Convergence in On-line Learning of Static and Dynamic Systems

Fuente: arXiv
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Main Authors: Wigren, Torbjörn, Zhang, Ruoqi, Mattsson, Per
Format: Preprint
Published: 2025
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author Wigren, Torbjörn
Zhang, Ruoqi
Mattsson, Per
author_facet Wigren, Torbjörn
Zhang, Ruoqi
Mattsson, Per
contents The paper derives analytical expressions for the asymptotic average updating direction of the adaptive moment generation (ADAM) algorithm when applied to recursive identification of nonlinear systems. It is proved that the standard hyper-parameter setting results in the same asymptotic average updating direction as a diagonally power normalized stochastic gradient algorithm. With the internal filtering turned off, the asymptotic average updating direction is instead equivalent to that of a sign-sign stochastic gradient algorithm. Global convergence to an invariant set follows, where a subset of parameters contain those that give a correct input-output description of the system. The paper also exploits a nonlinear dynamic model to embed structure in recurrent neural networks. A Monte-Carlo simulation study validates the results.
format Preprint
id arxiv_https___arxiv_org_abs_2501_03049
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Convergence in On-line Learning of Static and Dynamic Systems
Wigren, Torbjörn
Zhang, Ruoqi
Mattsson, Per
Systems and Control
The paper derives analytical expressions for the asymptotic average updating direction of the adaptive moment generation (ADAM) algorithm when applied to recursive identification of nonlinear systems. It is proved that the standard hyper-parameter setting results in the same asymptotic average updating direction as a diagonally power normalized stochastic gradient algorithm. With the internal filtering turned off, the asymptotic average updating direction is instead equivalent to that of a sign-sign stochastic gradient algorithm. Global convergence to an invariant set follows, where a subset of parameters contain those that give a correct input-output description of the system. The paper also exploits a nonlinear dynamic model to embed structure in recurrent neural networks. A Monte-Carlo simulation study validates the results.
title Convergence in On-line Learning of Static and Dynamic Systems
topic Systems and Control
url https://arxiv.org/abs/2501.03049