# Thompson Sampling for Noncompliant Bandits

arXiv: https://arxiv.org/abs/1812.00856 · HTML: https://mlsanity.com/paper/1812.00856/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2018.

## Built on by (most cited first, 3 of 3)

- [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)
- [Generator-Mediated Bandits: Thompson Sampling for GenAI-Powered Adaptive Interventions](https://mlsanity.com/paper/2505.16311/) (2025)

## Abstract (arXiv)

Thompson sampling, a Bayesian method for balancing exploration and exploitation in bandit problems, has theoretical guarantees and exhibits strong empirical performance in many domains. Traditional Thompson sampling, however, assumes perfect compliance, where an agent's chosen action is treated as the implemented action. This article introduces a stochastic noncompliance model that relaxes this assumption. We prove that any noncompliance in a 2-armed Bernoulli bandit increases existing regret bounds. With our noncompliance model, we derive Thompson sampling variants that explicitly handle both observed and latent noncompliance. With extensive empirical analysis, we demonstrate that our algorithms either match or outperform traditional Thompson sampling in both compliant and noncompliant environments.