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Title: On the Convergence of NEAR-DGD for Nonconvex Optimization with Second Order Guarantees
We consider the setting where the nodes in an undirected, connected network collaborate 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 a distributed first order method which permits adjusting the amount of communication between nodes relative to the amount of computation performed locally in order to balance convergence accuracy and total application cost. In this work, we generalize the convergence properties of a variant of NEAR-DGD from the strongly convex to the nonconvex case. Under mild assumptions, we show convergence to minimizers of a custom Lyapunov function. Moreover, we demonstrate that the gap between those minimizers and the second order stationary solutions of the original problem can become arbitrarily small depending on the choice of algorithm parameters. Finally, we accompany our theoretical analysis with a numerical experiment to evaluate the empirical performance of NEAR-DGD in the nonconvex setting.  more » « less
Award ID(s):
Author(s) / Creator(s):
Date Published:
Journal Name:
2021 60th IEEE Conference on Decision and Control (CDC)
Page Range / eLocation ID:
259 to 264
Medium: X
Sponsoring Org:
National Science Foundation
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