SGD can accelerate the identification of exceptional materials that may be overlooked by global AI models because it focuses on local descriptions. However, further developments are required in order to translate the SGD concept to the typical scenario of materials science, where datasets might be unbalanced, or not be representative of the whole materials space and the most important descriptive parameters are unknown. The multi-objective perspective introduced in this contribution provides an efficient framework for dealing with the compromise between generality and exceptionality in SGD. The combination of this strategy with efficient algorithms for SG search and with a systematic incorporation of new data points to better cover the materials space will further advance the AI-driven discovery of materials.