High Entropy Alloys are alloys that contain multiple principal alloying elements. While many HEAs have been shown to have unique properties, their discovery has been largely done through costly and time-consuming trial-and-error approaches, with only an infinitesimally small fraction of the entire possible composition space having been explored. In this talk, we will present a recently developed framework that has mapped the problem of exploring the HEA space to a Constraint Satisfaction Problem (CSP), whose solution is, in turn, a one-class classifier implemented as a Support Vector Data Descriptor (SVDD). The resulting algorithm is used to discover regions in the HEA Composition-Temperature space that satisfy desired phase constitution requirements that essentially are mathematical representations of alloy specifications. The framework is capable of identifying regions in the HEA space with arbitrary phase constitution attributes. We demonstrate, as an example, the targeted discovery of precipitation strengthened HEAs.