During the reign of Emperor Manuel I Komnenos (r. 1143–1180), Alexios accompanied his father Andronikos in exile, visiting, inter alia, the Kingdom of Georgia.
The Georgian king George III, their relative, granted to Andronikos several castles in Kakhetia in the east of Georgia.
Andronikos returned to Constantinople and usurped the Byzantine crown in 1183, only to be overthrown and killed in 1185.
At one point, he was even considered by some Georgian nobles as a candidate to become a consort of the queen regnant Tamar of Georgia.
[2] Since Andronikos I had no sons by a Georgian mistress at this time, modern scholars trace the origin of this family to Alexios, but the exact origin of the family name is disputed, not least because the attested genealogy of the Andronikashvili does not commence until the 16th century.