  In this paper, we show that the derived Picard group of a homologically
smooth Koszul connected cochain DG algebra is isomorphic to the opposite group
of the derived Picard group of its finite dimensional local Ext-algebra. As
applications, we compute the derived Picard groups of some important DG
algebras such as trivial DG polynomial algebras, trivial DG free algebras and
several non-trivial DG down-up algebras and DG free algebras.
