We present the Active Galactic Nuclei (AGN) classifier as currently implemented within the Fink broker. Features were built upon summary statistics of available photometric points, as well as color estimation enabled by symbolic regression. The learning stage includes an active learning loop, used to build an optimized training sample from labels reported in astronomical catalogs. Using this method to classify real alerts from the Zwicky Transient Facility (ZTF), we achieved 98.0% accuracy, 93.8% precision and 88.5% recall. We also describe the modifications necessary to enable processing data from the upcoming Vera C. Rubin Observatory Large Survey of Space and Time (LSST), and apply them to the training sample of the Extended LSST Astronomical Time-series Classification Challenge (ELAsTiCC). Results show that our designed feature space enables high performances of traditional machine learning algorithms in this binary classification task.