A fast randomized incremental gradient method for decentralized non-convex optimization

• URL: http://arxiv.org/abs/2011.03853v3
• Date: Thu, 30 Sep 2021 19:42:31 GMT
• Title: A fast randomized incremental gradient method for decentralized non-convex optimization
• Authors: Ran Xin and Usman A. Khan and Soummya Kar
• Abstract summary: We analyze a single-time randomized method called GT-SAGA GTSAGA for batch non- finite-sum context problems. We show the almost sure convergence of GT-SAGA to a first-order gradient stationary point.
• Score: 19.540926205375857
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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