  Bandit algorithms hold great promise for improving personalized
decision-making but are notoriously sample-hungry. In most health applications,
it is infeasible to fit a new bandit for each patient, and observable variables
are often insufficient to determine optimal treatments, ruling out applying
contextual bandits learned from multiple patients. Latent bandits offer both
rapid exploration and personalization beyond what context variables can reveal
but require that a latent variable model can be learned consistently. In this
work, we propose bandit algorithms based on nonlinear independent component
analysis that can be provably identified from observational data to a degree
sufficient to infer the optimal action in a new bandit instance consistently.
We verify this strategy in simulated data, showing substantial improvement over
learning independent multi-armed bandits for every instance.
