TY - JOUR
T1 - Optimal distributed convex optimization on slowly time-varying graphs
AU - Rogozin, Alexander
AU - Uribe, Cesar A.
AU - Gasnikov, Alexander V.
AU - Malkovsky, Nikolay
AU - Nedic, Angelia
N1 - Funding Information: Manuscript received June 22, 2019; revised September 4, 2019 and September 8, 2019; accepted September 26, 2019. Date of publication October 24, 2019; date of current version June 12, 2020. The work of A. Nedić and C.A. Uribe was supported by the National Science Foundation under Grant CPS 15-44953. The work of A. V. Gasnikov was supported by the Russian President under Grants MD-1320.2018.1. and RFBR 18-31-20005 mol_a_ved. The work of A. V. Gasnikov and C. A. Uribe was supported by Yahoo! Research Faculty Engagement Program. (Corresponding author: César A. Uribe.) A. Rogozin is with the Moscow Institute of Physics and Technology 141701, Moscow, Russia (e-mail:,[email protected]). Publisher Copyright: © 2014 IEEE.
PY - 2020/6
Y1 - 2020/6
N2 - We study optimal distributed first-order optimization algorithms when the network (i.e., communication constraints between the agents) changes with time. This problem is motivated by scenarios where agents experience network malfunctions. We provide a sufficient condition that guarantees a convergence rate with optimal (up to logarithmic terms) dependencies on the network and function parameters if the network changes are constrained to a small percentage α of the total number of iterations. We call such networks slowly time-varying networks. Moreover, we show that Nesterov's method has an iteration complexity of Ω (equation presented) for decentralized algorithms, where κΦ is the condition number of the objective function, and χ is a worst case bound on the condition number of the sequence of communication graphs. Additionally, we provide an explicit upper bound on α in terms of the condition number of the objective function and network topologies.
AB - We study optimal distributed first-order optimization algorithms when the network (i.e., communication constraints between the agents) changes with time. This problem is motivated by scenarios where agents experience network malfunctions. We provide a sufficient condition that guarantees a convergence rate with optimal (up to logarithmic terms) dependencies on the network and function parameters if the network changes are constrained to a small percentage α of the total number of iterations. We call such networks slowly time-varying networks. Moreover, we show that Nesterov's method has an iteration complexity of Ω (equation presented) for decentralized algorithms, where κΦ is the condition number of the objective function, and χ is a worst case bound on the condition number of the sequence of communication graphs. Additionally, we provide an explicit upper bound on α in terms of the condition number of the objective function and network topologies.
KW - Accelerated method
KW - distributed optimization
KW - time-varying graph
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U2 - 10.1109/TCNS.2019.2949439
DO - 10.1109/TCNS.2019.2949439
M3 - Article
SN - 2325-5870
VL - 7
SP - 829
EP - 841
JO - IEEE Transactions on Control of Network Systems
JF - IEEE Transactions on Control of Network Systems
IS - 2
M1 - 8882272
ER -