Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods
This work addresses optimization challenges in sequential decision-making for researchers in machine learning and optimization, but it is incremental as it builds on existing single-level regret analysis.
The paper tackles the problem of online bilevel optimization by extending regret bounds from single-level to bilevel settings, developing an online alternating gradient method that achieves regret bounds based on the path-length of minimizer sequences.
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.