Contextual Bandits with Budgeted Information Reveal
This addresses a practical challenge in digital health for clinicians by optimizing budget use for patient engagement, though it is incremental as it builds on existing bandit methods.
The paper tackles the problem of limited budgets for encouraging patients to take pro-treatment actions in digital health contextual bandits, introducing a novel algorithm that combines online primal-dual optimization with contextual bandit learning, achieving a sub-linear regret bound.
Contextual bandit algorithms are commonly used in digital health to recommend personalized treatments. However, to ensure the effectiveness of the treatments, patients are often requested to take actions that have no immediate benefit to them, which we refer to as pro-treatment actions. In practice, clinicians have a limited budget to encourage patients to take these actions and collect additional information. We introduce a novel optimization and learning algorithm to address this problem. This algorithm effectively combines the strengths of two algorithmic approaches in a seamless manner, including 1) an online primal-dual algorithm for deciding the optimal timing to reach out to patients, and 2) a contextual bandit learning algorithm to deliver personalized treatment to the patient. We prove that this algorithm admits a sub-linear regret bound. We illustrate the usefulness of this algorithm on both synthetic and real-world data.