The following VC dimension bound was established in this [answer][1] to [VC dimension of a certain derived class of binary functions](https://mathoverflow.net/questions/420474/vc-dimension-of-a-certain-derived-class-of-binary-functions),
$$
\operatorname{VCdim}(H) \le 2\cdot \operatorname{VCdim}(\operatorname{SG}(F)),
$$
where $\operatorname{SG}(F) := \{\{x \in X \mid f(x) \le 0\} \mid f \in F\}$ is the *subgraph* of $F$.

On the other hand, it's well-known that Rademacher complexity can be bounded via VC dimension like so.
$$
\mathbb E\, R_n(H) \lesssim\sqrt{\dfrac{\operatorname{VCdim}(H)}{n}}.
$$

We conclude that
$$
\mathbb E\,R_n(H) \lesssim \sqrt{\frac{\operatorname{VCdim}(\operatorname{SG}(F))}{n}}.
$$

In particular, because $\operatorname{VCdim}(\operatorname{SG}(F_{\text{lin}})) = d$, we conclude that

$$
\mathbb E\,\widetilde R_n(F_{\text{lin}}) \lesssim \sqrt{\frac{d}{n}}.
$$


  [1]: https://mathoverflow.net/a/420482/78539