TY - GEN
T1 - Distributed subgradient methods and quantization effects
AU - Nedić, Angelia
AU - Olshevsky, Alex
AU - Ozdaglar, Asuman
AU - Tsitsiklis, John N.
PY - 2008
Y1 - 2008
N2 - We consider a convex unconstrained optimization problem that arises in a network of agents whose goal is to cooperatively optimize the sum of the individual agent objective functions through local computations and communications. For this problem, we use averaging algorithms to develop distributed subgradient methods that can operate over a timevarying topology. Our focus is on the convergence rate of these methods and the degradation in performance when only quantized information is available. Based on our recent results on the convergence time of distributed averaging algorithms, we derive improved upper bounds on the convergence rate of the unquantized subgradient method. We then propose a distributed subgradient method under the additional constraint that agents can only store and communicate quantized information, and we provide bounds on its convergence rate that highlight the dependence on the number of quantization levels.
AB - We consider a convex unconstrained optimization problem that arises in a network of agents whose goal is to cooperatively optimize the sum of the individual agent objective functions through local computations and communications. For this problem, we use averaging algorithms to develop distributed subgradient methods that can operate over a timevarying topology. Our focus is on the convergence rate of these methods and the degradation in performance when only quantized information is available. Based on our recent results on the convergence time of distributed averaging algorithms, we derive improved upper bounds on the convergence rate of the unquantized subgradient method. We then propose a distributed subgradient method under the additional constraint that agents can only store and communicate quantized information, and we provide bounds on its convergence rate that highlight the dependence on the number of quantization levels.
UR - http://www.scopus.com/inward/record.url?scp=62949102367&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2008.4738860
DO - 10.1109/CDC.2008.4738860
M3 - Conference contribution
AN - SCOPUS:62949102367
SN - 9781424431243
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4177
EP - 4184
BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 47th IEEE Conference on Decision and Control, CDC 2008
Y2 - 9 December 2008 through 11 December 2008
ER -