Hyperfiniteness of boundary actions of acylindrically hyperbolic groups

We prove that for any countable acylidrically hyperbolic group $G$, there exists a generating set $S$ of $G$ such that the corresponding Cayley graph $\mathrm{\Gamma }(G,S)$ is hyperbolic, $\mathrm{\mid }\mathrm{\partial }\mathrm{\Gamma }(G,X)\mathrm{\mid }>2$, the natural action of $G$ on $\mathrm{\Gamma }(G,S)$ is acylindrical, and the natural action of $G$ on the Gromov boundary $\mathrm{\partial }\mathrm{\Gamma }(G,S)$ is hyperfinite. This result broadens a class of groups that admit a non-elementary acylindrical action on a hyperbolic space with hyperfinite boundary action.