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- W3141489350 abstract "We consider the setting where the nodes of 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." @default.
- W3141489350 created "2021-04-13" @default.
- W3141489350 creator A5046688950 @default.
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- W3141489350 date "2021-03-25" @default.
- W3141489350 modified "2023-09-25" @default.
- W3141489350 title "On the Convergence of NEAR-DGD for Nonconvex Optimization with Second Order Guarantees" @default.
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- W3141489350 doi "https://doi.org/10.48550/arxiv.2103.14233" @default.
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