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We consider the setting where the nodes of an undirected, connected networkcollaborate to solve a shared objective modeled as the sum of smooth functions.We assume that each summand is privately known by a unique node. NEAR-DGD is adistributed first order method which permits adjusting the amount ofcommunication between nodes relative to the amount of computation performedlocally in order to balance convergence accuracy and total application cost. Inthis work, we generalize the convergence properties of a variant of NEAR-DGDfrom the strongly convex to the nonconvex case. Under mild assumptions, we showconvergence to minimizers of a custom Lyapunov function. Moreover, wedemonstrate that the gap between those minimizers and the second orderstationary solutions of the original problem can become arbitrarily smalldepending on the choice of algorithm parameters. Finally, we accompany ourtheoretical analysis with a numerical experiment to evaluate the empiricalperformance of NEAR-DGD in the nonconvex setting.

On the Convergence of NEAR-DGD for Nonconvex Optimization with Second Order Guarantees