Online Uniform Sampling: Randomized Learning-Augmented Approximation Algorithms with Application to Digital Health

Xueqing Liu, Kyra Gan, Esmaeil Keyvanshokooh, Susan Murphy

Abstract: Motivated by applications in digital health, this work studies the novel problem of *online uniform sampling* (OUS), where the goal is to distribute a sampling budget uniformly across *unknown* decision times. In the OUS problem, the algorithm is given a budget $b$ and a time horizon $T$, and an adversary then chooses a value $\tau^* \in [b,T]$, which is revealed to the algorithm online. At each decision time $i \in [\tau^*]$, the algorithm must determine a sampling probability that maximizes the budget spent throughout the horizon, respecting budget constraint $b$, while achieving as uniform a distribution as possible over $\tau^*$. We present the first randomized algorithm designed for this problem and subsequently extend it to incorporate learning augmentation. We provide *worst-case* approximation guarantees for both algorithms, and illustrate the utility of the algorithms through both synthetic experiments and a real-world case study involving the HeartSteps mobile application. Our numerical results show strong empirical *average* performance of our proposed randomized algorithms against previously proposed heuristic solutions.

Primary Area: Optimization->Everything Else

Keywords: online optimization, randomized algorithms, learning augmentation, competitive analysis, digital health

Application-Driven Machine Learning: This submission is on Application-Driven Machine Learning.

Submission Number: 14668