Distributed stochastic gradient tracking methods

By Shi Pu, Angelia Nedić. Mathematical programming, 2018

380 citations recorded by the source corpus.

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 (DSGT) and a gossip-like stochastic gradient tracking method (GSGT). 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 stepsize choice). Under DSGT, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size n, which is a comparable performance to a centralized stochastic gradient algorithm. Moreover, we show that when the network is well-connected, GSGT incurs lower communication cost than DSGT while maintaining a similar computational cost. Numerical example further demonstrates the effectiveness of the proposed methods.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/67f9ed5384c542a0ccd2c4f9e533809edbd406a3

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Citations in the corpus

Push–Pull Gradient Methods for Distributed Optimization in Networks (2018, background): “References [31], [32] considered a stochastic variant of problem (1) in asynchronous networks.”
A Non-Asymptotic Analysis of Network Independence for Distributed Stochastic Gradient Descent (2019, background): “Recently, distributed implementation of stochastic gradient algorithms has received considerable interest [37, 41, 12, 3, 5, 42, 6, 7, 22, 17, 18, 30, 31, 38, 40, 14, 33, 29, 44, 1].”
A Sharp Estimate on the Transient Time of Distributed Stochastic Gradient Descent (2019, methodology): “The work in [48] considered a distributed stochastic gradient tracking method, which performs as well as centralized SGD under a small enough constant stepsize.”
Accelerated Distributed Nesterov Gradient Descent (2017, background): “More recent work [23]– [35] have improved these results to achieve linear convergence rates for strongly convex and smooth functions, or O( (1)t ) convergence rates for convex and smooth functions, which match the centralized gradient descent method as well.”