在线公平分配：推进近似比例性的前沿
Online Fair Division: Pushing the Frontier of Approximate Proportionality
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中文总结 AI 辅助
本文研究在线公平分配中近似比例性（PROP1）的确定性保证，提出无额外信息时Ω(1/log(nm))-PROP1算法并给出上界，以及有最大物品价值信息时1/2竞争比算法，推进了该领域前沿。
中文摘要 AI 辅助
在线公平分配刻画了这样一种分配问题：不可分割的资源随时间到达，并且必须在未来资源未知之前进行分配。在这种设定下，理解当分配决策是即时且不可撤销时，何种公平性仍然可以实现，是一个基本问题。我们研究在n个具有非负可加估值的智能体之间进行确定性在线分配，其中商品数量未知，且对手可以适应先前的分配决策。我们关注“至多一个商品的比例性”（PROP1），并考察未来信息的提前知晓如何影响可实现的保证。在没有额外信息的设定中，我们回答了Choo等人提出的一个开放问题，即是否可以获得PROP1的非平凡确定性近似。具体而言，我们提出一个确定性算法，保证Ω(1/log(nm))-PROP1，其中m是商品数量。此外，我们通过证明来补充这一结果：对于每个固定的n和所有足够大的m，每个确定性算法都存在一个包含m个商品的实例，其PROP1因子为O(log log m / log m)。我们还研究了算法提前知道每个智能体的最大物品价值（MIV）的设定。有了MIV信息，我们给出一个竞争比为1/2的确定性算法，改进了Choo等人中的1/n保证。我们还表明，即使对于具有精确MIV信息的两个智能体，也没有确定性算法能够实现任意接近1的竞争比。
英文摘要
Online fair division captures allocation problems in which indivisible resources arrive over time and must be assigned before future resources are known. Understanding what fairness remains achievable when allocation decisions are immediate and irrevocable is a fundamental question in this setting. We study deterministic online allocation among $n$ agents with nonnegative additive valuations, where the number of goods is unknown and the adversary can adapt to previous allocation decisions. We focus on proportionality up to one good (PROP1) and examine how advance information affects the achievable guarantees. Without additional future information, we give a deterministic algorithm that guarantees $Ω(\frac{1}{\log(nm)})$-PROP1 after every round, where $m$ is the number of goods at termination. We complement this result by showing that, for every $n$ and sufficiently large $m$, every deterministic algorithm has an adaptive instance with $m$ goods on which its allocation has PROP1 approximation guarantee $O(\frac{\log \log m}{\log m})$. Thus, when the number of agents is fixed, our upper and lower bounds on the competitive ratio differ by at most an $O(\log\log m)$ factor. These results answer an open question proposed by Choo et al. on whether a nontrivial deterministic approximation for PROP1 can be obtained. We also study the setting where the algorithm knows the predictions of the maximum item value for every agent. When the predictions are accurate, we give a deterministic $\frac{1}{2}$-PROP1 algorithm, improving the $\frac{1}{n}$ guarantee of Choo et al. to a constant. We further establish an explicit upper bound below one on the competitive ratio, even for two agents with accurate predictions. Finally, we give a single deterministic algorithm that guarantees $\frac{1}{2}$-PROP1 when predictions are accurate and $Ω(\frac{1}{\log (nm)})$-PROP1 for arbitrary predictions.
发表机构
- School of Computer Science and Technology, Shandong University（山东大学计算机科学与技术学院）
机构由 AI 辅助整理，请以论文原文为准。
