  We study decentralized non-convex finite-sum minimization problems described
over a network of nodes, where each node possesses a local batch of data
samples. In this context, we analyze a single-timescale randomized incremental
gradient method, called GT-SAGA. GT-SAGA is computationally efficient as it
evaluates one component gradient per node per iteration and achieves provably
fast and robust performance by leveraging node-level variance reduction and
network-level gradient tracking. For general smooth non-convex problems, we
show the almost sure and mean-squared convergence of GT-SAGA to a first-order
stationary point and further describe regimes of practical significance where
it outperforms the existing approaches and achieves a network
topology-independent iteration complexity respectively. When the global
function satisfies the Polyak-Lojaciewisz condition, we show that GT-SAGA
exhibits linear convergence to an optimal solution in expectation and describe
regimes of practical interest where the performance is network
topology-independent and improves upon the existing methods. Numerical
experiments are included to highlight the main convergence aspects of GT-SAGA
in non-convex settings.
