Bi-Level Optimization for Hierarchical Machine Learning Problems: Models, Algorithms and Applications

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

Advances in optimization have become the cornerstone for the success of many modern applications arising from fields like machine learning, signal processing and control. However, as applications become increasingly complex, simply scaling up the data and problem dimension is no longer sufficient to construct high-quality models. It is also important to jointly model different kinds of hierarchically coupled sub-tasks wherein the solution of one optimization problem builds upon that of others. Unlike standard single-level optimization problems, algorithms tailored for solving hierarchically coupled problems are less explored. Bi-level optimization (BLO) thus draws wide attention across the aforementioned fields due to its power in modeling the complicated hierarchical decision-making process. In this proposal, we plan to study the BLO problems, and in particular, a subclass of it with specific lower-level structures that is challenging and has strong applications in modeling the hierarchical structures arising in modern machine learning and engineering applications such as adversarial learning, inverse reinforcement learning, and continue learning. Specifically, we propose to study the hard instances of BLO where the lower level is nonconvex or constrained, which is much less explored and inherently difficult. This proposal intends to develop a suite of new approaches that not only advance the state-of-the-art BLO literature, but more importantly, can help accelerate the adoption of BLO as a generic tool to model, analyze, and innovate on a wide array of emerging ML applications. Further, we also plan to develop a benchmarking suite that evaluates the state-of-the-art BLO algorithms on relevant ML problems and beyond. This project will further integrate an educational plan with the research goals by i) revamping the existing optimization and ML courses with BLO components; ii) developing a new course project on applying BLO algorithms to ML problems; iii) directly involving undergraduate and graduate students in research, especially from under-represented groups; and iv) outreaching to the general public, in particular K-12 students. 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.