Parameter-Free FISTA by Adaptive Restart and Backtracking
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AUJOL, Jean-François | |
| hal.structure.identifier | Morphologie et Images [MORPHEME] | |
| dc.contributor.author | CALATRONI, Luca | |
| hal.structure.identifier | Institut National des Sciences Appliquées - Toulouse [INSA Toulouse] | |
| dc.contributor.author | DOSSAL, Charles | |
| hal.structure.identifier | Institut National des Sciences Appliquées - Toulouse [INSA Toulouse] | |
| dc.contributor.author | LABARRIÈRE, Hippolyte | |
| hal.structure.identifier | Institut National des Sciences Appliquées - Toulouse [INSA Toulouse] | |
| hal.structure.identifier | Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes [LAAS-ROC] | |
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| dc.contributor.author | RONDEPIERRE, Aude | |
| dc.date.accessioned | 2024-04-04T02:33:32Z | |
| dc.date.available | 2024-04-04T02:33:32Z | |
| dc.date.created | 2023-07 | |
| dc.date.issued | 2023-07-27 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190489 | |
| dc.description.abstractEn | We consider a combined restarting and adaptive backtracking strategy for the popular Fast IterativeShrinking-Thresholding Algorithm frequently employed for accelerating the convergence speed of large-scale structured convex optimization problems. Several variants of FISTA enjoy a provable linear convergence rate for the function values $F(x_n)$ of the form $\mathcal{O}( e^{-K\sqrt{\mu/L}~n})$ under the prior knowledge of problem conditioning, i.e. of the ratio between the (\L ojasiewicz) parameter $\mu$ determining the growth of the objective function and the Lipschitz constant $L$ of its smooth component. These parameters are nonetheless hard to estimate in many practical cases. Recent works address the problem by estimating either parameter via suitable adaptive strategies. In our work both parameters can be estimated at the same time by means of an algorithmic restarting scheme where, at each restart, a non-monotone estimation of $L$ is performed. For this scheme, theoretical convergence results are proved, showing that a $\mathcal{O}( e^{-K\sqrt{\mu/L}n})$ convergence speed can still be achieved along with quantitative estimates of the conditioning. The resulting Free-FISTA algorithm is therefore parameter-free. Several numerical results are reported to confirm the practical interest of its use in many exemplar problems. | |
| dc.description.sponsorship | Mathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond - ANR-19-CE23-0017 | |
| dc.language.iso | en | |
| dc.subject.en | Composite optimization | |
| dc.subject.en | Restart | |
| dc.subject.en | Backtracking | |
| dc.subject.en | Lojasiewicz property | |
| dc.subject.en | Lipschitz constant | |
| dc.subject.en | Acceleration | |
| dc.title.en | Parameter-Free FISTA by Adaptive Restart and Backtracking | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| dc.identifier.arxiv | 2206.06853 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04172497 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04172497v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2023-07-27&rft.au=AUJOL,%20Jean-Fran%C3%A7ois&CALATRONI,%20Luca&DOSSAL,%20Charles&LABARRI%C3%88RE,%20Hippolyte&RONDEPIERRE,%20Aude&rft.genre=preprint |
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