Impact of unlabelled documents for label prediction via SVM
It's a slight variation on your problem as described, but if your goal is to build a good model for predicting documents labeled $L$, I would initially formulate this as a recommender system problem, until you've reached a desirable point in the learning curve of your system. I did exactly this in a publication a few years back. In my approach, all labeled documents are used to train the SVM, while all those unlabeled are used for classifying. I use the signed margin distance of each classified document for ranking, and take the top-$n$ as the next $n$ documents the reviewers should assign a label $\in(L, L_{not})$. A side effect of this process is that you get to iteratively evaluate the performance of your classifier as you add new labeled documents to the model, which should get you what you need. If this approach sounds useful to you, I recommend looking over my paper, as I describe some performance metrics useful for this, in addition to outlining the specific procedure to use that will ensure you're not biasing your model.