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arXiv · 1809.08694

Second-order Guarantees of Distributed Gradient Algorithms

Amir Daneshmand·Gesualdo Scutari·Vyacheslav Kungurtsev
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Abstract

We consider distributed smooth nonconvex unconstrained optimization over networks, modeled as a connected graph. We examine the behavior of distributed gradient-based algorithms near strict saddle points. Specifically, we establish that (i) the renowned Distributed Gradient Descent (DGD) algorithm likely converges to a neighborhood of a Second-order Stationary (SoS) solution; and (ii) the more recent class of distributed algorithms based on gradient tracking--implementable also over digraphs--likely converges to exact SoS solutions, thus avoiding (strict) saddle-points. Furthermore, new convergence rate results to first-order critical points is established for the latter class of algorithms.

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Amir Daneshmand, Gesualdo Scutari, Vyacheslav Kungurtsev. 2018-09-23. Second-order Guarantees of Distributed Gradient Algorithms. https://arxiv.org/abs/1809.08694

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