期刊
MATHEMATICAL PROGRAMMING
卷 187, 期 1-2, 页码 409-457出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-020-01487-0
关键词
Distributed optimization; Stochastic optimization; Convex programming; Communication networks
类别
资金
- NSF [CCF-1717391]
- ONR [N00014-16-1-2245]
- Shenzhen Research Institute of Big Data (SRIBD) Startup Fund [JCYJ-SP2019090001]
This paper studies the problem of distributed multi-agent optimization and considers DSGT and GSGT methods. The results show that DSGT has good convergence performance, and when the network is well-connected, GSGT incurs lower communication costs while maintaining similar computational costs.
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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