mlsanityData to 7 Oct 2026

Safe Linear Stochastic Bandits

arXiv 1911.09501 ↗First posted 21 Nov 2019stat.ML cs.LGcited by 27

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Abstract (arXiv)

We introduce the safe linear stochastic bandit framework---a generalization of linear stochastic bandits---where, in each stage, the learner is required to select an arm with an expected reward that is no less than a predetermined (safe) threshold with high probability. We assume that the learner initially has knowledge of an arm that is known to be safe, but not necessarily optimal. Leveraging on this assumption, we introduce a learning algorithm that systematically combines known safe arms with exploratory arms to safely expand the set of safe arms over time, while facilitating safe greedy exploitation in subsequent stages. In addition to ensuring the satisfaction of the safety constraint at every stage of play, the proposed algorithm is shown to exhibit an expected regret that is no more than O(√Tlog (T)) after T stages of play.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Nov 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 3; 2023: 9; 2024: 1; 2025: 4; 2026: 4.

27 papers.

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  1. 2021DOPE: Doubly Optimistic and Pessimistic Exploration for Safe Reinforcement Learningcited by 34
  2. 2021An Efficient Pessimistic-Optimistic Algorithm for Stochastic Linear Bandits with General Constraintscited by 29
  3. 2021Safe Online Convex Optimization with Unknown Linear Safety Constraintscited by 13
  4. 2021Learning to Persuade on the Fly: Robustness Against Ignorancecited by 12
  5. 2022Interactively Learning Preference Constraints in Linear Banditscited by 11
  6. 2023Directional Optimism for Safe Linear Banditscited by 8
  7. 2023Safe Posterior Sampling for Constrained MDPs with Bounded Constraint Violationcited by 6
  8. 2025Provably Efficient RL for Linear MDPs under Instantaneous Safety Constraints in Non-Convex Feature Spacescited by 6
  9. 2021ESCADA: Efficient Safety and Context Aware Dose Allocation for Precision Medicinecited by 5
  10. 2023Convex Methods for Constrained Linear Banditscited by 5
  11. 2023Dynamic Regret Analysis of Safe Distributed Online Optimization for Convex and Non-convex Problemscited by 4
  12. 2023Near-optimal Conservative Exploration in Reinforcement Learning under Episode-wise Constraintscited by 4
15 more
  1. 2023Price of Safety in Linear Best Arm Identificationcited by 4
  2. 2022Safety Aware Changepoint Detection for Piecewise i.i.d. Banditscited by 2
  3. 2024Distributed Multi-Task Learning for Stochastic Bandits with Context Distribution and Stage-wise Constraintscited by 2
  4. 2021Safe Linear Leveling Banditscited by 1
  5. 2022Benefits of Monotonicity in Safe Exploration with Gaussian Processescited by 1
  6. 2023Probably Anytime-Safe Stochastic Combinatorial Semi-Banditscited by 1
  7. 2025Multi-Agent Stage-wise Conservative Linear Banditscited by 1
  8. 2026BanditLP: Large-Scale Stochastic Optimization for Personalized Recommendationscited by 1
  9. 2023Exploration of Unranked Items in Safe Online Learning to Re-Rankcited by 0
  10. 2023Robust Best-arm Identification in Linear Banditscited by 0
  11. 2025The Safety-Privacy Tradeoff in Linear Banditscited by 0
  12. 2025Secure Best Arm Identification in the Presence of a Copycatcited by 0
  13. 2026A Simple Reduction Scheme for Constrained Contextual Bandits with Adversarial Contexts via Regressioncited by 0
  14. 2026Multi-Task Representation Learning for Conservative Linear Banditscited by 0
  15. 2026Minimax Optimal Regret for Causal Logistic Bandits with Counterfactual Fairnesscited by 0