Online Decision-Making with High-Dimensional Covariates

Hamsa Bastani
Stanford University

Mohsen Bayati
Stanford Graduate School of Business

June 5, 2015

Abstract:

Big data has enabled decision-makers to tailor choices at the individual-level. This involves learning a model of decision rewards conditional on individual-specific covariates. In domains such as medical decision-making and personalized advertising, these covariates are often high-dimensional; however, typically only a small subset of these observed features are predictive of each decision’s success. 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. Furthermore, we illustrate the practical relevance of our algorithm by evaluating it on a real-world clinical problem of warfarin dosing. A patient’s optimal warfarin dosage depends on the patient’s genetic profile and medical records; incorrect initial dosage may result in adverse consequences such as stroke or bleeding. We show that our algorithm outperforms existing bandit methods as well as physicians to correctly dose a majority of patients.

Online Decision-Making with High-Dimensional Covariates

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