发表机构
The University of Wisconsin–Madison; The Chinese University of Hong Kong（威斯康星大学麦迪逊分校; 香港中文大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对递增回报的在线资源分配问题，提出同质奖励下的紧1/2竞争比算法及异质奖励下常数保证的修复算法，证明异质延迟奖励的固有困难。
AI 中文摘要
在线资源分配是收益管理、赞助搜索和平台运营中的一个基本问题。大多数先前的工作假设分配奖励非递增，以捕捉收益递减效应。我们转而研究递增回报，即向同一产品分配更多客户可以通过规模、可见性或网络效应解锁更大的价值。我们考虑将容量有限的产品分配给顺序到达的客户，其中每个产品的奖励取决于分配给它的客户总数。我们专注于完全兼容性，即每个产品可以分配给每个客户。客户数量对于在线算法是未知的。我们表明，代表性的经典方法，如在线贪心算法和基于线性规划的独立舍入，在此设置中可能表现任意差，即使产品共享一个共同的奖励函数。对于同质奖励函数，我们给出一个简单的多项式时间算法，实现紧的$1/2$竞争比。对于任意异质奖励函数，我们表明不存在独立于产品数量的常数竞争比：对于$m$个产品，最优竞争比可以小至$\Theta\left({1}/{\sqrt m}\right)$。这表明异质延迟奖励可以迫使任何在线算法猜测实现的到达数量。然后我们确定一个结构化的异质机制，它恢复了常数保证。当每个奖励函数是非负、非递减且离散凹时，我们设计了一个中间目标修复算法，具有确定性的路径保证$0.2466$。该算法反复计算更大需求水平的离线目标，并使用前缀鲁棒分配顺序将当前分配修复到该目标。这协调了累积，同时保持对提前停止的鲁棒性，并产生一个无分布假设的保证。
英文摘要
Online resource allocation is a fundamental problem in revenue management, sponsored search, and platform operations. Most prior work assumes nonincreasing assignment rewards, capturing diminishing returns. We instead study increasing returns, where assigning more customers to the same product can unlock larger value through scale, visibility, or network effects. We consider capacity-limited products assigned to sequentially arriving customers, where the reward of each product depends on the total number of customers assigned to it. We focus on full compatibility, where every product can be assigned to every customer. The number of customers is unknown to the online algorithm. We show that representative classical approaches, such as online greedy algorithm and LP-based independent rounding, can perform arbitrarily bad in this setting, even when products share a common bonus function. For homogeneous bonus functions, we give a simple polynomial-time algorithm that achieves a tight $1/2$-competitive ratio. For arbitrary heterogeneous bonus functions, we show that no constant competitive ratio independent of the number of products is possible: for $m$ products, the optimal competitive can be as small as $Θ\left({1}/{\sqrt m}\right)$. This shows that heterogeneous delayed rewards can force any online algorithm to guess the realized arrival counts. We then identify a structured heterogeneous regime that restores a constant guarantee. When each bonus function is nonnegative, nondecreasing, and discrete concave, we design an intermediate target repair algorithm with a deterministic pathwise guarantee of $0.2466$. The algorithm repeatedly computes an offline target for a larger demand level and repairs the current allocation toward it using a prefix-robust assignment order. This coordinates buildup while remaining robust to early stopping and yields a distribution-free guarantee.
