Adaptive Proximal Gradient Method for Convex Optimization

Fuente: arXiv
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Main Authors: Malitsky, Yura, Mishchenko, Konstantin
Format: Preprint
Published: 2023
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author Malitsky, Yura
Mishchenko, Konstantin
author_facet Malitsky, Yura
Mishchenko, Konstantin
contents In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local curvature information of smooth functions. We propose adaptive versions of GD and ProxGD that are based on observed gradient differences and, thus, have no added computational costs. Moreover, we prove convergence of our methods assuming only local Lipschitzness of the gradient. In addition, the proposed versions allow for even larger stepsizes than those initially suggested in [MM20].
format Preprint
id arxiv_https___arxiv_org_abs_2308_02261
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Adaptive Proximal Gradient Method for Convex Optimization
Malitsky, Yura
Mishchenko, Konstantin
Optimization and Control
Machine Learning
Numerical Analysis
In this paper, we explore two fundamental first-order algorithms in convex optimization, namely, gradient descent (GD) and proximal gradient method (ProxGD). Our focus is on making these algorithms entirely adaptive by leveraging local curvature information of smooth functions. We propose adaptive versions of GD and ProxGD that are based on observed gradient differences and, thus, have no added computational costs. Moreover, we prove convergence of our methods assuming only local Lipschitzness of the gradient. In addition, the proposed versions allow for even larger stepsizes than those initially suggested in [MM20].
title Adaptive Proximal Gradient Method for Convex Optimization
topic Optimization and Control
Machine Learning
Numerical Analysis
url https://arxiv.org/abs/2308.02261