Parameter-Free FISTA by Adaptive Restart and Backtracking
RONDEPIERRE, Aude
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes [LAAS-ROC]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
< Reduce
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes [LAAS-ROC]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Language
en
Document de travail - Pré-publication
This item was published in
2023-07-27
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Composite optimization
Restart
Backtracking
Lojasiewicz property
Lipschitz constant
Acceleration
ANR Project
Mathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond - ANR-19-CE23-0017
Origin
Hal imported