# Risk-Averse Best Arm Set Identification with Fixed Budget and Fixed Confidence

arXiv: https://arxiv.org/abs/2506.22253 · HTML: https://mlsanity.com/paper/2506.22253/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 27 Jun 2025.

## Builds on (most cited first, 8 of 8)

- [Being Optimistic to Be Conservative: Quickly Learning a CVaR Policy](https://mlsanity.com/paper/1911.01546/) (2019)
- [Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms](https://mlsanity.com/paper/1904.12672/) (2019)
- [Almost Optimal Variance-Constrained Best Arm Identification](https://mlsanity.com/paper/2201.10142/) (2022)
- [Strategies for Safe Multi-Armed Bandits with Logarithmic Regret and Risk](https://mlsanity.com/paper/2204.00706/) (2022)
- [Adaptive Algorithms for Relaxed Pareto Set Identification](https://mlsanity.com/paper/2307.00424/) (2023)
- [Bandit Pareto Set Identification: the Fixed Budget Setting](https://mlsanity.com/paper/2311.03992/) (2023)
- [Continuous Mean-Covariance Bandits](https://mlsanity.com/paper/2102.12090/) (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)

## Abstract (arXiv)

Decision making under uncertain environments in the maximization of expected reward while minimizing its risk is one of the ubiquitous problems in many subjects. Here, we introduce a novel problem setting in stochastic bandit optimization that jointly addresses two critical aspects of decision-making: maximizing expected reward and minimizing associated uncertainty, quantified via the mean-variance(MV) criterion. Unlike traditional bandit formulations that focus solely on expected returns, our objective is to efficiently and accurately identify the Pareto-optimal set of arms that strikes the best trade-off between expected performance and risk. We propose a unified meta-algorithmic framework capable of operating under both fixed-confidence and fixed-budget regimes, achieved through adaptive design of confidence intervals tailored to each scenario using the same sample exploration strategy. We provide theoretical guarantees on the correctness of the returned solutions in both settings. To complement this theoretical analysis, we conduct extensive empirical evaluations across synthetic benchmarks, demonstrating that our approach outperforms existing methods in terms of both accuracy and sample efficiency, highlighting its broad applicability to risk-aware decision-making tasks in uncertain environments.