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Document-level relation extraction (RE) aims at extracting relations among entities expressed across multiple sentences, which can be viewed as a multi-label classification problem. In a typical document, most entity pairs do not express any pre-defined relation and are labeled as "none" or "no relation". For good document-level RE performance, it is crucial to distinguish such none class instances (entity pairs) from those of pre-defined classes (relations). However, most existing methods only estimate the probability of pre-defined relations independently without considering the probability of "no relation". This ignores the context of entity pairs and the label correlations between the none class and pre-defined classes, leading to sub-optimal predictions. To address this problem, we propose a new multi-label loss that encourages large margins of label confidence scores between each pre-defined class and the none class, which enables captured label correlations and context-dependent thresholding for label prediction. To gain further robustness against positive-negative imbalance and mislabeled data that could appear in real-world RE datasets, we propose a margin regularization and a margin shifting technique. Experimental results demonstrate that our method significantly outperforms existing multi-label losses for document-level RE and works well in other multi-label tasks such as emotion classification when none class instances are available for training.