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We show that every automorphism of the group ${𝒢}_n:=Aut\left({𝔸}^n\right)$ of polynomial automorphisms of complex affine $n$-space ${𝔸}^n={ℂ}^n$ is inner up to field automorphisms when restricted to the subgroup $T{𝒢}_n$ of tame automorphisms. This generalizes a result of Julie Deserti who proved this in dimension $n=2$ where all automorphisms are tame: $T{𝒢}_2={𝒢}_2$. The methods are different, based on arguments from algebraic group actions.