  This paper presents a novel Jacobi-style iteration algorithm for solving the
problem of distributed submodular maximization, in which each agent determines
its own strategy from a finite set so that the global submodular objective
function is jointly maximized. Building on the multi-linear extension of the
global submodular function, we expect to achieve the solution from a
probabilistic, rather than deterministic, perspective, and thus transfer the
considered problem from a discrete domain into a continuous domain. Since it is
observed that an unbiased estimation of the gradient of multi-linear extension
function~can be obtained by sampling the agents' local decisions, a projected
stochastic gradient algorithm is proposed to solve the problem. Our algorithm
enables the distributed updates among all individual agents and is proved to
asymptotically converge to a desirable equilibrium solution. Such an
equilibrium solution is guaranteed to achieve at least 1/2-suboptimal bound,
which is comparable to the state-of-art in the literature. Moreover, we further
enhance the proposed algorithm by handling the scenario in which agents'
communication delays are present. The enhanced algorithmic framework admits a
more realistic distributed implementation of our approach. Finally, a movie
recommendation task is conducted on a real-world movie rating data set, to
validate the numerical performance of the proposed algorithms.
