Fund for Innovation and Success in Higher Education Act or the FINISH Act This bill establishes and revises programs to increase access to higher education for high-need students, increase their graduation rates, improve the efficiency of postsecondary education, and evaluate higher education programs. Specifically, the bill authorizes the Department of Education to award grants to institutions of higher education (IHEs) and other entities to develop and implement evidence-based innovations, including pay-for-success initiatives, in order to improve postsecondary access and increase graduation rates of high-need students; approve up to five pay-for-success pilot initiatives each fiscal year to allow IHEs and private entities to use grants for improvement of student outcomes; and independently evaluate the effectiveness and efficiency of all higher education grant programs. The bill also encourages IHEs to make all forms of postsecondary instructional content, including open educational resources (e.g., textbooks), widely available. Open educational resources either reside in the public domain or have been released under a copyright license that permits their free use, reuse, modification, and sharing with others.