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Accelerated Forward-Backward Optimization Using Deep Learning
Lund Univ, Dept Automat Control, S-22363 Lund, Sweden..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-6648-2378
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1118-6483
DeepMind, London, England..
2024 (English)In: SIAM Journal on Optimization, ISSN 1052-6234, E-ISSN 1095-7189, Vol. 34, no 2, p. 1236-1263Article in journal (Refereed) Published
Abstract [en]

We propose several deep -learning accelerated optimization solvers with convergence guarantees. We use ideas from the analysis of accelerated forward -backward schemes like FISTA, but instead of the classical approach of proving convergence for a choice of parameters, such as a step -size, we show convergence whenever the update is chosen in a specific set. Rather than picking a point in this set using some predefined method, we train a deep neural network to pick the best update within a given space. Finally, we show that the method is applicable to several cases of smooth and nonsmooth optimization and show superior results to established accelerated solvers.

Place, publisher, year, edition, pages
Society for Industrial & Applied Mathematics (SIAM) , 2024. Vol. 34, no 2, p. 1236-1263
Keywords [en]
convex optimization, deep learning, proximal-gradient algorithm, inverse problems
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-345940DOI: 10.1137/22M1532548ISI: 001196808600001Scopus ID: 2-s2.0-85190534496OAI: oai:DiVA.org:kth-345940DiVA, id: diva2:1854686
Note

QC 20240426

Available from: 2024-04-26 Created: 2024-04-26 Last updated: 2024-04-26Bibliographically approved

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Rudzusika, JevgenijaÖktem, Ozan

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