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Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods

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

MR1 & MR2 #0
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Sat 4 May 6 a.m. PDT — 8:30 a.m. PDT


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.

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