The Minerva Research initiative was created by Bush’s defense secretary: https://nap.nationalacademies.org/read/25482/chapter/3.

> The Minerva Research Initiative was launched in 2008 by Secretary of Defense Robert Gates, motivated by the recognition that DoD was underutilizing the intellectual capital of university-based social scientists

Congress doesn’t specifically appropriate money for it. It looks like Congress appropriates money for the DOD’s Basic Research Office, and money is siphoned to this initiative by the executive branch.

EDIT: Corrected which administration.