  Consider the problem of minimizing the expected value of a (possibly
nonconvex) cost function parameterized by a random (vector) variable, when the
expectation cannot be computed accurately (e.g., because the statistics of the
random variables are unknown and/or the computational complexity is
prohibitive). Classical sample stochastic gradient methods for solving this
problem may empirically suffer from slow convergence. In this paper, we propose
for the first time a stochastic parallel Successive Convex Approximation-based
(best-response) algorithmic framework for general nonconvex stochastic
sum-utility optimization problems, which arise naturally in the design of
multi-agent systems. The proposed novel decomposition enables all users to
update their optimization variables in parallel by solving a sequence of
strongly convex subproblems, one for each user. Almost surely convergence to
stationary points is proved. We then customize our algorithmic framework to
solve the stochastic sum rate maximization problem over
Single-Input-Single-Output (SISO) frequency-selective interference channels,
multiple-input-multiple-output (MIMO) interference channels, and MIMO
multiple-access channels. Numerical results show that our algorithms are much
faster than state-of-the-art stochastic gradient schemes while achieving the
same (or better) sum-rates.
