mlsanityData to 14 Oct 2026

Directional Optimism for Safe Linear Bandits

arXiv 2308.15006 ↗First posted 29 Aug 2023cs.LGcited by 8

Not on the map. Why?

Abstract (arXiv)

The safe linear bandit problem is a version of the classical stochastic linear bandit problem where the learner's actions must satisfy an uncertain constraint at all rounds. Due its applicability to many real-world settings, this problem has received considerable attention in recent years. By leveraging a novel approach that we call directional optimism, we find that it is possible to achieve improved regret guarantees for both well-separated problem instances and action sets that are finite star convex sets. Furthermore, we propose a novel algorithm for this setting that improves on existing algorithms in terms of empirical performance, while enjoying matching regret guarantees. Lastly, we introduce a generalization of the safe linear bandit setting where the constraints are convex and adapt our algorithms and analyses to this setting by leveraging a novel convex-analysis based approach.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 31 of its 53 references that are in the map. First posted on arXiv 29 Aug 2023.

Builds on

31 of 53 references.

References · 31

  1. 2017Constrained Policy Optimizationcited by 983
  2. 2013Bandits with Knapsackscited by 164
  3. 2019Learning with Good Feature Representations in Bandits and in RL with a Generative Modelcited by 127
  4. 2020Safe Reinforcement Learning in Constrained Markov Decision Processescited by 115
  5. 2019Linear Stochastic Bandits Under Safety Constraintscited by 90
  6. 2015Linear Contextual Bandits with Knapsackscited by 82
  7. 2021Learning Policies with Zero or Bounded Constraint Violation for Constrained MDPscited by 80
  8. 2018Stagewise Safe Bayesian Optimization with Gaussian Processescited by 79
  9. 2020Stochastic Bandits with Linear Constraintscited by 68
  10. 2016Conservative Banditscited by 59
  11. 2016Conservative Contextual Linear Banditscited by 57
  12. 2014Resourceful Contextual Banditscited by 45
19 more
  1. 2015An efficient algorithm for contextual bandits with knapsacks, and an extension to concave objectivescited by 43
  2. 2019Safe Linear Thompson Sampling with Side Informationcited by 37
  3. 2021Safe Reinforcement Learning with Linear Function Approximationcited by 35
  4. 2021DOPE: Doubly Optimistic and Pessimistic Exploration for Safe Reinforcement Learningcited by 35
  5. 2015Algorithms with Logarithmic or Sublinear Regret for Constrained Contextual Banditscited by 29
  6. 2021An Efficient Pessimistic-Optimistic Algorithm for Stochastic Linear Bandits with General Constraintscited by 29
  7. 2020Stage-wise Conservative Linear Banditscited by 28
  8. 2019Safe Linear Stochastic Banditscited by 27
  9. 2021Best Arm Identification with Safety Constraintscited by 25
  10. 2023Learning Safety Constraints from Demonstrations with Unknown Rewardscited by 19
  11. 2019Safe Convex Learning under Uncertain Constraintscited by 17
  12. 2022Active Learning with Safety Constraintscited by 16
  13. 2022Safe Exploration for Efficient Policy Evaluation and Comparisoncited by 15
  14. 2022Strategies for Safe Multi-Armed Bandits with Logarithmic Regret and Riskcited by 15
  15. 2020Budget-Constrained Bandits over General Cost and Reward Distributionscited by 14
  16. 2022Interactively Learning Preference Constraints in Linear Banditscited by 11
  17. 2022Group Meritocratic Fairness in Linear Contextual Banditscited by 9
  18. 2020Safe Learning under Uncertain Objectives and Constraintscited by 7
  19. 2020Decentralized Multi-Agent Linear Bandits with Safety Constraintscited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 4; 2026: 1.

8 papers.

  1. 2025Provably Efficient RL for Linear MDPs under Instantaneous Safety Constraints in Non-Convex Feature Spacescited by 7
  2. 2025Provably Efficient RL under Episode-Wise Safety in Constrained MDPs with Linear Function Approximationcited by 6
  3. 2024SaVeR: Optimal Data Collection Strategy for Safe Policy Evaluation in Tabular MDPcited by 3
  4. 2024Optimistic Safety for Online Convex Optimization with Unknown Linear Constraintscited by 1
  5. 2025Constrained Online Decision-Making: A Unified Frameworkcited by 1
  6. 2024Learning to Explore with Lagrangians for Bandits under Unknown Linear Constraintscited by 0
  7. 2025Constrained Linear Thompson Samplingcited by 0
  8. 2026Safety by Design: Realized-Cost Constraints for Contextual Bandits with Continuous Actionscited by 0