Empirical Rademacher complexity
= Empirical Rademacher complexity
{c}
{title2=$\widehat{\mathcal R}$}
For a fixed sample $z_{1:n}$, the empirical Rademacher complexity is
$$
\widehat{\mathcal R}(\mathcal F(z_{1:n}))
=\mathbb E_\varepsilon\left[
\sup_{f\in\mathcal F}\frac1n\sum_{i=1}^n\varepsilon_i f(z_i)
\right].
$$
Taking its <expected value> over the sample gives $\mathcal R_n(\mathcal F)$.