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