2024 AISTATS AISTATS 2024

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 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.

🌉 Interdisciplinary Bridge — Machine Learning and Mathematics & Optimization
🐝 Cross-Pollinator — Artificial Intelligence, Computer Science, Computer Vision, Data Science & Analytics, Deep Learning, Interdisciplinary, Knowledge & Reasoning, Machine Learning, Mathematics & Optimization, Natural Language Processing, Reinforcement Learning, Robotics, Security & Privacy, Speech & Audio
🧭 Keyword Pioneer — alternating gradient