# Best Arm Identification in Generalized Linear Bandits

arXiv: https://arxiv.org/abs/1905.08224 · HTML: https://mlsanity.com/paper/1905.08224/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2019.

## Built on by (most cited first, 18 of 18)

- [Minimax Optimal Fixed-Budget Best Arm Identification in Linear Bandits](https://mlsanity.com/paper/2105.13017/) (2021)
- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion](https://mlsanity.com/paper/2310.18554/) (2023)
- [Nearly Minimax Optimal Regret for Multinomial Logistic Bandit](https://mlsanity.com/paper/2405.09831/) (2024)
- [Pure Exploration in Kernel and Neural Bandits](https://mlsanity.com/paper/2106.12034/) (2021)
- [A Map of Bandits for E-commerce](https://mlsanity.com/paper/2107.00680/) (2021)
- [Sample Constrained Treatment Effect Estimation](https://mlsanity.com/paper/2210.06594/) (2022)
- [Contextual Bandits in a Survey Experiment on Charitable Giving: Within-Experiment Outcomes versus Policy Learning](https://mlsanity.com/paper/2211.12004/) (2022)
- [Stochastic Online Instrumental Variable Regression: Regrets for Endogeneity and Bandit Feedback](https://mlsanity.com/paper/2302.09357/) (2023)
- [Pure Exploration in Asynchronous Federated Bandits](https://mlsanity.com/paper/2310.11015/) (2023)
- [Price of Safety in Linear Best Arm Identification](https://mlsanity.com/paper/2309.08709/) (2023)
- [Certified Multi-Fidelity Zeroth-Order Optimization](https://mlsanity.com/paper/2308.00978/) (2023)
- [Optimal Exploration is no harder than Thompson Sampling](https://mlsanity.com/paper/2310.06069/) (2023)
- [Near Optimal Pure Exploration in Logistic Bandits](https://mlsanity.com/paper/2410.20640/) (2024)
- [Best Arm Identification under Additive Transfer Bandits](https://mlsanity.com/paper/2112.04083/) (2021)
- [Experimental Design for Semiparametric Bandits](https://mlsanity.com/paper/2506.13390/) (2025)
- [Best Agent Identification for General Game Playing](https://mlsanity.com/paper/2507.00451/) (2025)
- [Best Arm Identification in Generalized Linear Bandits via Hybrid Feedback](https://mlsanity.com/paper/2605.05745/) (2026)

## Abstract (arXiv)

Motivated by drug design, we consider the best-arm identification problem in generalized linear bandits. More specifically, we assume each arm has a vector of covariates, there is an unknown vector of parameters that is common across the arms, and a generalized linear model captures the dependence of rewards on the covariate and parameter vectors. The problem is to minimize the number of arm pulls required to identify an arm that is sufficiently close to optimal with a sufficiently high probability. Building on recent progress in best-arm identification for linear bandits (Xu et al. 2018), we propose the first algorithm for best-arm identification for generalized linear bandits, provide theoretical guarantees on its accuracy and sampling efficiency, and evaluate its performance in various scenarios via simulation.