Distributed optimization for Generalized Phase Retrieval over Networks

Ziping Zhao; Songtao Lu; Mingyi Hong; Daniel P. Palomar

doi:10.1109/ACSSC.2018.8645496

Distributed optimization for Generalized Phase Retrieval over Networks

Ziping Zhao, Songtao Lu, Mingyi Hong, Daniel P. Palomar

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Scopus citations

Abstract

In this paper, we will solve the generalized phase retrieval (PR) problem over a network, where each agent only has a subset of the measurements. The problem is formulated as minimizing the squared loss between the measurements and linear sensing intensity. To solve the problem in a distributed setting, an algorithm named distributed Wirtinger flow (DWF) is proposed. Theoretical analyses show that the proposed DWF algorithm converges to the (approximate) KKT points of the original problem globally in a sublinear rate. The performance of the DWF algorithm is numerically compared with the state-of-the-art method. Simulation results show that DWF is able to recover a high-quality solution for the original PR problem.

Original language	English (US)
Title of host publication	Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018
Editors	Michael B. Matthews
Publisher	IEEE Computer Society
Pages	48-52
Number of pages	5
ISBN (Electronic)	9781538692189
DOIs	https://doi.org/10.1109/ACSSC.2018.8645496
State	Published - Feb 19 2019
Event	52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 - Pacific Grove, United States Duration: Oct 28 2018 → Oct 31 2018

Publication series

Name	Conference Record - Asilomar Conference on Signals, Systems and Computers
Volume	2018-October
ISSN (Print)	1058-6393

Conference

Conference	52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018
Country/Territory	United States
City	Pacific Grove
Period	10/28/18 → 10/31/18

Bibliographical note

Funding Information:
This work was supported in part by the University of Minnesota and the Hong Kong University of Science and Technology via bilateral collaboration funds, and in part by the Sponsorship Scheme for Targeted Strategic Partnership FP602 of the Hong Kong University of Science and Technology. The work of Z. Zhao was supported by the Hong Kong PhD Fellowship Scheme.

Publisher Copyright:
© 2018 IEEE.

Keywords

Quadratic systems
decentralized optimization
distributed learning
nonconvex optimization
statistical learning over networks

Publisher link

10.1109/ACSSC.2018.8645496

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Cite this

Zhao, Z., Lu, S., Hong, M., & Palomar, D. P. (2019). Distributed optimization for Generalized Phase Retrieval over Networks. In M. B. Matthews (Ed.), Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 (pp. 48-52). Article 8645496 (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2018-October). IEEE Computer Society. https://doi.org/10.1109/ACSSC.2018.8645496

Distributed optimization for Generalized Phase Retrieval over Networks. / Zhao, Ziping; Lu, Songtao; Hong, Mingyi et al.
Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018. ed. / Michael B. Matthews. IEEE Computer Society, 2019. p. 48-52 8645496 (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2018-October).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Zhao, Z, Lu, S, Hong, M & Palomar, DP 2019, Distributed optimization for Generalized Phase Retrieval over Networks. in MB Matthews (ed.), Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018., 8645496, Conference Record - Asilomar Conference on Signals, Systems and Computers, vol. 2018-October, IEEE Computer Society, pp. 48-52, 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018, Pacific Grove, United States, 10/28/18. https://doi.org/10.1109/ACSSC.2018.8645496

Zhao Z, Lu S, Hong M, Palomar DP. Distributed optimization for Generalized Phase Retrieval over Networks. In Matthews MB, editor, Conference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018. IEEE Computer Society. 2019. p. 48-52. 8645496. (Conference Record - Asilomar Conference on Signals, Systems and Computers). doi: 10.1109/ACSSC.2018.8645496

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abstract = "In this paper, we will solve the generalized phase retrieval (PR) problem over a network, where each agent only has a subset of the measurements. The problem is formulated as minimizing the squared loss between the measurements and linear sensing intensity. To solve the problem in a distributed setting, an algorithm named distributed Wirtinger flow (DWF) is proposed. Theoretical analyses show that the proposed DWF algorithm converges to the (approximate) KKT points of the original problem globally in a sublinear rate. The performance of the DWF algorithm is numerically compared with the state-of-the-art method. Simulation results show that DWF is able to recover a high-quality solution for the original PR problem.",

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N2 - In this paper, we will solve the generalized phase retrieval (PR) problem over a network, where each agent only has a subset of the measurements. The problem is formulated as minimizing the squared loss between the measurements and linear sensing intensity. To solve the problem in a distributed setting, an algorithm named distributed Wirtinger flow (DWF) is proposed. Theoretical analyses show that the proposed DWF algorithm converges to the (approximate) KKT points of the original problem globally in a sublinear rate. The performance of the DWF algorithm is numerically compared with the state-of-the-art method. Simulation results show that DWF is able to recover a high-quality solution for the original PR problem.

AB - In this paper, we will solve the generalized phase retrieval (PR) problem over a network, where each agent only has a subset of the measurements. The problem is formulated as minimizing the squared loss between the measurements and linear sensing intensity. To solve the problem in a distributed setting, an algorithm named distributed Wirtinger flow (DWF) is proposed. Theoretical analyses show that the proposed DWF algorithm converges to the (approximate) KKT points of the original problem globally in a sublinear rate. The performance of the DWF algorithm is numerically compared with the state-of-the-art method. Simulation results show that DWF is able to recover a high-quality solution for the original PR problem.

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Distributed optimization for Generalized Phase Retrieval over Networks

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