Lovasz extension subgradient for non-submodular functions

Question

Let $f(S) : \{0,1\}^n \to \mathbb{R}$ be a set function and let $F(z): [0,1]^n \to \mathbb{R}$ be its Lovasz extension.

If the set function $f(S)$ is submodular, then a subgradient of the Lovasz extension $F(z)$ can be computed relatively quickly (e.g. page 21 of https://www.di.ens.fr/~fbach/submodular_fbach_eth_april_2016.pdf).

I am wondering: are there any easy-to-compute formulas for a subgradient of the Lovasz extension $F(z)$ if the set function $f(S)$ is not submodular?

Thanks!