Sampling labeled data for anomaly detection
I guess it depends on how you define an anomaly. If you already know and are sure that everything other than k_max can be defined as an anomaly then sure what you mention makes sense, assuming the fact that there is not a significant overlap between k_max and other classes in your feature space. I would train an auto encoder and learn an error function, classify anything that doesn't fit the error bounds as anomalous. 

If you don't know what should be considered an anomaly, I would suggest looking at the Isolation Forrest Algorithm (https://cs.nju.edu.cn/zhouzh/zhouzh.files/publication/icdm08b.pdf) which is a tree based method used for outlier detection. This would allow you to use an unsupervised (untagged with classes) dataset and figure out what should be considered as a 'clean/healthy' example for your anomaly detection algorithm and the outliers can be used as anomalous examples. 

Here is another article that you might find useful, trying to do a similar thing I am trying to suggest here: https://towardsdatascience.com/anomaly-detection-for-dummies-15f148e559c1