# Risk-Averse Multi-Armed Bandit Problems under Mean-Variance Measure

arXiv: https://arxiv.org/abs/1604.05257 · HTML: https://mlsanity.com/paper/1604.05257/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2016.

## Built on by (most cited first, 20 of 20)

- [The Fragility of Optimized Bandit Algorithms](https://mlsanity.com/paper/2109.13595/) (2021)
- [Almost Optimal Variance-Constrained Best Arm Identification](https://mlsanity.com/paper/2201.10142/) (2022)
- [Constrained Pure Exploration Multi-Armed Bandits with a Fixed Budget](https://mlsanity.com/paper/2211.14768/) (2022)
- [Federated Multi-Armed Bandits Under Byzantine Attacks](https://mlsanity.com/paper/2205.04134/) (2022)
- [ESCADA: Efficient Safety and Context Aware Dose Allocation for Precision Medicine](https://mlsanity.com/paper/2111.13415/) (2021)
- [The Survival Bandit Problem](https://mlsanity.com/paper/2206.03019/) (2022)
- [Risk-sensitive Bandits: Arm Mixture Optimality and Regret-efficient Algorithms](https://mlsanity.com/paper/2503.08896/) (2025)
- [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)
- [Risk-Averse Multi-Armed Bandits with Unobserved Confounders: A Case Study in Emotion Regulation in Mobile Health](https://mlsanity.com/paper/2209.04356/) (2022)
- [Conditionally Risk-Averse Contextual Bandits](https://mlsanity.com/paper/2210.13573/) (2022)
- [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)
- [Balancing Risk and Reward: An Automated Phased Release Strategy](https://mlsanity.com/paper/2305.09626/) (2023)
- [A Risk-Averse Framework for Non-Stationary Stochastic Multi-Armed Bandits](https://mlsanity.com/paper/2310.19821/) (2023)
- [Conformal bandits: bringing statistical validity and reward efficiency under weak arm separability](https://mlsanity.com/paper/2512.09850/) (2025)
- [Risk-Averse Wasserstein Distributionally Robust Online Learning](https://mlsanity.com/paper/2602.20403/) (2026)
- [Softmax gradient policy for variance minimization and risk-averse multi armed bandits](https://mlsanity.com/paper/2604.00241/) (2026)
- [Dominant Arm Identification with Mixing and Recycling Observed Samples](https://mlsanity.com/paper/2608.01545/) (2026)

## Abstract (arXiv)

The multi-armed bandit problems have been studied mainly under the measure of expected total reward accrued over a horizon of length T. In this paper, we address the issue of risk in multi-armed bandit problems and develop parallel results under the measure of mean-variance, a commonly adopted risk measure in economics and mathematical finance. We show that the model-specific regret and the model-independent regret in terms of the mean-variance of the reward process are lower bounded by Omega(log T) and Omega(T2/3), respectively. We then show that variations of the UCB policy and the DSEE policy developed for the classic risk-neutral MAB achieve these lower bounds.