# Risk-sensitive Bandits: Arm Mixture Optimality and Regret-efficient Algorithms

arXiv: https://arxiv.org/abs/2503.08896 · HTML: https://mlsanity.com/paper/2503.08896/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Top Two Algorithms Revisited](https://mlsanity.com/paper/2206.05979/) (2022)
- [Off-Policy Risk Assessment in Contextual Bandits](https://mlsanity.com/paper/2104.08977/) (2021)
- [Optimal Thompson Sampling strategies for support-aware CVaR bandits](https://mlsanity.com/paper/2012.05754/) (2020)
- [Risk-Averse Multi-Armed Bandit Problems under Mean-Variance Measure](https://mlsanity.com/paper/1604.05257/) (2016)
- [Distribution oblivious, risk-aware algorithms for multi-armed bandits with unbounded rewards](https://mlsanity.com/paper/1906.00569/) (2019)
- [A Wasserstein distance approach for concentration of empirical risk estimates](https://mlsanity.com/paper/1902.10709/) (2019)
- [An Alternative to Variance: Gini Deviation for Risk-averse Policy Gradient](https://mlsanity.com/paper/2307.08873/) (2023)
- [A Unifying Theory of Thompson Sampling for Continuous Risk-Averse Bandits](https://mlsanity.com/paper/2108.11345/) (2021)
- [Policy Gradient Methods for Distortion Risk Measures](https://mlsanity.com/paper/2107.04422/) (2021)
- [Choquet regularization for reinforcement learning](https://mlsanity.com/paper/2208.08497/) (2022)
- [A Distribution Optimization Framework for Confidence Bounds of Risk Measures](https://mlsanity.com/paper/2306.07059/) (2023)

## Built on by (most cited first, 3 of 3)

- [Concave Statistical Utility Maximization Bandits via Influence-Function Gradients](https://mlsanity.com/paper/2604.22140/) (2026)
- [Matching Markets meet Cumulative Prospect Theory: Towards Optimal and Adversarially Robust Learning](https://mlsanity.com/paper/2606.19883/) (2026)
- [Discrepancy-Rounded Fair Bandits with Static and Time-Varying Exposure Floors](https://mlsanity.com/paper/2607.22935/) (2026)

## Abstract (arXiv)

This paper introduces a general framework for risk-sensitive bandits that integrates the notions of risk-sensitive objectives by adopting a rich class of distortion riskmetrics. The introduced framework subsumes the various existing risk-sensitive models. An important and hitherto unknown observation is that for a wide range of riskmetrics, the optimal bandit policy involves selecting a mixture of arms. This is in sharp contrast to the convention in the multi-arm bandit algorithms that there is generally a solitary arm that maximizes the utility, whether purely reward-centric or risk-sensitive. This creates a major departure from the principles for designing bandit algorithms since there are uncountable mixture possibilities. The contributions of the paper are as follows: (i) it formalizes a general framework for risk-sensitive bandits, (ii) identifies standard risk-sensitive bandit models for which solitary arm selections is not optimal, (iii) and designs regret-efficient algorithms whose sampling strategies can accurately track optimal arm mixtures (when mixture is optimal) or the solitary arms (when solitary is optimal). The algorithms are shown to achieve a regret that scales according to O((log T/T )nu), where T is the horizon, and nu>0 is a riskmetric-specific constant.