Instrument-Armed Bandits
This work addresses a gap in bandit literature for dynamic clinical trials and human interventions, though it is incremental as it extends an existing model.
The authors tackled the problem of noncompliance in multi-armed bandits, where treatments may differ from arm pulls due to human factors, by introducing the instrument-armed bandit model and developing new algorithms that achieve sublinear regret bounds, outperforming standard methods in numerical examples.
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.