# Instrument-Armed Bandits

arXiv: https://arxiv.org/abs/1705.07377 · HTML: https://mlsanity.com/paper/1705.07377/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2017.

## Built on by (most cited first, 10 of 10)

- [Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses](https://mlsanity.com/paper/2107.05762/) (2021)
- [Concentrated Differential Privacy for Bandits](https://mlsanity.com/paper/2309.00557/) (2023)
- [Stochastic Online Instrumental Variable Regression: Regrets for Endogeneity and Bandit Feedback](https://mlsanity.com/paper/2302.09357/) (2023)
- [Adaptive Instrument Design for Indirect Experiments](https://mlsanity.com/paper/2312.02438/) (2023)
- [Adaptive Experimentation When You Can't Experiment](https://mlsanity.com/paper/2406.10738/) (2024)
- [Incentivizing Compliance with Algorithmic Instruments](https://mlsanity.com/paper/2107.10093/) (2021)
- [Contextual Bandit with Herding Effects: Algorithms and Recommendation Applications](https://mlsanity.com/paper/2408.14432/) (2024)
- [Generator-Mediated Bandits: Thompson Sampling for GenAI-Powered Adaptive Interventions](https://mlsanity.com/paper/2505.16311/) (2025)
- [Dual Instrumental Method for Confounded Kernelized Bandits](https://mlsanity.com/paper/2209.03224/) (2022)
- [What Do We Care About in Bandits with Noncompliance? BRACE: Bandits with Recommendations, Abstention, and Certified Effects](https://mlsanity.com/paper/2603.09532/) (2026)

## Abstract (arXiv)

We extend the classic multi-armed bandit (MAB) model to the setting of noncompliance, where the arm pull is a mere instrument and the treatment applied may differ from it, which gives rise to the instrument-armed bandit (IAB) problem. The IAB setting is relevant whenever the experimental units are human since free will, ethics, and the law may prohibit unrestricted or forced application of treatment. In particular, the setting is relevant in bandit models of dynamic clinical trials and other controlled trials on human interventions. Nonetheless, the setting has not been fully investigate in the bandit literature. We show that there are various and divergent notions of regret in this setting, all of which coincide only in the classic MAB setting. We characterize the behavior of these regrets and analyze standard MAB algorithms. We argue for a particular kind of regret that captures the causal effect of treatments but show that standard MAB algorithms cannot achieve sublinear control on this regret. Instead, we develop new algorithms for the IAB problem, prove new regret bounds for them, and compare them to standard MAB algorithms in numerical examples.