Parallel stochastic decomposition algorithms for multi-agent systems

Yang Yang, Gesualdo Scutari, Daniel Pérez Palomar

Abstract: In a stochastic optimization problem, the objective function is given in the form of the expectation with respect to some random variables. In many applications, this expectation cannot be computed accurately (e.g., because the statistics of the random variables are unknown). The common approach followed in the literature to deal with this issue is using stochastic gradient schemes, which however suffer from slow convergence. In this paper, we propose for the first time a class of provably convergent Jacobi best-response algorithms for general nonconvex stochastic sum-utility optimization problems, which arise naturally in the design of wireless multi-user interfering 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. Finally, we customize our algorithms to solve the stochastic sum rate maximization problem over MIMO interference channels and multiple access channels. Numerical results show that our algorithms are much faster than state-of-the-art stochastic gradient schemes.