We consider a document classification problem where document labels are absent but only relevant keywords of a target class and unlabeled documents are given. Although heuristic methods based on pseudo-labeling have been considered, theoretical understanding of this problem has still been limited. Moreover, previous methods cannot easily incorporate well-developed techniques in supervised text classification. In this paper, we propose a theoretically guaranteed learning framework that is simple to implement and has flexible choices of models, e.g., linear models or neural networks. We demonstrate how to optimize the area under the receiver operating characteristic curve (AUC) effectively and also discuss how to adjust it to optimize other well-known evaluation metrics such as the accuracy and F1-measure. Finally, we show the effectiveness of our framework using benchmark datasets.