If we use a generalized quadratic loss in a SVM model, what generalization performance bounds can be derived?

Question

If we write an objective function: $$\frac{1}{2}||\vec{w}||^2 + C \sqrt{\vec{\xi}}' S \sqrt{\vec{\xi}}$$ with the usual SVM constraints, and $S_{i,j} = e^{-\gamma || \vec{x_i} - \vec{x_i}||^2}$, where $\gamma$ is an hyper-parameter, what generalization bounds can be derived?

A more detailed treatment of this problem can be found at: GQL