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For a convex class of functions $F$, a regularization functions $\Psi(\cdot)$ and given the random data $(X_i, Y_i)_{i=1}^N$, we study estimation properties of regularization procedures of the form \begin{equation*} \hat f \in {\rm argmin}_{f\in F}\Big(\frac{1}{N}\sum_{i=1}^N\big(Y_i-f(X_i)\big)^2+\lambda \Psi(f)\Big) \end{equation*} for some well chosen regularization parameter $\lambda$.
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