We propose a non-iterative method to optimize pseudo-labeling thresholds for learning object detection from a collection of low-cost datasets, each of which is annotated for only a subset of all the object classes. A popular approach to this problem is first to train teacher models and then to use their confident predictions as pseudo ground-truth labels when training a student model. To obtain the best result, however, thresholds for prediction confidence must be adjusted. This process typically involves iterative search and repeated training of student models and is time-consuming. Therefore, we develop a method to optimize the thresholds without iterative optimization by maximizing the $F_\beta$-score on a validation dataset, which measures the quality of pseudo labels and can be measured without training a student model. We experimentally demonstrate that our proposed method achieves an mAP comparable to that of grid search on the COCO and VOC datasets.