# An Information-Theoretic Analysis of Thompson Sampling

arXiv: https://arxiv.org/abs/1403.5341 · HTML: https://mlsanity.com/paper/1403.5341/

## Key facts

- Cited by 178 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2014.

## Built on by (most cited first, 30 of 178)

- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Feel-Good Thompson Sampling for Contextual Bandits and Reinforcement Learning](https://mlsanity.com/paper/2110.00871/) (2021)
- [Reinforcement Learning, Bit by Bit](https://mlsanity.com/paper/2103.04047/) (2021)
- [Reason for Future, Act for Now: A Principled Framework for Autonomous LLM Agents with Provable Sample Efficiency](https://mlsanity.com/paper/2309.17382/) (2023)
- [Bayesian decision-making under misspecified priors with applications to meta-learning](https://mlsanity.com/paper/2107.01509/) (2021)
- [Neural Contextual Bandits without Regret](https://mlsanity.com/paper/2107.03144/) (2021)
- [Hierarchical Bayesian Bandits](https://mlsanity.com/paper/2111.06929/) (2021)
- [From Predictions to Decisions: The Importance of Joint Predictive Distributions](https://mlsanity.com/paper/2107.09224/) (2021)
- [Disentangling Epistemic and Aleatoric Uncertainty in Reinforcement Learning](https://mlsanity.com/paper/2206.01558/) (2022)
- [An Analysis of Ensemble Sampling](https://mlsanity.com/paper/2203.01303/) (2022)
- [Regret Bounds for Information-Directed Reinforcement Learning](https://mlsanity.com/paper/2206.04640/) (2022)
- [Deciding What to Learn: A Rate-Distortion Approach](https://mlsanity.com/paper/2101.06197/) (2021)
- [Online Multi-Armed Bandits with Adaptive Inference](https://mlsanity.com/paper/2102.13202/) (2021)
- [Efficient Exploration in Continuous-time Model-based Reinforcement Learning](https://mlsanity.com/paper/2310.19848/) (2023)
- [Non-Stationary Bandit Learning via Predictive Sampling](https://mlsanity.com/paper/2205.01970/) (2022)
- [An Information-Theoretic Perspective on Credit Assignment in Reinforcement Learning](https://mlsanity.com/paper/2103.06224/) (2021)
- [Understanding the Eluder Dimension](https://mlsanity.com/paper/2104.06970/) (2021)
- [Batched Thompson Sampling](https://mlsanity.com/paper/2110.00202/) (2021)
- [Deep Hierarchy in Bandits](https://mlsanity.com/paper/2202.01454/) (2022)
- [Lifting the Information Ratio: An Information-Theoretic Analysis of Thompson Sampling for Contextual Bandits](https://mlsanity.com/paper/2205.13924/) (2022)
- [Deciding What to Model: Value-Equivalent Sampling for Reinforcement Learning](https://mlsanity.com/paper/2206.02072/) (2022)
- [Bayesian Design Principles for Frequentist Sequential Learning](https://mlsanity.com/paper/2310.00806/) (2023)
- [Impatient Bandits: Optimizing Recommendations for the Long-Term Without Delay](https://mlsanity.com/paper/2307.09943/) (2023)
- [Sliding-Window Thompson Sampling for Non-Stationary Settings](https://mlsanity.com/paper/2409.05181/) (2024)
- [Toward Efficient Exploration by Large Language Model Agents](https://mlsanity.com/paper/2504.20997/) (2025)
- [Thompson Sampling with a Mixture Prior](https://mlsanity.com/paper/2106.05608/) (2021)
- [Metalearning Linear Bandits by Prior Update](https://mlsanity.com/paper/2107.05320/) (2021)
- [The Value of Information When Deciding What to Learn](https://mlsanity.com/paper/2110.13973/) (2021)
- [Weak Signal Asymptotics for Sequentially Randomized Experiments](https://mlsanity.com/paper/2101.09855/) (2021)
- [Mixed-Effect Thompson Sampling](https://mlsanity.com/paper/2205.15124/) (2022)

## 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.