# Substitution Function

This is a function that is used in Strong and Weak Aggregating Algorithms to make their prediction. They mix losses of the experts using their weights, and receive the so-called generalized prediction. It is not always a real prediction, and the substitution function is needed to make it. The substitution function {$S$} is such a function that for {$\gamma=S(g)$} the {$\lambda(\omega,\gamma) \le g(\omega)$} for all {$\omega \in \Omega$}. For various loss functions substitution functions are different.