Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods.

Abstract

This paper introduces an online bilevel optimization setting 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 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.