  In this paper, we consider the problem of stochastic optimization, where the
objective function is in terms of the expectation of a (possibly non-convex)
cost function that is parametrized by a random variable. While the convergence
speed is critical for many emerging applications, most existing stochastic
optimization methods suffer from slow convergence. Furthermore, the emerging
technology of parallel computing has motivated an increasing demand for
designing new stochastic optimization schemes that can handle parallel
optimization for implementation in distributed systems. We propose a fast
parallel stochastic optimization framework that can solve a large class of
possibly non-convex stochastic optimization problems that may arise in
applications with multi-agent systems. In the proposed method, each agent
updates its control variable in parallel, by solving a convex quadratic
subproblem independently. The convergence of the proposed method to the optimal
solution for convex problems and to a stationary point for general non-convex
problems is established. The proposed algorithm can be applied to solve a large
class of optimization problems arising in important applications from various
fields, such as machine learning and wireless networks. As a representative
application of our proposed stochastic optimization framework, we focus on
large-scale support vector machines and demonstrate how our algorithm can
efficiently solve this problem, especially in modern applications with huge
datasets. Using popular real-world datasets, we present experimental results to
demonstrate the merits of our proposed framework by comparing its performance
to the state-of-the-art in the literature. Numerical results show that the
proposed method can significantly outperform the state-of-the-art methods in
terms of the convergence speed while having the same or lower complexity and
storage requirement.
