mlsanityData to 7 Oct 2026

A Simple Unified Framework for High Dimensional Bandit Problems

arXiv 2102.09626 ↗First posted 18 Feb 2021cs.LG stat.MLcited by 21

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Abstract (arXiv)

Stochastic high dimensional bandit problems with low dimensional structures are useful in different applications such as online advertising and drug discovery. In this work, we propose a simple unified algorithm for such problems and present a general analysis framework for the regret upper bound of our algorithm. We show that under some mild unified assumptions, our algorithm can be applied to different high dimensional bandit problems. Our framework utilizes the low dimensional structure to guide the parameter estimation in the problem, therefore our algorithm achieves the comparable regret bounds in the LASSO bandit, as well as novel bounds in the low-rank matrix bandit, the group sparse matrix bandit, and in a new problem: the multi-agent LASSO bandit.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). Builds on 10 of its 39 references that are in the map. First posted on arXiv 18 Feb 2021.

Builds on

10 of 39 references.

References · 10

  1. 2020High-Dimensional Sparse Linear Banditscited by 61
  2. 2019Bilinear Bandits with Low-rank Structurecited by 54
  3. 2019Doubly-Robust Lasso Banditcited by 49
  4. 2020Low-Rank Generalized Linear Bandit Problemscited by 48
  5. 2020Sparsity-Agnostic Lasso Banditcited by 44
  6. 2017Stochastic Low-Rank Banditscited by 28
  7. 2016Stochastic Rank-1 Banditscited by 23
  8. 2019Solving Bernoulli Rank-One Bandits with Unimodal Thompson Samplingcited by 23
  9. 2017Bernoulli Rank-1 Bandits for Click Feedbackcited by 11
  10. 2016Structured Stochastic Linear Banditscited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 3; 2023: 6; 2024: 5; 2025: 5; 2026: 1.

21 papers.

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  1. 2023Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversioncited by 24
  2. 2024Efficient Frameworks for Generalized Low-Rank Matrix Bandit Problemscited by 19
  3. 2022Thompson Sampling for High-Dimensional Sparse Linear Contextual Banditscited by 16
  4. 2024Efficient Low-Rank Matrix Estimation, Experimental Design, and Arm-Set-Dependent Low-Rank Banditscited by 9
  5. 2021Model Selection for Generic Contextual Banditscited by 7
  6. 2023Anytime Model Selection in Linear Banditscited by 6
  7. 2025Single Index Bandits: Generalized Linear Contextual Bandits with Unknown Reward Functionscited by 6
  8. 2023High-dimensional Contextual Bandit Problem without Sparsitycited by 5
  9. 2026Provably Efficient Regularized Online RLHF with Generalized Bilinear Preferencescited by 5
  10. 2022Federated Online Sparse Decision Makingcited by 3
  11. 2023High-dimensional Linear Bandits with Knapsackscited by 3
  12. 2024Sparsity-Agnostic Linear Bandits with Adaptive Adversariescited by 2
9 more
  1. 2022Advertising Media and Target Audience Optimization via High-dimensional Banditscited by 1
  2. 2023Fixed-Budget Best-Arm Identification in Sparse Linear Banditscited by 1
  3. 2023Efficient Generalized Low-Rank Tensor Contextual Banditscited by 1
  4. 2025A Unified Regularization Approach to High-Dimensional Generalized Tensor Banditscited by 1
  5. 2025High-dimensional Nonparametric Contextual Bandit Problemcited by 1
  6. 2025On the necessity of adaptive regularisation:Optimal anytime online learning on boldsymbolℓp-ballscited by 1
  7. 2024Differentially Private High Dimensional Banditscited by 0
  8. 2024Sparse Linear Bandits with Blocking Constraintscited by 0
  9. 2025Navigating Sparsities in High-Dimensional Linear Contextual Banditscited by 0