TY - GEN
T1 - Geometrically convergent distributed optimization with uncoordinated step-sizes
AU - Nedich, Angelia
AU - Olshevsky, Alex
AU - Shi, Wei
AU - Uribe, Cesar A.
N1 - Funding Information:
This research is supported partially by the National Science Foundation under grants CNS 15-44953 and AFOSR FA-95501510394.
Publisher Copyright:
© 2017 American Automatic Control Council (AACC).
PY - 2017/6/29
Y1 - 2017/6/29
N2 - A recent algorithmic family for distributed optimization, DIGing's, have been shown to have geometric convergence over time-varying undirected/directed graphs [1]. Nevertheless, an identical step-size for all agents is needed. In this paper, we study the convergence rates of the Adapt-Then-Combine (ATC) variation of the DIGing algorithm under uncoordinated step-sizes. We show that the ATC variation of DIGing algorithm converges geometrically fast even if the step-sizes are different among the agents. In addition, our analysis implies that the ATC structure can accelerate convergence compared to the distributed gradient descent (DGD) structure which has been used in the original DIGing algorithm.
AB - A recent algorithmic family for distributed optimization, DIGing's, have been shown to have geometric convergence over time-varying undirected/directed graphs [1]. Nevertheless, an identical step-size for all agents is needed. In this paper, we study the convergence rates of the Adapt-Then-Combine (ATC) variation of the DIGing algorithm under uncoordinated step-sizes. We show that the ATC variation of DIGing algorithm converges geometrically fast even if the step-sizes are different among the agents. In addition, our analysis implies that the ATC structure can accelerate convergence compared to the distributed gradient descent (DGD) structure which has been used in the original DIGing algorithm.
UR - http://www.scopus.com/inward/record.url?scp=85027031271&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85027031271&partnerID=8YFLogxK
U2 - 10.23919/ACC.2017.7963560
DO - 10.23919/ACC.2017.7963560
M3 - Conference contribution
AN - SCOPUS:85027031271
T3 - Proceedings of the American Control Conference
SP - 3950
EP - 3955
BT - 2017 American Control Conference, ACC 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 American Control Conference, ACC 2017
Y2 - 24 May 2017 through 26 May 2017
ER -