Online Uniform Risk Times Sampling: First Approximation Algorithms, Learning Augmentation with Full Confidence Interval Integration

In digital health, the strategy of allocating a limited treatment budget across available risk times is crucial to reduce user fatigue. This strategy, however, encounters a significant obstacle due to the unknown actual number of risk times, a factor not adequately addressed by existing methods lacking theoretical guarantees. This paper introduces, for the first time, the online uniform risk times sampling problem within the approximation algorithm framework. We propose two online approximation algorithms for this problem, one with and one without learning augmentation, and provide rigorous theoretical performance guarantees for them using competitive ratio analysis. We assess the performance of our algorithms using both synthetic experiments and a real-world case study on HeartSteps mobile applications.

Contextual Bandits with Budgeted Information Reveal

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.