) (2022)
- [Contextual Linear Bandits under Noisy Features: Towards Bayesian Oracles](https://mlsanity.com/paper/1703.01347/) (2017)
- [Squeeze All: Novel Estimator and Self-Normalized Bound for Linear Contextual Bandits](https://mlsanity.com/paper/2206.05404/) (2022)
- [Thompson Sampling in Partially Observable Contextual Bandits](https://mlsanity.com/paper/2402.10289/) (2024)
- [Partially Observable Contextual Bandits with Linear Payoffs](https://mlsanity.com/paper/2409.11521/) (2024)
- [Lasso Bandit with Compatibility Condition on Optimal Arm](https://mlsanity.com/paper/2406.00823/) (2024)
- [A Doubly Robust Approach to Sparse Reinforcement Learning](https://mlsanity.com/paper/2310.15286/) (2023)
- [Linear Bandits with Feature Feedback](https://mlsanity.com/paper/1903.03705/) (2019)
- [Symmetric Linear Bandits with Hidden Symmetry](https://mlsanity.com/paper/2405.13899/) (2024)

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

- [Pre-Trained AI Model Assisted Online Decision-Making under Missing Covariates: A Theoretical Perspective](https://mlsanity.com/paper/2507.07852/) (2025)
- [Deconfounded Warm-Start Thompson Sampling with Applications to Precision Medicine](https://mlsanity.com/paper/2505.17283/) (2025)
- [Learning with Incomplete Context: Linear Contextual Bandits with Pretrained Imputation](https://mlsanity.com/paper/2510.09908/) (2025)
- [Stochastic Linear Bandits with Partially Observed Actions](https://mlsanity.com/paper/2607.08971/) (2026)

## Abstract (arXiv)

We study the linear bandit problem that accounts for partially observable features. Without proper handling, unobserved features can lead to linear regret in the decision horizon T, as their influence on rewards is unknown. To tackle this challenge, we propose a novel theoretical framework and an algorithm with sublinear regret guarantees. The core of our algorithm consists of (i) feature augmentation, by appending basis vectors that are orthogonal to the row space of the observed features; and (ii) the introduction of a doubly robust estimator. Our approach achieves a regret bound of tildeO(√(d + dh)T), where d is the dimension of the observed features and dh depends on the extent to which the unobserved feature space is contained in the observed one, thereby capturing the intrinsic difficulty of the problem. Notably, our algorithm requires no prior knowledge of the unobserved feature space, which may expand as more features become hidden. Numerical experiments confirm that our algorithm outperforms both non-contextual multi-armed bandits and linear bandit algorithms depending solely on observed features.