论文标题
与样品分配的在线资源分配
Online Resource Allocation with Samples
论文作者
论文摘要
我们研究了在不确定性的在线资源分配问题,内容涉及需求以及对资源的每种需求(代理)的奖励。尽管处理资源分配问题的需求不确定性一直是文献中许多论文的主题,但几乎没有探索不知道奖励的挑战。缺乏对代理人奖励的知识的灵感来自于为具有未知有效性/价值的新资源(例如新开发的疫苗或药物)分配单位的问题。对于这种设置,我们假设我们可以在分配期开始之前\ emph {test}市场。在测试期间,我们用概率$ p $对市场中的每个代理进行了对。我们研究了如何在对抗性到达过程中在我们的在线资源分配问题中最佳利用\ emph {示例信息}。我们提出了一种渐近最佳算法,该算法可实现$1-θ(1/(p \ sqrt {m}))$竞争比率,其中$ m $是资源可用单位的数量。通过表征任何随机和确定性算法的竞争比率的上限,我们表明我们的竞争比率为$1-θ(1/(p \ sqrt {m}))$对于任何$ p =ω(1/\ sqrt {m})$都很紧。造型信息可以使用渐近最优性,突出了为新资源运行测试期的重要优势。我们使用包含不同年龄段的COVID-19相关住院患者的数据集证明了我们提出的算法的功效。
We study an online resource allocation problem under uncertainty about demand and about the reward of each type of demand (agents) for the resource. Even though dealing with demand uncertainty in resource allocation problems has been the topic of many papers in the literature, the challenge of not knowing rewards has been barely explored. The lack of knowledge about agents' rewards is inspired by the problem of allocating units of a new resource (e.g., newly developed vaccines or drugs) with unknown effectiveness/value. For such settings, we assume that we can \emph{test} the market before the allocation period starts. During the test period, we sample each agent in the market with probability $p$. We study how to optimally exploit the \emph{sample information} in our online resource allocation problem under adversarial arrival processes. We present an asymptotically optimal algorithm that achieves $1-Θ(1/(p\sqrt{m}))$ competitive ratio, where $m$ is the number of available units of the resource. By characterizing an upper bound on the competitive ratio of any randomized and deterministic algorithm, we show that our competitive ratio of $1-Θ(1/(p\sqrt{m}))$ is tight for any $p =ω(1/\sqrt{m})$. That asymptotic optimality is possible with sample information highlights the significant advantage of running a test period for new resources. We demonstrate the efficacy of our proposed algorithm using a dataset that contains the number of COVID-19 related hospitalized patients across different age groups.