## Title data

Guo, Zheng-Chu ; Christmann, Andreas ; Shi, Lei:

**Optimality of Robust Online Learning.**

Fudan University Shanghai, China
,
2023
. - 26 p.

DOI: https://doi.org/10.48550/arXiv.2304.10060

## Related URLs

## Project information

Project financing: |
Andere |
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## Abstract in another language

In this paper, we study an online learning algorithm with a robust loss function Lσ for regression over a reproducing kernel Hilbert space (RKHS). The loss function Lσ involving a scaling parameter σ>0 can cover a wide range of commonly used robust losses. The proposed algorithm is then a robust alternative for online least squares regression aiming to estimate the conditional mean function. For properly chosen σ and step size, we show that the last iterate of this online algorithm can achieve optimal capacity independent convergence in the mean square distance. Moreover, if additional information on the underlying function space is known, we also establish optimal capacity dependent rates for strong convergence in RKHS. To the best of our knowledge, both of the two results are new to the existing literature of online learning.

## Further data

Item Type: | Preprint, postprint |
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Keywords: | Online learning; Robust regression; Convergence analysis; Reproducing kernel Hilbert space |

Subject classification: | 68T05, 62J02, 68Q32, 62L20 |

Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VII - Stochastics and Machine Learning Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VII - Stochastics and Machine Learning > Chair Mathematics VII - Stochastics and mashine learning - Univ.-Prof. Dr. Andreas Christmann |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 25 Apr 2023 05:11 |

Last Modified: | 25 Apr 2023 05:11 |

URI: | https://eref.uni-bayreuth.de/id/eprint/76097 |