  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.
