Convergence in On-line Learning of Static and Dynamic Systems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908606413144064 |
|---|---|
| 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 |