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arXiv 2402.01995cs.LGmath.OC
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在线均匀采样:随机学习增强近似算法及其在数字健康中的应用

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

Duke-NUS Medical School(杜克-国大医学院);Cornell Tech(康奈尔理工学院);Texas A&M(德克萨斯农工大学);Harvard University(哈佛大学);Amazon(亚马逊公司)

Xueqing Liu, Kyra Gan, Esmaeil Keyvanshokooh, Susan Murphy

AI总结:

本文针对数字健康场景中的在线均匀采样问题,提出首个随机算法及其学习增强版本,给出最坏情况近似保证,并通过合成实验与HeartSteps真实案例验证其优于已有启发式方法的平均性能。

摘要:

受数字健康领域应用的启发,本文研究了在线均匀采样(OUS)这一新问题,其目标是在未知决策时间上均匀分配采样预算。在OUS问题中,算法被给定一个预算$b$和一个时间范围$T$,随后对手选择一个值$τ^* \in [b,T]$,该值在线揭示给算法。在每个决策时间$i \in [τ^*]$,算法必须确定一个采样概率,在遵守预算约束$b$的同时,最大化整个时间范围内花费的预算,并在$τ^*$上尽可能实现均匀分布。我们提出了首个针对该问题的随机算法,并随后将其扩展以纳入学习增强。我们为两种算法提供了最坏情况近似保证,并通过合成实验和涉及HeartSteps移动应用的真实案例研究展示了算法的实用性。我们的数值结果表明,与先前提出的启发式解决方案相比,我们提出的随机算法在经验平均性能上表现强劲。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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