# Adaptive Multiple-Arm Identification

arXiv: https://arxiv.org/abs/1706.01026 · HTML: https://mlsanity.com/paper/1706.01026/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2017.

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

- [Sequential Learning of the Pareto Front for Multi-objective Bandits](https://mlsanity.com/paper/2501.17513/) (2025)
- [Optimal Streaming Algorithms for Multi-Armed Bandits](https://mlsanity.com/paper/2410.17835/) (2024)
- [Adaptive Sampling for Heterogeneous Rank Aggregation from Noisy Pairwise Comparisons](https://mlsanity.com/paper/2110.04136/) (2021)
- [Experimentation and Commitment under Reward Shifts](https://mlsanity.com/paper/2607.23432/) (2026)

## Abstract (arXiv)

We study the problem of selecting K arms with the highest expected rewards in a stochastic n-armed bandit game. This problem has a wide range of applications, e.g., A/B testing, crowdsourcing, simulation optimization. Our goal is to develop a PAC algorithm, which, with probability at least 1-δ, identifies a set of K arms with the aggregate regret at most ε. The notion of aggregate regret for multiple-arm identification was first introduced in citeZhou:14 , which is defined as the difference of the averaged expected rewards between the selected set of arms and the best K arms. In contrast to citeZhou:14 that only provides instance-independent sample complexity, we introduce a new hardness parameter for characterizing the difficulty of any given instance. We further develop two algorithms and establish the corresponding sample complexity in terms of this hardness parameter. The derived sample complexity can be significantly smaller than state-of-the-art results for a large class of instances and matches the instance-independent lower bound upto a log(ε-1) factor in the worst case. We also prove a lower bound result showing that the extra log(ε-1) is necessary for instance-dependent algorithms using the introduced hardness parameter.