  In this paper, we consider the problem of black box continuous submodular
maximization where we only have access to the function values and no
information about the derivatives is provided. For a monotone and continuous
DR-submodular function, and subject to a bounded convex body constraint, we
propose Black-box Continuous Greedy, a derivative-free algorithm that provably
achieves the tight $[(1-1/e)OPT-\epsilon]$ approximation guarantee with
$O(d/\epsilon^3)$ function evaluations. We then extend our result to the
stochastic setting where function values are subject to stochastic zero-mean
noise. It is through this stochastic generalization that we revisit the
discrete submodular maximization problem and use the multi-linear extension as
a bridge between discrete and continuous settings. Finally, we extensively
evaluate the performance of our algorithm on continuous and discrete submodular
objective functions using both synthetic and real data.
