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

Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods