Classical false discovery rate (FDR) controlling procedures offer strong and interpretable guarantees but often lack flexibility to work with complex data. By contrast, machine learning-based classification algorithms have superior performances on modern datasets but typically fall short of error-controlling guarantees. In this paper, we make these two meet by introducing a new adaptive novelty detection procedure with FDR control, called AdaDetect. We illustrate our approach with classical real-world datasets, for which random forest and neural network versions of AdaDetect are particularly efficient.