# Statistically Robust, Risk-Averse Best Arm Identification in Multi-Armed Bandits

arXiv: https://arxiv.org/abs/2008.13629 · HTML: https://mlsanity.com/paper/2008.13629/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2020.

## Built on by (most cited first, 4 of 4)

- [Almost Optimal Variance-Constrained Best Arm Identification](https://mlsanity.com/paper/2201.10142/) (2022)
- [Risk averse non-stationary multi-armed bandits](https://mlsanity.com/paper/2109.13977/) (2021)
- [Variance-Optimal Arm Selection: Misallocation Minimization and Best Arm Identification](https://mlsanity.com/paper/2505.11985/) (2025)
- [An Algorithm for Fixed Budget Best Arm Identification with Combinatorial Exploration](https://mlsanity.com/paper/2502.01429/) (2025)

## Abstract (arXiv)

Traditional multi-armed bandit (MAB) formulations usually make certain assumptions about the underlying arms' distributions, such as bounds on the support or their tail behaviour. Moreover, such parametric information is usually 'baked' into the algorithms. In this paper, we show that specialized algorithms that exploit such parametric information are prone to inconsistent learning performance when the parameter is misspecified. Our key contributions are twofold: (i) We establish fundamental performance limits of statistically robust MAB algorithms under the fixed-budget pure exploration setting, and (ii) We propose two classes of algorithms that are asymptotically near-optimal. Additionally, we consider a risk-aware criterion for best arm identification, where the objective associated with each arm is a linear combination of the mean and the conditional value at risk (CVaR). Throughout, we make a very mild 'bounded moment' assumption, which lets us work with both light-tailed and heavy-tailed distributions within a unified framework.