发表机构
University of Oxford（牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究广义分配预算约束下离散公平分配的在线变体，确定有界密度扩展条件并获近似算法，研究资源增强及刻画保证改进，还开发学习增强框架，证明其性质及单独预测边际的不足。
AI 中文摘要
我们研究了广义分配预算约束下离散公平分配的在线变体。商品逐一到达，必须不可撤销地分配给可行的代理或慈善机构（持有所有未分配商品），公平性仅根据每个接收者捆绑包的预算可行子集来评估。首先表明，无额外结构时，即使在高度对称实例中，也没有确定性在线算法能保证对可行无嫉妒的任何固定近似。接着确定有界密度扩展作为恢复有意义保证的结构条件，得到任意物品大小的近似算法，且在常见估值和足够小的商品下，这些保证可强化到最优确定性边界。还研究了资源增强，即在线算法允许比公平基准稍大的预算，并刻画了可实现保证的改进。最后，基于预测联合价值 - 大小类型开发了学习增强框架，证明了在完美预测下的一致性、对预测误差的鲁棒性，并表明单独预测价值和大小边际不足以恢复强公平保证。
英文摘要
We study an online variant of discrete fair division under generalized assignment budget constraints. Goods arrive one at a time and must be assigned irrevocably to a feasible agent or to charity, which holds all unallocated goods, while fairness is evaluated only against budget-feasible subsets of every recipient's bundle. We first show that, without additional structure, no deterministic online algorithm can guarantee any fixed approximation to feasible envy-freeness, even in highly symmetric instances. We then identify bounded density spread as a structural condition that restores meaningful guarantees, obtaining approximation algorithms for arbitrary item sizes and showing that, under common valuations and sufficiently small goods, these guarantees can be strengthened to an optimal deterministic frontier. We further study resource augmentation, where the online algorithm is allowed slightly larger budgets than the fairness benchmark, and characterize the resulting improvement in the achievable guarantees. Finally, we develop a learning-augmented framework based on predicting joint value-size types, proving consistency under perfect predictions, robustness to prediction error, and showing that separate predictions of value and size marginals are insufficient to recover strong fairness guarantees.
