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An Information-Theoretic Analysis of Thompson Sampling

arXiv 1403.5341 ↗First posted 21 Mar 2014cs.LGcited by 178

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Abstract (arXiv)

We provide an information-theoretic analysis of Thompson sampling that applies across a broad range of online optimization problems in which a decision-maker must learn from partial feedback. This analysis inherits the simplicity and elegance of information theory and leads to regret bounds that scale with the entropy of the optimal-action distribution. This strengthens preexisting results and yields new insight into how information improves performance.

Key facts. Cited by 178 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Mar 2014.

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Citing papers per year: 2020: 2; 2021: 34; 2022: 28; 2023: 29; 2024: 27; 2025: 28; 2026: 30.

178 papers.

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  1. 2020Is Pessimism Provably Efficient for Offline RL?cited by 362
  2. 2021Feel-Good Thompson Sampling for Contextual Bandits and Reinforcement Learningcited by 65
  3. 2021Reinforcement Learning, Bit by Bitcited by 59
  4. 2023Reason for Future, Act for Now: A Principled Framework for Autonomous LLM Agents with Provable Sample Efficiencycited by 46
  5. 2021Bayesian decision-making under misspecified priors with applications to meta-learningcited by 43
  6. 2021Neural Contextual Bandits without Regretcited by 40
  7. 2021Hierarchical Bayesian Banditscited by 33
  8. 2021From Predictions to Decisions: The Importance of Joint Predictive Distributionscited by 28
  9. 2022Disentangling Epistemic and Aleatoric Uncertainty in Reinforcement Learningcited by 27
  10. 2022Regret Bounds for Information-Directed Reinforcement Learningcited by 24
  11. 2021Deciding What to Learn: A Rate-Distortion Approachcited by 23
  12. 2022An Analysis of Ensemble Samplingcited by 23
38 more
  1. 2021Online Multi-Armed Bandits with Adaptive Inferencecited by 21
  2. 2022Non-Stationary Bandit Learning via Predictive Samplingcited by 21
  3. 2023Efficient Exploration in Continuous-time Model-based Reinforcement Learningcited by 21
  4. 2021An Information-Theoretic Perspective on Credit Assignment in Reinforcement Learningcited by 20
  5. 2021Understanding the Eluder Dimensioncited by 19
  6. 2021Batched Thompson Samplingcited by 19
  7. 2022Lifting the Information Ratio: An Information-Theoretic Analysis of Thompson Sampling for Contextual Banditscited by 19
  8. 2022Deciding What to Model: Value-Equivalent Sampling for Reinforcement Learningcited by 19
  9. 2022Deep Hierarchy in Banditscited by 18
  10. 2023Impatient Bandits: Optimizing Recommendations for the Long-Term Without Delaycited by 17
  11. 2023Bayesian Design Principles for Frequentist Sequential Learningcited by 17
  12. 2021Thompson Sampling with a Mixture Priorcited by 15
  13. 2021Metalearning Linear Bandits by Prior Updatecited by 15
  14. 2021The Value of Information When Deciding What to Learncited by 15
  15. 2024Sliding-Window Thompson Sampling for Non-Stationary Settingscited by 15
  16. 2025Toward Efficient Exploration by Large Language Model Agentscited by 15
  17. 2022Mixed-Effect Thompson Samplingcited by 14
  18. 2024Bayesian Design Principles for Offline-to-Online Reinforcement Learningcited by 14
  19. 2021Weak Signal Asymptotics for Sequentially Randomized Experimentscited by 13
  20. 2023Leveraging Demonstrations to Improve Online Learning: Quality Matterscited by 13
  21. 2021An empirical evaluation of active inference in multi-armed banditscited by 12
  22. 2021Diffusion Approximations for Thompson Sampling in the Small Gap Regimecited by 12
  23. 2022Optimistic Posterior Sampling for Reinforcement Learning with Few Samples and Tight Guaranteescited by 12
  24. 2022Bayesian Fixed-Budget Best-Arm Identificationcited by 12
  25. 2023An Information-Theoretic Analysis of Nonstationary Bandit Learningcited by 11
  26. 2023Probabilistic Inference in Reinforcement Learning Done Rightcited by 11
  27. 2021A Payload Optimization Method for Federated Recommender Systemscited by 10
  28. 2023Fast and Regret Optimal Best Arm Identification: Fundamental Limits and Low-Complexity Algorithmscited by 10
  29. 2024Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlocited by 10
  30. 2021Applications of the Free Energy Principle to Machine Learning and Neurosciencecited by 9
  31. 2022Incentivizing Combinatorial Bandit Explorationcited by 9
  32. 2022Batch Bayesian optimisation via density-ratio estimation with guaranteescited by 9
  33. 2023A Definition of Non-Stationary Banditscited by 9
  34. 2024On the Importance of Uncertainty in Decision-Making with Large Language Modelscited by 9
  35. 2021Linear Bandit Algorithms with Sublinear Time Complexitycited by 8
  36. 2024Beyond Worst-case Attacks: Robust RL with Adaptive Defense via Non-dominated Policiescited by 8
  37. 2024Automated Discovery of Pairwise Interactions from Unstructured Datacited by 8
  38. 2025When and why randomised exploration works (in linear bandits)cited by 8

50 most cited of 178 All 178 (JSON)