期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 66, 期 5, 页码 2045-2060出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2020.3008713
关键词
Convergence; Approximation algorithms; Cost function; Sun; Minimization; Gradient methods; Big-data optimization; distributed optimization; nonconvex optimization
资金
- European Research Council under the European Union's Horizon 2020 Research and Innovation Programme [638992-OPT4SMART]
- USA National Science Foundation [CIF 1564044, CIF 1719205, CMMI 1832688]
- Army Research Office [W911NF1810238]
- U.S. Department of Defense (DOD) [W911NF1810238] Funding Source: U.S. Department of Defense (DOD)
This study focuses on distributed big-data nonconvex optimization in multiagent networks. A novel distributed solution method is proposed, where agents update one block of the entire decision vector in an uncoordinated fashion to address nonconvexity and reduce communication overhead in large-scale problems. Numerical results demonstrate the effectiveness of the algorithm and highlight the impact of block dimension on communication overhead and convergence speed.
We study distributed big-data nonconvex optimization in multiagent networks. We consider the (constrained) minimization of the sum of a smooth (possibly) nonconvex function, i.e., the agents' sum-utility, plus a convex (possibly) nonsmooth regularizer. Our interest is on big-data problems in which there is a large number of variables to optimize. If treated by means of standard distributed optimization algorithms, these large-scale problems may be intractable due to the prohibitive local computation and communication burden at each node. We propose a novel distributed solution method where, at each iteration, agents update in an uncoordinated fashion only one block of the entire decision vector. To deal with the nonconvexity of the cost function, the novel scheme hinges on successive convex approximation techniques combined with a novel blockwise perturbed push-sum consensus protocol, which is instrumental to perform local block-averaging operations and tracking of gradient averages. Asymptotic convergence to stationary solutions of the nonconvex problem is established. Finally, numerical results show the effectiveness of the proposed algorithm and highlight how the block dimension impacts on the communication overhead and practical convergence speed.
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