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arXiv · 1803.07741

A Distributed Stochastic Gradient Tracking Method

Shi Pu·Angelia Nedić
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Abstract

In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method. We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant step size choice). More importantly, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size, which is a comparable performance to a centralized stochastic gradient algorithm. Numerical examples further demonstrate the effectiveness of the method.

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Shi Pu, Angelia Nedić. 2018-03-21. A Distributed Stochastic Gradient Tracking Method. https://arxiv.org/abs/1803.07741

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