# Robust Best-arm Identification in Linear Bandits

arXiv: https://arxiv.org/abs/2311.04731 · HTML: https://mlsanity.com/paper/2311.04731/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 37 references that are in the map.
- First posted on arXiv 8 Nov 2023.

## Builds on (most cited first, 17 of 17)

- [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014)
- [Ethical Machine Learning in Health Care](https://mlsanity.com/paper/2009.10576/) (2020)
- [Best-Arm Identification in Linear Bandits](https://mlsanity.com/paper/1409.6110/) (2014)
- [Sequential Experimental Design for Transductive Linear Bandits](https://mlsanity.com/paper/1906.08399/) (2019)
- [Linear Stochastic Bandits Under Safety Constraints](https://mlsanity.com/paper/1908.05814/) (2019)
- [Stochastic Bandits with Linear Constraints](https://mlsanity.com/paper/2006.10185/) (2020)
- [Stochastic Linear Bandits Robust to Adversarial Attacks](https://mlsanity.com/paper/2007.03285/) (2020)
- [Gamification of Pure Exploration for Linear Bandits](https://mlsanity.com/paper/2007.00953/) (2020)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2205.06811/) (2022)
- [Safe Linear Thompson Sampling with Side Information](https://mlsanity.com/paper/1911.02156/) (2019)
- [Robust Stochastic Linear Contextual Bandits Under Adversarial Attacks](https://mlsanity.com/paper/2106.02978/) (2021)
- [Safe Linear Stochastic Bandits](https://mlsanity.com/paper/1911.09501/) (2019)
- [Deep Reinforcement Learning for Closed-Loop Blood Glucose Control](https://mlsanity.com/paper/2009.09051/) (2020)
- [Best Arm Identification with Safety Constraints](https://mlsanity.com/paper/2111.12151/) (2021)
- [Interactively Learning Preference Constraints in Linear Bandits](https://mlsanity.com/paper/2206.05255/) (2022)
- [Safe Linear Leveling Bandits](https://mlsanity.com/paper/2112.06728/) (2021)

## Abstract (arXiv)

We study the robust best-arm identification problem (RBAI) in the case of linear rewards. The primary objective is to identify a near-optimal robust arm, which involves selecting arms at every round and assessing their robustness by exploring potential adversarial actions. This approach is particularly relevant when utilizing a simulator and seeking to identify a robust solution for real-world transfer. To this end, we present an instance-dependent lower bound for the robust best-arm identification problem with linear rewards. Furthermore, we propose both static and adaptive bandit algorithms that achieve sample complexity that matches the lower bound. In synthetic experiments, our algorithms effectively identify the best robust arm and perform similarly to the oracle strategy. As an application, we examine diabetes care and the process of learning insulin dose recommendations that are robust with respect to inaccuracies in standard calculators. Our algorithms prove to be effective in identifying robust dosage values across various age ranges of patients.