Before revision:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and(2) there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.
After revision:  These key properties are:(1) the algorithms produce ``simple'' exponential families of black-box strategies, and there exist\emph{efficient ways to extend their output to the black-box case, which also preserve the approximation ratio exactly.