mlsanityData to 14 Oct 2026

Conservative Contextual Linear Bandits

arXiv 1611.06426 ↗First posted 19 Nov 2016stat.ML cs.LGcited by 57

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Abstract (arXiv)

Safety is a desirable property that can immensely increase the applicability of learning algorithms in real-world decision-making problems. It is much easier for a company to deploy an algorithm that is safe, i.e., guaranteed to perform at least as well as a baseline. In this paper, we study the issue of safety in contextual linear bandits that have application in many different fields including personalized ad recommendation in online marketing. We formulate a notion of safety for this class of algorithms. We develop a safe contextual linear bandit algorithm, called conservative linear UCB (CLUCB), that simultaneously minimizes its regret and satisfies the safety constraint, i.e., maintains its performance above a fixed percentage of the performance of a baseline strategy, uniformly over time. We prove an upper-bound on the regret of CLUCB and show that it can be decomposed into two terms: 1) an upper-bound for the regret of the standard linear UCB algorithm that grows with the time horizon and 2) a constant (does not grow with the time horizon) term that accounts for the loss of being conservative in order to satisfy the safety constraint. We empirically show that our algorithm is safe and validate our theoretical analysis.

Key facts. Cited by 57 papers in the map (data through 14 Oct 2026). First posted on arXiv 19 Nov 2016.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 10; 2022: 11; 2023: 12; 2024: 4; 2025: 5; 2026: 15.

57 papers.

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  1. 2021Learning Policies with Zero or Bounded Constraint Violation for Constrained MDPscited by 80
  2. 2022Regret Minimization with Performative Feedbackcited by 40
  3. 2021An Efficient Pessimistic-Optimistic Algorithm for Stochastic Linear Bandits with General Constraintscited by 29
  4. 2022Learning Infinite-Horizon Average-Reward Markov Decision Processes with Constraintscited by 29
  5. 2021Best Arm Identification with Safety Constraintscited by 25
  6. 2022On Kernelized Multi-Armed Bandits with Constraintscited by 23
  7. 2024Truly No-Regret Learning in Constrained MDPscited by 23
  8. 2022Policy Optimization with Linear Temporal Logic Constraintscited by 19
  9. 2022Active Learning with Safety Constraintscited by 16
  10. 2022Safe Exploration for Efficient Policy Evaluation and Comparisoncited by 15
  11. 2021Bandit Algorithms for Precision Medicinecited by 12
  12. 2022Interactively Learning Preference Constraints in Linear Banditscited by 11
38 more
  1. 2021A Reduction-Based Framework for Conservative Bandits and Reinforcement Learningcited by 9
  2. 2023Directional Optimism for Safe Linear Banditscited by 8
  3. 2022Leveraging Initial Hints for Free in Stochastic Linear Banditscited by 7
  4. 2022Stochastic Conservative Contextual Linear Banditscited by 6
  5. 2021ESCADA: Efficient Safety and Context Aware Dose Allocation for Precision Medicinecited by 5
  6. 2023Learning for Edge-Weighted Online Bipartite Matching with Robustness Guaranteescited by 5
  7. 2023Near-optimal Conservative Exploration in Reinforcement Learning under Episode-wise Constraintscited by 5
  8. 2023Convex Methods for Constrained Linear Banditscited by 5
  9. 2021Safe Data Collection for Offline and Online Policy Learningcited by 4
  10. 2021Adaptive Multi-Goal Explorationcited by 4
  11. 2023Price of Safety in Linear Best Arm Identificationcited by 4
  12. 2021Conservative Contextual Combinatorial Cascading Banditcited by 3
  13. 2023The Impact of the Geometric Properties of the Constraint Set in Safe Optimization with Bandit Feedbackcited by 3
  14. 2024SaVeR: Optimal Data Collection Strategy for Safe Policy Evaluation in Tabular MDPcited by 3
  15. 2025KL-regularization Itself is Differentially Private in Bandits and RLHFcited by 3
  16. 2021Continuous Mean-Covariance Banditscited by 2
  17. 2022Safety Aware Changepoint Detection for Piecewise i.i.d. Banditscited by 2
  18. 2022Distributed Stochastic Bandit Learning with Delayed Context Observationcited by 2
  19. 2023Fair Active Learning in Low-Data Regimescited by 2
  20. 2024Distributed Multi-Task Learning for Stochastic Bandits with Context Distribution and Stage-wise Constraintscited by 2
  21. 2023Probably Anytime-Safe Stochastic Combinatorial Semi-Banditscited by 1
  22. 2023Risk-Aware Continuous Control with Neural Contextual Banditscited by 1
  23. 2025Multi-Agent Stage-wise Conservative Linear Banditscited by 1
  24. 2026Sample Complexity Bounds for Stochastic Shortest Path with a Generative Modelcited by 1
  25. 2026Online Learning with LLM Experts from Limited Feedbackcited by 1
  26. 2023Leveraging User-Triggered Supervision in Contextual Banditscited by 0
  27. 2023Exploration of Unranked Items in Safe Online Learning to Re-Rankcited by 0
  28. 2023Conservative Exploration for Policy Optimization via Off-Policy Policy Evaluationcited by 0
  29. 2024Learning to Explore with Lagrangians for Bandits under Unknown Linear Constraintscited by 0
  30. 2025The Good, the Bad, and the Sampled: a No-Regret Approach to Safe Online Classificationcited by 0
  31. 2025Learning When Not to Learn: Risk-Sensitive Abstention in Bandits with Unbounded Rewardscited by 0
  32. 2025BALLAST: Bandit-Assisted Learning for Latency-Aware Stable Timeouts in Raftcited by 0
  33. 2026Bandit Algorithms for Deep Brain Stimulationcited by 0
  34. 2026BONSAI: Bayesian Optimization with Natural Simplicity and Interpretabilitycited by 0
  35. 2026Quality-preserving Model for Electronics Production Quality Tests Reductioncited by 0
  36. 2026Replicable Bandits with UCB based Explorationcited by 0
  37. 2026NH-CROP: Robust Pricing for Governed Language Data Assets under Cost Uncertaintycited by 0
  38. 2026When (and How) to Trust the Expert: Diagnosing Query-Time Expert-Guided Reinforcement Learningcited by 0

50 most cited of 57 All 57 (JSON)