Title: One-Vs-All AUC Maximization: an effective solution to the low-resource named entity recognition problem. Abstract: Named entity recognition (NER), a sequence labelling/token classification task, has been traditionally considered a multi-class classification problem, the learning objective of which is to either optimise the multi-class cross entropy loss (CE) or train a conditional random field (CRF). However, these standard learning objectives, though scalable to large NER datasets and used in state-of-the-art work, largely ignore the problem of imbalanced label distributions that is inherent in all NER corpora. We show this leads to degraded performance in low-resource settings. While reformulating this standard multi-class labelling problem as a one-vs-all (OVA) learning problem, we propose to optimise the NER model with an AUC-based alternative loss function that is more capable of handling imbalanced datasets. As OVA often leads to a higher training time compared to the standard multi-class setting, we also develop two training strategies, one trains together the labels that share similar linguistic characteristics, and another employs a meta-learning approach to speed convergence. In order to motivate some of our experiments and better interpret the results, we also develop a Bayesian theory for what is the  AUC function during learning. Experimental results under low-resource NER settings from benchmark corpora show that our methods can achieve consistently better performance compared with the learning objectives commonly used in NER. We also give evidence that our methods are robust and agnostic to the underlying NER embeddings, models, domains, and label distributions. The code to replicate this work will be released upon the publication of this paper.