Online Learning in Reproducing Kernel Hilbert Space With Non-IID Data

Xiwei Zhang; Tao Li

doi:10.1109/CDC49753.2023.10384155

Online Learning in Reproducing Kernel Hilbert Space With Non-IID Data

Xiwei Zhang
, Tao Li^*

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We analyze the convergence of online regularized learning algorithm based on dependent and non-stationary online data streams for the nonparametric regression problem in reproducing kernel Hilbert space (RKHS). We show that the algorithm achieves mean-square convergence if the algorithm gain and regularization parameter are chosen appropriately, the online data streams are weakly dependent and satisfy the eigenvalue-wise persistence of excitation condition. Especially, for the case with independent but non-identically distributed online data streams, we give more intuitive convergence conditions on the drifts of the probability measures induced by the data.

Original language	English
Title of host publication	2023 62nd IEEE Conference on Decision and Control, CDC 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6610-6615
Number of pages	6
ISBN (Electronic)	9798350301243
DOIs	https://doi.org/10.1109/CDC49753.2023.10384155
State	Published - 2023
Event	62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore Duration: 13 Dec 2023 → 15 Dec 2023

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	62nd IEEE Conference on Decision and Control, CDC 2023
Country/Territory	Singapore
City	Singapore
Period	13/12/23 → 15/12/23

Access to Document

10.1109/CDC49753.2023.10384155

Cite this

@inproceedings{b95c497d7a3a45848c9150340360e14e,

title = "Online Learning in Reproducing Kernel Hilbert Space With Non-IID Data",

abstract = "We analyze the convergence of online regularized learning algorithm based on dependent and non-stationary online data streams for the nonparametric regression problem in reproducing kernel Hilbert space (RKHS). We show that the algorithm achieves mean-square convergence if the algorithm gain and regularization parameter are chosen appropriately, the online data streams are weakly dependent and satisfy the eigenvalue-wise persistence of excitation condition. Especially, for the case with independent but non-identically distributed online data streams, we give more intuitive convergence conditions on the drifts of the probability measures induced by the data.",

author = "Xiwei Zhang and Tao Li",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 62nd IEEE Conference on Decision and Control, CDC 2023 ; Conference date: 13-12-2023 Through 15-12-2023",

year = "2023",

doi = "10.1109/CDC49753.2023.10384155",

language = "英语",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "6610--6615",

booktitle = "2023 62nd IEEE Conference on Decision and Control, CDC 2023",

address = "美国",

}

Zhang, X & Li, T 2023, Online Learning in Reproducing Kernel Hilbert Space With Non-IID Data. in 2023 62nd IEEE Conference on Decision and Control, CDC 2023. Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 6610-6615, 62nd IEEE Conference on Decision and Control, CDC 2023, Singapore, Singapore, 13/12/23. https://doi.org/10.1109/CDC49753.2023.10384155

Online Learning in Reproducing Kernel Hilbert Space With Non-IID Data. / Zhang, Xiwei; Li, Tao.
2023 62nd IEEE Conference on Decision and Control, CDC 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 6610-6615 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Online Learning in Reproducing Kernel Hilbert Space With Non-IID Data

AU - Zhang, Xiwei

AU - Li, Tao

PY - 2023

Y1 - 2023

N2 - We analyze the convergence of online regularized learning algorithm based on dependent and non-stationary online data streams for the nonparametric regression problem in reproducing kernel Hilbert space (RKHS). We show that the algorithm achieves mean-square convergence if the algorithm gain and regularization parameter are chosen appropriately, the online data streams are weakly dependent and satisfy the eigenvalue-wise persistence of excitation condition. Especially, for the case with independent but non-identically distributed online data streams, we give more intuitive convergence conditions on the drifts of the probability measures induced by the data.

AB - We analyze the convergence of online regularized learning algorithm based on dependent and non-stationary online data streams for the nonparametric regression problem in reproducing kernel Hilbert space (RKHS). We show that the algorithm achieves mean-square convergence if the algorithm gain and regularization parameter are chosen appropriately, the online data streams are weakly dependent and satisfy the eigenvalue-wise persistence of excitation condition. Especially, for the case with independent but non-identically distributed online data streams, we give more intuitive convergence conditions on the drifts of the probability measures induced by the data.

UR - https://www.scopus.com/pages/publications/85184811507

U2 - 10.1109/CDC49753.2023.10384155

DO - 10.1109/CDC49753.2023.10384155

M3 - 会议稿件

AN - SCOPUS:85184811507

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 6610

EP - 6615

BT - 2023 62nd IEEE Conference on Decision and Control, CDC 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 62nd IEEE Conference on Decision and Control, CDC 2023

Y2 - 13 December 2023 through 15 December 2023

ER -

Online Learning in Reproducing Kernel Hilbert Space With Non-IID Data

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