Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/164461
Title: Distributed online convex optimization with time-varying coupled inequality constraints
Authors: Yi, Xinlei
Li, Xiuxian
Xie, Lihua
Johansson, Karl H.
Keywords: Engineering::Electrical and electronic engineering
Issue Date: 2020
Source: Yi, X., Li, X., Xie, L. & Johansson, K. H. (2020). Distributed online convex optimization with time-varying coupled inequality constraints. IEEE Transactions On Signal Processing, 68, 731-746. https://dx.doi.org/10.1109/TSP.2020.2964200
Project: RG72/19
Journal: IEEE Transactions on Signal Processing
Abstract: This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex functions. A distributed online primal-dual dynamic mirror descent algorithm is proposed to solve this problem, where the local cost, regularization, and constraint functions are held privately and revealed only after each time slot. Without assuming Slater's condition, we first derive regret and constraint violation bounds for the algorithm and show how they depend on the stepsize sequences, the accumulated dynamic variation of the comparator sequence, the number of agents, and the network connectivity. As a result, under some natural decreasing stepsize sequences, we prove that the algorithm achieves sublinear dynamic regret and constraint violation if the accumulated dynamic variation of the optimal sequence also grows sublinearly. We also prove that the algorithm achieves sublinear static regret and constraint violation under mild conditions. Assuming Slater's condition, we show that the algorithm achieves smaller bounds on the constraint violation. In addition, smaller bounds on the static regret are achieved when the objective function is strongly convex. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.
URI: https://hdl.handle.net/10356/164461
ISSN: 1053-587X
DOI: 10.1109/TSP.2020.2964200
Schools: School of Electrical and Electronic Engineering 
Rights: © 2020 IEEE. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:EEE Journal Articles

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