Randomized gradient-free distributed online optimization via a dynamic regret analysis
This work considers an online distributed optimization problem, with a group of agents whose local objective functions vary with time. Moreover, the value of the objective function is revealed to the corresponding agent after the decision is executed per time-step. Thus, each agent can only update t...
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sg-ntu-dr.10356-1706972023-09-26T06:06:18Z Randomized gradient-free distributed online optimization via a dynamic regret analysis Pang, Yipeng Hu, Guoqiang School of Electrical and Electronic Engineering Engineering::Electrical and electronic engineering Online Convex Optimization Distributed Algorithms This work considers an online distributed optimization problem, with a group of agents whose local objective functions vary with time. Moreover, the value of the objective function is revealed to the corresponding agent after the decision is executed per time-step. Thus, each agent can only update the decision variable based on the revealed value and information collected from the neighbors, without the knowledge on the explicit expression of the objective function. To solve this problem, an online gradient-free distributed projected gradient descent (DPGD) algorithm is presented, where each agent locally approximates the gradient based on two point values. With some standard assumptions on the communication graph and the objective functions, we provide the bound for the dynamic regret as a function of the minimizer path length, step-size and smoothing parameter. Under appropriate selections of the step-size and smoothing parameter, we prove that the dynamic regret is sublinear with respect to the time duration T if the minimizer path length also grows sublinearly. Finally, the effectiveness of the proposed algorithm is illustrated through numerical simulations. 2023-09-26T02:58:40Z 2023-09-26T02:58:40Z 2023 Journal Article Pang, Y. & Hu, G. (2023). Randomized gradient-free distributed online optimization via a dynamic regret analysis. IEEE Transactions On Automatic Control, 1-8. https://dx.doi.org/10.1109/TAC.2023.3237975 0018-9286 https://hdl.handle.net/10356/170697 10.1109/TAC.2023.3237975 2-s2.0-85147281503 1 8 en IEEE Transactions on Automatic Control © 2023 IEEE. All rights reserved. |
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Engineering::Electrical and electronic engineering Online Convex Optimization Distributed Algorithms Pang, Yipeng Hu, Guoqiang Randomized gradient-free distributed online optimization via a dynamic regret analysis |
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This work considers an online distributed optimization problem, with a group of agents whose local objective functions vary with time. Moreover, the value of the objective function is revealed to the corresponding agent after the decision is executed per time-step. Thus, each agent can only update the decision variable based on the revealed value and information collected from the neighbors, without the knowledge on the explicit expression of the objective function. To solve this problem, an online gradient-free distributed projected gradient descent (DPGD) algorithm is presented, where each agent locally approximates the gradient based on two point values. With some standard assumptions on the communication graph and the objective functions, we provide the bound for the dynamic regret as a function of the minimizer path length, step-size and smoothing parameter. Under appropriate selections of the step-size and smoothing parameter, we prove that the dynamic regret is sublinear with respect to the time duration T if the minimizer path length also grows sublinearly. Finally, the effectiveness of the proposed algorithm is illustrated through numerical simulations. |
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School of Electrical and Electronic Engineering |
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School of Electrical and Electronic Engineering Pang, Yipeng Hu, Guoqiang |
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Article |
author |
Pang, Yipeng Hu, Guoqiang |
author_sort |
Pang, Yipeng |
title |
Randomized gradient-free distributed online optimization via a dynamic regret analysis |
title_short |
Randomized gradient-free distributed online optimization via a dynamic regret analysis |
title_full |
Randomized gradient-free distributed online optimization via a dynamic regret analysis |
title_fullStr |
Randomized gradient-free distributed online optimization via a dynamic regret analysis |
title_full_unstemmed |
Randomized gradient-free distributed online optimization via a dynamic regret analysis |
title_sort |
randomized gradient-free distributed online optimization via a dynamic regret analysis |
publishDate |
2023 |
url |
https://hdl.handle.net/10356/170697 |
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1779156274522357760 |