使用少量样本的在线分配

中文摘要 AI 辅助

我们研究在线分配问题，其中$n$个请求针对$m$种资源以对抗性顺序到达，并且必须立即且不可撤销地服务。该框架涵盖了在线资源分配（目标是在资源预算约束下最大化价值）和在线负载均衡（目标是最小化完工时间）。我们在大预算或大完工时间机制下寻求$(1\pm\epsilon)$-竞争比算法。我们考虑一种采样模型，它推广了以下两种被广泛研究的采样模型。在单样本先知不等式（$\mathsf{SSPI}$）模型中，请求$t$来自未知分布$\mathcal{D}_t$，算法在在线阶段之前获得每个$\mathcal{D}_t$的一个独立样本。在$p$-样本模型中，请求是对抗性的，但均匀随机的$p$比例预先作为训练数据揭示。尽管在较简单的随机顺序模型（$\mathsf{RO}$）中已知近最优算法，其中请求以均匀随机顺序到达，但先前针对$\mathsf{SSPI}$和$p$-样本的算法是问题特定的，并且在$\epsilon$、$m$和$n$上产生明显更差的依赖关系。我们的主要贡献是一个通用框架，它将$\mathsf{RO}$算法转换为$p$-预览模型的算法，该模型推广了$\mathsf{SSPI}$和$p$-样本。作为结果，我们在这些对抗性顺序采样模型中为在线资源分配、广义在线负载均衡和在线混合打包-覆盖问题获得了近最优界，显著改进了[Ghuge, Singla, Wang (STOC'25)]和[Gupta and Molinaro (SODA'26)]的界。

英文摘要

We study online allocation problems where $n$ requests over $m$ resources arrive in an adversarial order and must be served immediately and irrevocably. This framework captures both Online Resource Allocation, where the goal is to maximize value subject to resource budgets, and Online Load Balancing, where the goal is to minimize the makespan. We seek $(1\pmε)$-competitive algorithms in the large-budget or large-makespan regime. We consider a sampling model that generalizes the following two well-studied sampling models. In the Single-Sample Prophet Inequality ($\mathsf{SSPI}$) model, request $t$ is drawn from an unknown distribution $\mathcal{D}_t$, and the algorithm is given one independent sample from each $\mathcal{D}_t$ before the online phase. In the $p$-$\mathsf{Sample}$ model, the requests are adversarial, but a uniformly random $p$-fraction is revealed upfront as training data. Although near-optimal algorithms are known in the easier random-order model ($\mathsf{RO}$), where the requests arrive in a uniformly random order, prior algorithms for $\mathsf{SSPI}$ and $p$-$\mathsf{Sample}$ were problem-specific and incurred substantially worse dependencies on $ε$, $m$, and $n$. Our main contribution is a general framework that converts $\mathsf{RO}$ algorithms into algorithms for the $p$-$\mathsf{Preview}$ model, a model that generalizes both $\mathsf{SSPI}$ and $p$-$\mathsf{Sample}$. As consequences, we obtain near-optimal bounds for Online Resource Allocation, generalized Online Load Balancing, and online mixed packing-covering problems in these adversarial-order sampling models, significantly improving the bounds of [Ghuge, Singla, Wang (STOC'25)] and [Gupta and Molinaro (SODA'26)].

发表机构

• Georgia Institute of Technology（佐治亚理工学院）

机构由 AI 辅助整理，请以论文原文为准。