Rademacher excess-risk bound for empirical risk minimization

For a zero-one-valued loss class $\mathcal{F}$, the excess misclassification risk of an empirical risk minimizer $\hat{h}$ over a population minimizer $h^{\ast }$ satisfieswith probability at least $1-\delta$. The proof combines Rademacher symmetrization with the Bounded differences inequality for the supremum of the empirical excess-loss process.

The observable version isIt follows by another application of the Bounded differences inequality to the Empirical Rademacher complexity.