Named entity recognition (NER), a task that identifies and categorizes named entities such as persons or organizations from text, is traditionally framed as a multi-class classification problem. However, this approach often overlooks the issues of imbalanced label distributions, particularly in low-resource settings, which is common in certain NER contexts, like biomedical NER (bioNER). To address these issues, we propose an innovative reformulation of the multi-class problem as a one-vs-all (OVA) learning problem and introduce a loss function based on the area under the receiver operating characteristic curve (AUC). To enhance the efficiency of our OVA-based approach, we propose two training strategies: one groups labels with similar linguistic characteristics, and another employs meta-learning. The superiority of our approach is confirmed by its performance, which surpasses traditional NER learning in varying NER settings.