|
Growing availability of data has enabled decision-makers to tailor choices at the individual-level in a variety of domains such as personalized medicine. This involves learning a model of decision rewards conditional on individual-specific covariates. In many practical settings, these covariates are "high-dimensional". We formulate this problem as a multi-armed bandit with high-dimensional covariates, and present a new efficient bandit algorithm based on the LASSO estimator. Our regret analysis establishes that our algorithm achieves near-optimal performance in comparison to an oracle that knows all the problem parameters. The key step in our analysis is proving a new oracle inequality that guarantees the convergence of the LASSO estimator despite the non-i.i.d. data induced by the bandit policy.
We illustrate the practical relevance of our algorithm by evaluating it on a warfarin dosing problem. A patient's optimal warfarin dosage depends on the patient's genetic profile and medical records; incorrect initial dosage may result in stroke or bleeding. We show that our algorithm outperforms existing bandit methods as well as physicians to correctly dose a majority of patients.
|
