  We prove that the automorphism group of every infinitely-ended finitely
generated group is acylindrically hyperbolic. In particular
$\mathrm{Aut}(\mathbb{F}_n)$ is acylindrically hyperbolic for every $n\ge 2$.
More generally, if $G$ is a group which is not virtually cyclic, and hyperbolic
relative to a finite collection $\mathcal{P}$ of finitely generated proper
subgroups, then $\mathrm{Aut}(G,\mathcal{P})$ is acylindrically hyperbolic. As
a consequence, a free-by-cyclic group $\mathbb{F}_n\rtimes_{\varphi}\mathbb{Z}$
is acylindrically hyperbolic if and only if $\varphi$ has infinite order in
$\mathrm{Out}(\mathbb{F}_n)$.
