  In this paper, we consider the unconstrained submodular maximization problem.
We propose the first algorithm for this problem that achieves a tight
$(1/2-\varepsilon)$-approximation guarantee using $\tilde{O}(\varepsilon^{-1})$
adaptive rounds and a linear number of function evaluations. No previously
known algorithm for this problem achieves an approximation ratio better than
$1/3$ using less than $\Omega(n)$ rounds of adaptivity, where $n$ is the size
of the ground set. Moreover, our algorithm easily extends to the maximization
of a non-negative continuous DR-submodular function subject to a box constraint
and achieves a tight $(1/2-\varepsilon)$-approximation guarantee for this
problem while keeping the same adaptive and query complexities.
