Solution (source code)

= Solution

The Rademacher contraction lemma for ReLU (which is 1-Lipschitz and vanishes at zero), duality between $\ell_1$ and $\ell_\infty$, and part (d) give $\mathcal R_n(\mathcal H)\le2\lambda\sqrt{2\log(2p)/n}$. Combining with part (c) gives the claimed $4\lambda\sqrt{2\log(2p)}/\sqrt n$.