# High dimensional stochastic linear contextual bandit with missing covariates

arXiv: https://arxiv.org/abs/2207.11165 · HTML: https://mlsanity.com/paper/2207.11165/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 22 Jul 2022.

## Builds on (most cited first, 4 of 4)

- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [Doubly-Robust Lasso Bandit](https://mlsanity.com/paper/1907.11362/) (2019)
- [Sparsity-Agnostic Lasso Bandit](https://mlsanity.com/paper/2007.08477/) (2020)
- [Errors-in-variables models with dependent measurements](https://mlsanity.com/paper/1611.04701/) (2016)

## Built on by (most cited first, 2 of 2)

- [Pre-Trained AI Model Assisted Online Decision-Making under Missing Covariates: A Theoretical Perspective](https://mlsanity.com/paper/2507.07852/) (2025)
- [Learning with Incomplete Context: Linear Contextual Bandits with Pretrained Imputation](https://mlsanity.com/paper/2510.09908/) (2025)

## Abstract (arXiv)

Recent works in bandit problems adopted lasso convergence theory in the sequential decision-making setting. Even with fully observed contexts, there are technical challenges that hinder the application of existing lasso convergence theory: 1) proving the restricted eigenvalue condition under conditionally sub-Gaussian noise and 2) accounting for the dependence between the context variables and the chosen actions. This paper studies the effect of missing covariates on regret for stochastic linear bandit algorithms. Our work provides a high-probability upper bound on the regret incurred by the proposed algorithm in terms of covariate sampling probabilities, showing that the regret degrades due to missingness by at most zetamin2, where zetamin is the minimum probability of observing covariates in the context vector. We illustrate our algorithm for the practical application of experimental design for collecting gene expression data by a sequential selection of class discriminating DNA probes.