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Decentralized optimization is a promising parallel computation paradigm forlarge-scale data analytics and machine learning problems defined over a networkof nodes. This paper is concerned with decentralized non-convex compositeproblems with population or empirical risk. In particular, the networked nodesare tasked to find an approximate stationary point of the average of local,smooth, possibly non-convex risk functions plus a possibly non-differentiableextended valued convex regularizer. Under this general formulation, we proposethe first provably efficient, stochastic proximal gradient framework, calledProxGT. Specifically, we construct and analyze several instances of ProxGT thatare tailored respectively for different problem classes of interest.Remarkably, we show that the sample complexities of these instances are networktopology-independent and achieve linear speedups compared to that of thecorresponding centralized optimal methods implemented on a single node.

A Stochastic Proximal Gradient Framework for Decentralized Non-Convex  Composite Optimization: Topology-Independent Sample Complexity and  Communication Efficiency