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Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods
July 06, 2022 Β· Declared Dead Β· π International Conference on Artificial Intelligence and Statistics
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Authors
Davoud Ataee Tarzanagh, Parvin Nazari, Bojian Hou, Li Shen, Laura Balzano
arXiv ID
2207.02829
Category
math.OC: Optimization & Control
Cross-listed
cs.DS,
cs.LG
Citations
15
Venue
International Conference on Artificial Intelligence and Statistics
Last Checked
5 months ago
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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