Voir la notice de l'article provenant de la source Numdam
We present a new algorithm to solve min-max or min-min problems out of the convex world. We use rigidity assumptions, ubiquitous in learning, making our method – the backtrack Hölder algorithm applicable to many optimization problems. Our approach takes advantage of hidden regularity properties and allows us, in particular, to devise a simple algorithm of ridge type. An original feature of our method is to come with automatic step size adaptation which departs from the usual overly cautious backtracking methods. In a general framework, we provide convergence theoretical guarantees and rates. We apply our findings on simple Generative Adversarial Network (GAN) problems obtaining promising numerical results. It is worthwhile mentioning that a byproduct of our approach is a simple recipe for general Hölderian backtracking optimization.
Bolte, Jérôme 1 ; Glaudin, Lilian 2 ; Pauwels, Edouard 3 ; Serrurier, Mathieu 4
CC-BY 4.0
@article{OJMO_2023__4__A8_0,
author = {Bolte, J\'er\^ome and Glaudin, Lilian and Pauwels, Edouard and Serrurier, Mathieu},
title = {The backtrack {H\"older} gradient method with application to min-max and min-min problems},
journal = {Open Journal of Mathematical Optimization},
eid = {8},
pages = {1--17},
publisher = {Universit\'e de Montpellier},
volume = {4},
year = {2023},
doi = {10.5802/ojmo.24},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/ojmo.24/}
}
TY - JOUR AU - Bolte, Jérôme AU - Glaudin, Lilian AU - Pauwels, Edouard AU - Serrurier, Mathieu TI - The backtrack Hölder gradient method with application to min-max and min-min problems JO - Open Journal of Mathematical Optimization PY - 2023 SP - 1 EP - 17 VL - 4 PB - Université de Montpellier UR - http://geodesic.mathdoc.fr/articles/10.5802/ojmo.24/ DO - 10.5802/ojmo.24 LA - en ID - OJMO_2023__4__A8_0 ER -
%0 Journal Article %A Bolte, Jérôme %A Glaudin, Lilian %A Pauwels, Edouard %A Serrurier, Mathieu %T The backtrack Hölder gradient method with application to min-max and min-min problems %J Open Journal of Mathematical Optimization %D 2023 %P 1-17 %V 4 %I Université de Montpellier %U http://geodesic.mathdoc.fr/articles/10.5802/ojmo.24/ %R 10.5802/ojmo.24 %G en %F OJMO_2023__4__A8_0
Bolte, Jérôme; Glaudin, Lilian; Pauwels, Edouard; Serrurier, Mathieu. The backtrack Hölder gradient method with application to min-max and min-min problems. Open Journal of Mathematical Optimization, Tome 4 (2023), article no. 8, 17 p.. doi: 10.5802/ojmo.24
Cité par Sources :