Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods

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.

Published at AISTATS 2024. V7: minor edits to the statement of Lemma 18 and Assumption A