F-Divergence

An $\text{emph}f-divergence$ between $P$ and $Q$ is defined via a convex function

$$f:(0,\infty )\to \mathbb{R},f(1)=0,$$

by

$$D_f(P\Vert Q)=\int f(r(x))dQ(x)={\mathbb{E}}_{x\sim Q}\left[f\left(\frac{p(x)}{q(x)}\right)\right].$$

Different choices of $f$ yield different familiar divergences.

Difference with KL Divergence?

KL divergence is a special case of the KL divergence, where $f(t)=t\log t$.