# Sample complexity of partition identification using multi-armed bandits

arXiv: https://arxiv.org/abs/1811.05654 · HTML: https://mlsanity.com/paper/1811.05654/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2018.

## Built on by (most cited first, 13 of 13)

- [Bandits with many optimal arms](https://mlsanity.com/paper/2103.12452/) (2021)
- [The Role of Contextual Information in Best Arm Identification](https://mlsanity.com/paper/2106.14077/) (2021)
- [Reward Maximization for Pure Exploration: Minimax Optimal Good Arm Identification for Nonparametric Multi-Armed Bandits](https://mlsanity.com/paper/2410.15564/) (2024)
- [Optimal Best Arm Identification in Two-Armed Bandits with a Fixed Budget under a Small Gap](https://mlsanity.com/paper/2201.04469/) (2022)
- [Best Arm Identification with Contextual Information under a Small Gap](https://mlsanity.com/paper/2209.07330/) (2022)
- [Testing the Feasibility of Linear Programs with Bandit Feedback](https://mlsanity.com/paper/2406.15648/) (2024)
- [Best Group Identification in Multi-Objective Bandits](https://mlsanity.com/paper/2505.17869/) (2025)
- [Best Arm Identification under Additive Transfer Bandits](https://mlsanity.com/paper/2112.04083/) (2021)
- [Pure Exploration with Infinite Answers](https://mlsanity.com/paper/2505.22473/) (2025)
- [Non-Asymptotic Analysis of (Sticky) Track-and-Stop](https://mlsanity.com/paper/2505.22475/) (2025)
- [Fixed-Confidence Multiple Change Point Identification under Bandit Feedback](https://mlsanity.com/paper/2507.08994/) (2025)
- [Batch Entanglement Detection in Parameterized Qubit States using Classical Bandit Algorithms](https://mlsanity.com/paper/2406.19738/) (2024)
- [agent-risk: Risk Assessment for Changes to AI Agents](https://mlsanity.com/paper/2610.16280/) (2026)

## Abstract (arXiv)

Given a vector of probability distributions, or arms, each of which can be sampled independently, we consider the problem of identifying the partition to which this vector belongs from a finitely partitioned universe of such vector of distributions. We study this as a pure exploration problem in multi armed bandit settings and develop sample complexity bounds on the total mean number of samples required for identifying the correct partition with high probability. This framework subsumes well studied problems such as finding the best arm or the best few arms. We consider distributions belonging to the single parameter exponential family and primarily consider partitions where the vector of means of arms lie either in a given set or its complement. The sets considered correspond to distributions where there exists a mean above a specified threshold, where the set is a half space and where either the set or its complement is a polytope, or more generally, a convex set. In these settings, we characterize the lower bounds on mean number of samples for each arm highlighting their dependence on the problem geometry. Further, inspired by the lower bounds, we propose algorithms that can match these bounds asymptotically with decreasing probability of error. Applications of this framework may be diverse. We briefly discuss one associated with finance.