Before revision:  second, we    exploit structural properties of these algorithms and generalize them to the black-box setting. 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:  second, we exploit structural properties of (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.