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arXiv · 2207.02829

Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods

Davoud Ataee Tarzanagh·Parvin Nazari·Bojian Hou·Li Shen·Laura Balzano
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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 online single-level 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.

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Davoud Ataee Tarzanagh, Parvin Nazari, Bojian Hou, Li Shen, Laura Balzano. 2022-07-06. Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods. https://arxiv.org/abs/2207.02829

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