This paper proposes a distributed algorithm over quantized communication networks for unconstrained optimization with smooth cost functions. We consider a multi-agent system whose local communication is represented by a fixed and connected graph. Each agent updates a state and an auxiliary variable for the estimates of the optimal solution and the average gradient of the entire cost function by a consensus-based optimization algorithm. The state and the auxiliary variable are sent to neighbor agents through a uniform quantizer. We show a convergence rate of the proposed algorithm with respect to the errors between the cost at the time-averaged state and the optimal cost. Numerical examples show that the estimated solution by the proposed quantized algorithm converges to the optimal solution.
Naoki HAYASHI
Osaka University
Yuichi KAJIYAMA
Osaka University
Shigemasa TAKAI
Osaka University
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Naoki HAYASHI, Yuichi KAJIYAMA, Shigemasa TAKAI, "Consensus-Based Quantized Algorithm for Convex Optimization with Smooth Cost Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 2, pp. 435-442, February 2020, doi: 10.1587/transfun.2019MAP0008.
Abstract: This paper proposes a distributed algorithm over quantized communication networks for unconstrained optimization with smooth cost functions. We consider a multi-agent system whose local communication is represented by a fixed and connected graph. Each agent updates a state and an auxiliary variable for the estimates of the optimal solution and the average gradient of the entire cost function by a consensus-based optimization algorithm. The state and the auxiliary variable are sent to neighbor agents through a uniform quantizer. We show a convergence rate of the proposed algorithm with respect to the errors between the cost at the time-averaged state and the optimal cost. Numerical examples show that the estimated solution by the proposed quantized algorithm converges to the optimal solution.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019MAP0008/_p
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@ARTICLE{e103-a_2_435,
author={Naoki HAYASHI, Yuichi KAJIYAMA, Shigemasa TAKAI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Consensus-Based Quantized Algorithm for Convex Optimization with Smooth Cost Functions},
year={2020},
volume={E103-A},
number={2},
pages={435-442},
abstract={This paper proposes a distributed algorithm over quantized communication networks for unconstrained optimization with smooth cost functions. We consider a multi-agent system whose local communication is represented by a fixed and connected graph. Each agent updates a state and an auxiliary variable for the estimates of the optimal solution and the average gradient of the entire cost function by a consensus-based optimization algorithm. The state and the auxiliary variable are sent to neighbor agents through a uniform quantizer. We show a convergence rate of the proposed algorithm with respect to the errors between the cost at the time-averaged state and the optimal cost. Numerical examples show that the estimated solution by the proposed quantized algorithm converges to the optimal solution.},
keywords={},
doi={10.1587/transfun.2019MAP0008},
ISSN={1745-1337},
month={February},}
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TY - JOUR
TI - Consensus-Based Quantized Algorithm for Convex Optimization with Smooth Cost Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 435
EP - 442
AU - Naoki HAYASHI
AU - Yuichi KAJIYAMA
AU - Shigemasa TAKAI
PY - 2020
DO - 10.1587/transfun.2019MAP0008
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 2020
AB - This paper proposes a distributed algorithm over quantized communication networks for unconstrained optimization with smooth cost functions. We consider a multi-agent system whose local communication is represented by a fixed and connected graph. Each agent updates a state and an auxiliary variable for the estimates of the optimal solution and the average gradient of the entire cost function by a consensus-based optimization algorithm. The state and the auxiliary variable are sent to neighbor agents through a uniform quantizer. We show a convergence rate of the proposed algorithm with respect to the errors between the cost at the time-averaged state and the optimal cost. Numerical examples show that the estimated solution by the proposed quantized algorithm converges to the optimal solution.
ER -