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：本文研究了在线场景下不可分割物品的公平分配问题，其中物品依次到达且必须立即分配。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）等主流公平概念，我们探讨了获取未来信息如何改变可实现保证的理论界限。在完全无信息时，即使针对近似公平性，我们证明了强不可能性结果。在归一化信息（代理人的总值）条件下，我们提出一种算法实现了优于已知结果的公平性保证，并针对更强公平概念给出了匹配的不可能性结论。在频率预测（无序价值多重集）条件下，我们设计了一种元算法，可将离线“基于份额”保证的广泛类别提升至在线场景，匹配已知最优离线界限。最后，我们为两种模型提供了学习增强变体：在含噪声总值或含噪声频率预测情形下，我们的保证具有鲁棒性，且随误差参数呈现优雅退化。