Online Uniform Sampling: Randomized Learning-Augmented Approximation Algorithms with Application to Digital Health
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913553895653376 |
|---|---|
| author | Liu, Xueqing Gan, Kyra Keyvanshokooh, Esmaeil Murphy, Susan |
| author_facet | Liu, Xueqing Gan, Kyra Keyvanshokooh, Esmaeil Murphy, Susan |
| contents | 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 $τ^* \in [b,T]$, which is revealed to the algorithm online. At each decision time $i \in [τ^*]$, 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 $τ^*$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Online Uniform Sampling: Randomized Learning-Augmented Approximation Algorithms with Application to Digital Health Liu, Xueqing Gan, Kyra Keyvanshokooh, Esmaeil Murphy, Susan Machine Learning Optimization and Control 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 $τ^* \in [b,T]$, which is revealed to the algorithm online. At each decision time $i \in [τ^*]$, 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 $τ^*$. 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. |
| title | Online Uniform Sampling: Randomized Learning-Augmented Approximation Algorithms with Application to Digital Health |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2402.01995 |