Distributed stochastic gradient tracking methods

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 ha...

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Vydáno v:Mathematical programming Ročník 187; číslo 1-2; s. 409 - 457
Hlavní autoři: Pu, Shi, Nedić, Angelia
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2021
Springer Nature B.V
Témata:
Algorithms
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Computing costs
Cost function
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Multiagent systems
Numerical Analysis
Optimization
Theoretical
Tracking
68Q25
Distributed optimization
90C25
90C15
Stochastic optimization
Communication networks
Convex programming
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí: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.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-020-01487-0