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Main Authors: Gibson, Travis E., Acharya, Sawal, Parashar, Anjali, Gaudio, Joseph E., Annaswamy, Anurdha M.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2405.13765
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author Gibson, Travis E.
Acharya, Sawal
Parashar, Anjali
Gaudio, Joseph E.
Annaswamy, Anurdha M.
author_facet Gibson, Travis E.
Acharya, Sawal
Parashar, Anjali
Gaudio, Joseph E.
Annaswamy, Anurdha M.
contents Gradient based optimization algorithms deployed in Machine Learning (ML) applications are often analyzed and compared by their convergence rates or regret bounds. While these rates and bounds convey valuable information they don't always directly translate to stability guarantees. Stability and similar concepts, like robustness, will become ever more important as we move towards deploying models in real-time and safety critical systems. In this work we build upon the results in Gaudio et al. 2021 and Moreu & Annaswamy 2022 for gradient descent with second order dynamics when applied to explicitly time varying cost functions and provide more general stability guarantees. These more general results can aid in the design and certification of these optimization schemes so as to help ensure safe and reliable deployment for real-time learning applications. We also hope that the techniques provided here will stimulate and cross-fertilize the analysis that occurs on the same algorithms from the online learning and stochastic optimization communities.
format Preprint
id arxiv_https___arxiv_org_abs_2405_13765
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the stability of gradient descent with second order dynamics for time-varying cost functions
Gibson, Travis E.
Acharya, Sawal
Parashar, Anjali
Gaudio, Joseph E.
Annaswamy, Anurdha M.
Machine Learning
Optimization and Control
Gradient based optimization algorithms deployed in Machine Learning (ML) applications are often analyzed and compared by their convergence rates or regret bounds. While these rates and bounds convey valuable information they don't always directly translate to stability guarantees. Stability and similar concepts, like robustness, will become ever more important as we move towards deploying models in real-time and safety critical systems. In this work we build upon the results in Gaudio et al. 2021 and Moreu & Annaswamy 2022 for gradient descent with second order dynamics when applied to explicitly time varying cost functions and provide more general stability guarantees. These more general results can aid in the design and certification of these optimization schemes so as to help ensure safe and reliable deployment for real-time learning applications. We also hope that the techniques provided here will stimulate and cross-fertilize the analysis that occurs on the same algorithms from the online learning and stochastic optimization communities.
title On the stability of gradient descent with second order dynamics for time-varying cost functions
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2405.13765