We study the problem of fairly allocating indivisible goods to agents in an online setting, where goods arrive sequentially and must be allocated irrevocably. Focusing on the popular fairness notions of envy-freeness, proportionality, and maximin share fairness (and their approximate variants), we investigate how access to future information changes what guarantees are achievable. Without any information, we prove strong impossibility results even for approximate fairness. With normalization information (agents' total values), we provide an algorithm that achieves stronger fairness guarantees than previously known results, and show matching impossibilities for stronger notions. With frequency predictions (value multisets without order), we design a meta-algorithm that lifts a broad class of offline ''share-based'' guarantees to the online setting, matching the best-known offline bounds. Finally, we provide learning-augmented variants of both models: under noisy totals or noisy frequency predictions, our guarantees are robust and degrade gracefully with the error parameters.

翻译：我们研究了在线环境中不可分割物品的公平分配问题，在该问题中物品依次到达且必须立即进行不可撤销的分配。聚焦于无嫉妒性、比例性和最大最小份额公平性（及其近似变体）等经典公平概念，我们探讨对未来信息的获取如何改变可实现的保障界限。在无任何信息的情况下，我们证明了即使对于近似公平性也存在强不可能性结果。在具备归一化信息（代理人的总估值）的条件下，我们提出的算法能实现比已知结果更强的公平性保障，并展示了针对更强公平概念的匹配不可能性。在具备频率预测（不含顺序的价值多重集）的条件下，我们设计了一种元算法，能将广泛的一类离线"基于份额"的保障提升至在线环境，并匹配最优的离线界限。最后，我们为两种模型都提供了学习增强变体：在存在噪声总值或噪声频率预测时，我们的保障具有鲁棒性，且随误差参数而优雅退化。