AISTATS 2024poster13 citations

Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods

Davoud Ataee Tarzanagh, Parvin Nazari, Bojian Hou, Li Shen, Laura Balzano

Abstract

This paper introduces \textit{online bilevel optimization} in which a sequence of time-varying bilevel problems is revealed one after the other. We extend the known regret bounds for single-level online algorithms to the bilevel setting. Specifically, we provide new notions of \textit{bilevel regret}, develop an online alternating time-averaged gradient method that is capable of leveraging smoothness, and give regret bounds in terms of the path-length of the inner and outer minimizer sequences.

BibTeX
@InProceedings{pmlr-v238-ataee-tarzanagh24a,
  title = 	 {Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods},
  author =       {Ataee Tarzanagh, Davoud and Nazari, Parvin and Hou, Bojian and Shen, Li and Balzano, Laura},
  booktitle = 	 {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {2854--2862},
  year = 	 {2024},
  editor = 	 {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
  volume = 	 {238},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {02--04 May},
  publisher =    {PMLR},
  pdf = 	 {https://proceedings.mlr.press/v238/ataee-tarzanagh24a/ataee-tarzanagh24a.pdf},
  url = 	 {https://proceedings.mlr.press/v238/ataee-tarzanagh24a.html},
  abstract = 	 {This paper introduces \textit{online bilevel optimization} in which a sequence of time-varying bilevel problems is revealed one after the other. We extend the known regret bounds for single-level online algorithms to the bilevel setting. Specifically, we provide new notions of \textit{bilevel regret}, develop an online alternating time-averaged gradient method that is capable of leveraging smoothness, and give regret bounds in terms of the path-length of the inner and outer minimizer sequences.}
}
Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods · AISTATS 2024