A Constant Step Stochastic Douglas-Rachford Algorithm with Application to non Separable Regularizations

Adil Salim; Pascal Bianchi; Walid Hachem

doi:10.1109/ICASSP.2018.8461469

A Constant Step Stochastic Douglas-Rachford Algorithm with Application to non Separable Regularizations

Adil Salim
, Pascal Bianchi
, Walid Hachem

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

Abstract

The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions separately. The paper investigates a stochastic version of the algorithm where both functions are random and the step size is constant. We establish that the iterates of the algorithm stay close to the set of solution with high probability when the step size is small enough. Application to structured regularization is considered.

Original language	English
Title of host publication	2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2886-2890
Number of pages	5
ISBN (Print)	9781538646588
DOIs	https://doi.org/10.1109/ICASSP.2018.8461469
Publication status	Published - 10 Sept 2018
Externally published	Yes
Event	2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Calgary, Canada Duration: 15 Apr 2018 → 20 Apr 2018

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume	2018-April
ISSN (Print)	1520-6149

Conference

Conference	2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
Country/Territory	Canada
City	Calgary
Period	15/04/18 → 20/04/18

Keywords

Douglas Rachford algorithm
Proximal methods
Stochastic optimization
Structured regularizations

Access to Document

10.1109/ICASSP.2018.8461469

Cite this

Salim, A., Bianchi, P., & Hachem, W. (2018). A Constant Step Stochastic Douglas-Rachford Algorithm with Application to non Separable Regularizations. In 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings (pp. 2886-2890). Article 8461469 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2018-April). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2018.8461469

Salim, Adil ; Bianchi, Pascal ; Hachem, Walid. / A Constant Step Stochastic Douglas-Rachford Algorithm with Application to non Separable Regularizations. 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 2886-2890 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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abstract = "The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions separately. The paper investigates a stochastic version of the algorithm where both functions are random and the step size is constant. We establish that the iterates of the algorithm stay close to the set of solution with high probability when the step size is small enough. Application to structured regularization is considered.",

keywords = "Douglas Rachford algorithm, Proximal methods, Stochastic optimization, Structured regularizations",

author = "Adil Salim and Pascal Bianchi and Walid Hachem",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 ; Conference date: 15-04-2018 Through 20-04-2018",

year = "2018",

month = sep,

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doi = "10.1109/ICASSP.2018.8461469",

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series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

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Salim, A, Bianchi, P & Hachem, W 2018, A Constant Step Stochastic Douglas-Rachford Algorithm with Application to non Separable Regularizations. in 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings., 8461469, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 2018-April, Institute of Electrical and Electronics Engineers Inc., pp. 2886-2890, 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018, Calgary, Canada, 15/04/18. https://doi.org/10.1109/ICASSP.2018.8461469

A Constant Step Stochastic Douglas-Rachford Algorithm with Application to non Separable Regularizations. / Salim, Adil; Bianchi, Pascal; Hachem, Walid.
2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2018. p. 2886-2890 8461469 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2018-April).

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

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N2 - The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions separately. The paper investigates a stochastic version of the algorithm where both functions are random and the step size is constant. We establish that the iterates of the algorithm stay close to the set of solution with high probability when the step size is small enough. Application to structured regularization is considered.

AB - The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions separately. The paper investigates a stochastic version of the algorithm where both functions are random and the step size is constant. We establish that the iterates of the algorithm stay close to the set of solution with high probability when the step size is small enough. Application to structured regularization is considered.

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KW - Proximal methods

KW - Stochastic optimization

KW - Structured regularizations

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Salim A, Bianchi P, Hachem W. A Constant Step Stochastic Douglas-Rachford Algorithm with Application to non Separable Regularizations. In 2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2018. p. 2886-2890. 8461469. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2018.8461469

A Constant Step Stochastic Douglas-Rachford Algorithm with Application to non Separable Regularizations

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