Convergence of the Iterates for Momentum and RMSProp for Local Smooth Functions: Adaptation is the Key

Fuente: arXiv
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Main Authors: Bensaid, Bilel, Poëtte, Gaël, Turpault, Rodolphe
Format: Preprint
Published: 2024
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author Bensaid, Bilel
Poëtte, Gaël
Turpault, Rodolphe
author_facet Bensaid, Bilel
Poëtte, Gaël
Turpault, Rodolphe
contents Both accelerated and adaptive gradient methods are among state of the art algorithms to train neural networks. The tuning of hyperparameters is needed to make them work efficiently. For classical gradient descent, a general and efficient way to adapt hyperparameters is the Armijo backtracking. The goal of this work is to generalize the Armijo linesearch to Momentum and RMSProp, two popular optimizers of this family, by means of stability theory of dynamical systems. We establish convergence results, under the Lojasiewicz assumption, for these strategies. As a direct result, we obtain the first guarantee on the convergence of the iterates for RMSProp, in the non-convex setting without the classical bounded assumptions.
format Preprint
id arxiv_https___arxiv_org_abs_2407_15471
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Convergence of the Iterates for Momentum and RMSProp for Local Smooth Functions: Adaptation is the Key
Bensaid, Bilel
Poëtte, Gaël
Turpault, Rodolphe
Optimization and Control
Both accelerated and adaptive gradient methods are among state of the art algorithms to train neural networks. The tuning of hyperparameters is needed to make them work efficiently. For classical gradient descent, a general and efficient way to adapt hyperparameters is the Armijo backtracking. The goal of this work is to generalize the Armijo linesearch to Momentum and RMSProp, two popular optimizers of this family, by means of stability theory of dynamical systems. We establish convergence results, under the Lojasiewicz assumption, for these strategies. As a direct result, we obtain the first guarantee on the convergence of the iterates for RMSProp, in the non-convex setting without the classical bounded assumptions.
title Convergence of the Iterates for Momentum and RMSProp for Local Smooth Functions: Adaptation is the Key
topic Optimization and Control
url https://arxiv.org/abs/2407.15471