Variance reduced stochastic optimization over directed graphs with row and column stochastic weights

• URL: http://arxiv.org/abs/2202.03346v1
• Date: Mon, 7 Feb 2022 16:44:48 GMT
• Title: Variance reduced stochastic optimization over directed graphs with row and column stochastic weights
• Authors: Muhammad I. Qureshi, Ran Xin, Soummya Kar, Usman A. Khan
• Abstract summary: AB-SAGA is a finite-sum distributed over strongly convex functions. We show that for a constant step-size, AB-SAGA converges linearly to the global optimal.
• Score: 18.53372294049107
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper proposes AB-SAGA, a first-order distributed stochastic optimization method to minimize a finite-sum of smooth and strongly convex functions distributed over an arbitrary directed graph. AB-SAGA removes the uncertainty caused by the stochastic gradients using a node-level variance reduction and subsequently employs network-level gradient tracking to address the data dissimilarity across the nodes. Unlike existing methods that use the nonlinear push-sum correction to cancel the imbalance caused by the directed communication, the consensus updates in AB-SAGA are linear and uses both row and column stochastic weights. We show that for a constant step-size, AB-SAGA converges linearly to the global optimal. We quantify the directed nature of the underlying graph using an explicit directivity constant and characterize the regimes in which AB-SAGA achieves a linear speed-up over its centralized counterpart. Numerical experiments illustrate the convergence of AB-SAGA for strongly convex and nonconvex problems.

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