在线房屋分配与补贴

中文摘要 AI 辅助

房屋分配是一个基本问题，其中每个智能体恰好被分配一所房屋。经典模型假设所有房屋在分配计算之前都是可用的，然而许多实际场景要求随着房屋随时间变得可用而做出决策。我们引入了在线房屋分配问题，其中房屋顺序到达，算法必须在不知道未来到达信息的情况下维持一个分配。与在线公平分配不同，每智能体一所房屋的约束使得重新分配成为问题固有的一部分，因为接受新到达的房屋可能需要重新分配先前已分配的房屋。我们在基于补贴的公平性下研究在线房屋分配，其中货币补贴消除智能体之间的嫉妒。我们证明，使用有界重新分配可以始终在线维持无嫉妒性，并且在最坏情况下，长度与智能体数量成线性关系的重新分配链是不可避免的。相比之下，最小化总补贴从根本上更难：没有确定性的在线算法能对抗自适应对手，也没有随机化的在线算法能对抗非自适应对手，即使只有两个智能体和四所房屋，也无法获得有界竞争比。我们通过证明当房屋数量最多比智能体数量多一所时，精确的在线补贴最小化是可能的，并且这一保证在额外房屋数量方面是最优的，来补充这些不可能性结果。最后，我们开发了学习增强算法，在准确预测下恢复离线最优解，同时在预测不准确时提供明确的鲁棒性保证。

英文摘要

House allocation is a fundamental problem in which each agent is assigned exactly one house. While the classical model assumes that all houses are available before the allocation is computed, many practical settings require decisions to be made as houses become available over time. We introduce the online house allocation problem, where houses arrive sequentially and the algorithm must maintain an allocation without knowledge of future arrivals. Unlike online fair division, the one-house-per-agent constraint makes recourse an inherent part of the problem, as accepting a newly arrived house may require reassigning previously allocated houses. We study online house allocation under subsidy-based fairness, where monetary subsidies eliminate envy among agents. We show that envy-freeability can always be maintained online using bounded recourse and that reassignment chains of length linear in the number of agents are unavoidable in the worst case. In contrast, minimizing the total subsidy is fundamentally harder: no deterministic online algorithm against an adaptive adversary, and no randomized online algorithm against a non-adaptive adversary, admits a bounded competitive ratio, even for two agents and four houses. We complement these impossibilities by showing that exact online subsidy minimization is possible whenever there is at most one extra house beyond the number of agents, and that this guarantee is best possible with respect to the number of extra houses. Finally, we develop learning-augmented algorithms that recover the offline optimum under accurate predictions while providing explicit robustness guarantees when predictions are inaccurate.

发表机构

• University of Oxford（牛津大学）
• National University of Singapore（新加坡国立大学）
• Carleton University（卡尔顿大学）

机构由 AI 辅助整理，请以论文原文为准。