Strongly convex optimization error bounds

Suppose I want to minimize a function $G(f)$ using first order strongly convex methods and I get a solution $f^*$, where we restrict our solution set to strongly convex $f$. Now let $f_0$ be the theoretical minimizer for $G(f)$, not necessarily strongly convex.

Are there results out there that discuss how to bound $G(f^*)-G(f_0)$? We can assume our functions are smooth, but mainly I just want to know if there are any results out there.