Distributed Stochastic Optimization Framework for Large-Scale Non-Convex Stochastic Problems
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 highly 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 associated control variable in parallel, by solving a low-complexity convex sub-problem 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, numerical results show that the proposed method can significantly outperform the state-of-the-art methods in the literature in terms of the convergence speed while having the same or lower complexity and storage requirement.