# Thompson Sampling Algorithms for Mean-Variance Bandits

arXiv: https://arxiv.org/abs/2002.00232 · HTML: https://mlsanity.com/paper/2002.00232/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2020.

## Built on by (most cited first, 27 of 27)

- [Almost Optimal Variance-Constrained Best Arm Identification](https://mlsanity.com/paper/2201.10142/) (2022)
- [A Multi-Armed Bandit Approach to Online Selection and Evaluation of Generative Models](https://mlsanity.com/paper/2406.07451/) (2024)
- [Pretraining Decision Transformers with Reward Prediction for In-Context Multi-task Structured Bandit Learning](https://mlsanity.com/paper/2406.05064/) (2024)
- [A Unifying Theory of Thompson Sampling for Continuous Risk-Averse Bandits](https://mlsanity.com/paper/2108.11345/) (2021)
- [Regret Distribution in Stochastic Bandits: Optimal Trade-off between Expectation and Tail Risk](https://mlsanity.com/paper/2304.04341/) (2023)
- [A Survey of Risk-Aware Multi-Armed Bandits](https://mlsanity.com/paper/2205.05843/) (2022)
- [Kolmogorov-Smirnov Test-Based Actively-Adaptive Thompson Sampling for Non-Stationary Bandits](https://mlsanity.com/paper/2105.14586/) (2021)
- [The Survival Bandit Problem](https://mlsanity.com/paper/2206.03019/) (2022)
- [Only Pay for What Is Uncertain: Variance-Adaptive Thompson Sampling](https://mlsanity.com/paper/2303.09033/) (2023)
- [Continuous Mean-Covariance Bandits](https://mlsanity.com/paper/2102.12090/) (2021)
- [Thompson Sampling for Gaussian Entropic Risk Bandits](https://mlsanity.com/paper/2105.06960/) (2021)
- [Conditionally Risk-Averse Contextual Bandits](https://mlsanity.com/paper/2210.13573/) (2022)
- [Optimizing Sharpe Ratio: Risk-Adjusted Decision-Making in Multi-Armed Bandits](https://mlsanity.com/paper/2406.06552/) (2024)
- [DAK-UCB: Diversity-Aware Prompt Routing for LLMs and Generative Models](https://mlsanity.com/paper/2603.23140/) (2026)
- [Risk-averse Contextual Multi-armed Bandit Problem with Linear Payoffs](https://mlsanity.com/paper/2206.12463/) (2022)
- [Risk-Aware Linear Bandits: Theory and Applications in Smart Order Routing](https://mlsanity.com/paper/2208.02389/) (2022)
- [Probably Anytime-Safe Stochastic Combinatorial Semi-Bandits](https://mlsanity.com/paper/2301.13393/) (2023)
- [Variance-Optimal Arm Selection: Misallocation Minimization and Best Arm Identification](https://mlsanity.com/paper/2505.11985/) (2025)
- [Order Optimal Regret Bounds for Sharpe Ratio Optimization under Thompson Sampling](https://mlsanity.com/paper/2508.13749/) (2025)
- [Mini-Batch Robustness Verification of Deep Neural Networks](https://mlsanity.com/paper/2508.15454/) (2025)
- [Thompson Sampling for Unimodal Bandits](https://mlsanity.com/paper/2106.08187/) (2021)
- [Thompson Sampling for Linear Bandit Problems with Normal-Gamma Priors](https://mlsanity.com/paper/2303.03348/) (2023)
- [Balancing Risk and Reward: An Automated Phased Release Strategy](https://mlsanity.com/paper/2305.09626/) (2023)
- [Adaptive Data Augmentation for Thompson Sampling](https://mlsanity.com/paper/2506.14479/) (2025)
- [Fast Online Learning with Gaussian Prior-Driven Hierarchical Unimodal Thompson Sampling](https://mlsanity.com/paper/2602.15972/) (2026)
- [Asymptotic Optimality of Thompson Sampling for Risk-Averse Bandits with Sub-Gaussian Rewards](https://mlsanity.com/paper/2606.09191/) (2026)
- [Dominant Arm Identification with Mixing and Recycling Observed Samples](https://mlsanity.com/paper/2608.01545/) (2026)

## Abstract (arXiv)

The multi-armed bandit (MAB) problem is a classical learning task that exemplifies the exploration-exploitation tradeoff. However, standard formulations do not take into account em risk. In online decision making systems, risk is a primary concern. In this regard, the mean-variance risk measure is one of the most common objective functions. Existing algorithms for mean-variance optimization in the context of MAB problems have unrealistic assumptions on the reward distributions. We develop Thompson Sampling-style algorithms for mean-variance MAB and provide comprehensive regret analyses for Gaussian and Bernoulli bandits with fewer assumptions. Our algorithms achieve the best known regret bounds for mean-variance MABs and also attain the information-theoretic bounds in some parameter regimes. Empirical simulations show that our algorithms significantly outperform existing LCB-based algorithms for all risk tolerances.