Collaborative Research: An Online Bilevel Optimization Framework for Accelerated Learning in Time-varying Environments

Bilevel optimization is a powerful paradigm used to solve modern problems in signal processing and machine learning, such as multi-task learning, sequential decision making, robust adversarial training, and hyperparameter fine-tuning. More recently, the online bilevel optimization framework has been proposed to handle practical applications where environments and datasets change over time. These online problems are challenging because streaming data require fast decisions on-the-fly, and only limited information about the objectives can be sampled due to their rapid variations. In general, online bilevel optimization is largely unexplored, calling for a systematic in-depth investigation. The primary goal of this project is to comprehensively study online bilevel optimization, aiming to (i) speed up online bilevel algorithms, improve their scalability, and ensure their performance, and (ii) explore two real-world applications to further leverage the advantages of online bilevel optimization in solving practical problems. The proposed program will focus on the following research innovations to significantly broaden timely applications of online bilevel optimization in real-world problems: (i) algorithmic and analytical foundation for online bilevel optimization; (ii) a novel approach for online robust adversarial training via the lens of online compositional bilevel optimization; (iii) accelerated online multi-agent meta-learning design via online nonconvex bilevel optimization; and (iv) extensive experiments to validate the proposed approaches and algorithms. This project will also provide exciting training and research opportunities through topic courses, tutorial presentations, undergraduate research programs, and K-12 programs. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.