38 C.F.R. § 21.5800
(a) Courses permitted. An individual may receive educational assistance and subsistence allowance only while receiving instruction in a postsecondary course offered at any institution in the United States (including the District of Columbia, the Commonwealth of Puerto Rico, Guam and the U.S. Virgin Islands) that is accredited by a nationally recognized accrediting agency or association or by an accrediting agency or association recognized by the Secretary of Education.
(Authority: 10 U.S.C. 2142)
(b) Courses precluded. An individual shall receive neither educational assistance nor subsistence allowance while pursuing any of the following courses:
(4) Courses which do not require the student to receive instruction at the institution. These include—
(iii) Courses offered through independent study.
(Authority: 10 U.S.C. 2143)