Let $\cal{M}$ be a finite von Neumann algebra and $\cal{N}$ be a von Neumann subalgebra of $\cal{M}$.
The von Neumann  algebra $\cal{M}$ is is amenable relative to
 $\cal{N}$ if there exists a norm one projection of $<\cal{M},\cal{N}>$ onto
$\cal{M}$. See Nicolas Monod, Sorin Popa, On co-Amenability for groups and von
Neumann algebras. (https://arxiv.org/abs/math/0301348).

Question: Can we characterize  the relative amenability of  von Neumann  algebras   in terms of  first Hochschild cohomology group?