# Dynamic Batch Learning in High-Dimensional Sparse Linear Contextual Bandits

arXiv: https://arxiv.org/abs/2008.11918 · HTML: https://mlsanity.com/paper/2008.11918/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2020.

## Built on by (most cited first, 28 of 28)

- [Doubly Robust Distributionally Robust Off-Policy Evaluation and Learning](https://mlsanity.com/paper/2202.09667/) (2022)
- [Generalized Linear Bandits with Limited Adaptivity](https://mlsanity.com/paper/2404.06831/) (2024)
- [Information Directed Sampling for Sparse Linear Bandits](https://mlsanity.com/paper/2105.14267/) (2021)
- [Batched Thompson Sampling](https://mlsanity.com/paper/2110.00202/) (2021)
- [Contextual Information-Directed Sampling](https://mlsanity.com/paper/2205.10895/) (2022)
- [Thompson Sampling for High-Dimensional Sparse Linear Contextual Bandits](https://mlsanity.com/paper/2211.05964/) (2022)
- [Variance-Aware Sparse Linear Bandits](https://mlsanity.com/paper/2205.13450/) (2022)
- [An Experimental Design for Anytime-Valid Causal Inference on Multi-Armed Bandits](https://mlsanity.com/paper/2311.05794/) (2023)
- [Infrequent Resolving Algorithm for Online Linear Programming](https://mlsanity.com/paper/2408.00465/) (2024)
- [Online Learning of Energy Consumption for Navigation of Electric Vehicles](https://mlsanity.com/paper/2111.02314/) (2021)
- [Optimal Multitask Linear Regression and Contextual Bandits under Sparse Heterogeneity](https://mlsanity.com/paper/2306.06291/) (2023)
- [Reward Imputation with Sketching for Contextual Batched Bandits](https://mlsanity.com/paper/2210.06719/) (2022)
- [High-dimensional Linear Bandits with Knapsacks](https://mlsanity.com/paper/2311.01327/) (2023)
- [Provably Efficient High-Dimensional Bandit Learning with Batched Feedbacks](https://mlsanity.com/paper/2311.13180/) (2023)
- [Batched Nonparametric Contextual Bandits](https://mlsanity.com/paper/2402.17732/) (2024)
- [Worst-case Performance of Greedy Policies in Bandits with Imperfect Context Observations](https://mlsanity.com/paper/2204.04773/) (2022)
- [Stochastic Contextual Bandits with Long Horizon Rewards](https://mlsanity.com/paper/2302.00814/) (2023)
- [IBCB: Efficient Inverse Batched Contextual Bandit for Behavioral Evolution History](https://mlsanity.com/paper/2403.16075/) (2024)
- [FLIPHAT: Joint Differential Privacy for High Dimensional Sparse Linear Bandits](https://mlsanity.com/paper/2405.14038/) (2024)
- [A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits](https://mlsanity.com/paper/2501.10722/) (2025)
- [Few Batches or Little Memory, But Not Both: Simultaneous Space and Adaptivity Constraints in Stochastic Bandits](https://mlsanity.com/paper/2603.13742/) (2026)
- [Learning in Distributed Contextual Linear Bandits Without Sharing the Context](https://mlsanity.com/paper/2206.04180/) (2022)
- [Batched Online Contextual Sparse Bandits with Sequential Inclusion of Features](https://mlsanity.com/paper/2409.09199/) (2024)
- [Anomaly Detection in Networked Bandits](https://mlsanity.com/paper/2508.20076/) (2025)
- [Stochastic Matching Bandits with Rare Optimization Updates](https://mlsanity.com/paper/2509.04194/) (2025)
- [Navigating Sparsities in High-Dimensional Linear Contextual Bandits](https://mlsanity.com/paper/2510.08435/) (2025)
- [The Adaptivity Barrier in Batched Nonparametric Bandits: Sharp Characterization of the Price of Unknown Margin](https://mlsanity.com/paper/2511.03708/) (2025)
- [Learning to target with network interference](https://mlsanity.com/paper/2605.27794/) (2026)

## Abstract (arXiv)

We study the problem of dynamic batch learning in high-dimensional sparse linear contextual bandits, where a decision maker, under a given maximum-number-of-batch constraint and only able to observe rewards at the end of each batch, can dynamically decide how many individuals to include in the next batch (at the end of the current batch) and what personalized action-selection scheme to adopt within each batch. Such batch constraints are ubiquitous in a variety of practical contexts, including personalized product offerings in marketing and medical treatment selection in clinical trials. We characterize the fundamental learning limit in this problem via a regret lower bound and provide a matching upper bound (up to log factors), thus prescribing an optimal scheme for this problem. To the best of our knowledge, our work provides the first inroad into a theoretical understanding of dynamic batch learning in high-dimensional sparse linear contextual bandits. Notably, even a special case of our result -- when no batch constraint is present -- yields that the simple exploration-free algorithm using the LASSO estimator already achieves the minimax optimal regret bound for standard online learning in high-dimensional linear contextual bandits (for the no-margin case), a result that appears unknown in the emerging literature of high-dimensional contextual bandits.