Multi-Level Multi-Objective Stochastic Methods for Learning and Optimization
Abstract
This project aims to develop state-of-the-art stochastic methodologies and rigorous theoretical analyses to expand the knowledge of multi-level, multi-objective optimization in innovative directions. These methods will address relevant problems arising in machine learning, cybersecurity, and defense, such as adversarial learning, network interdiction, and power network defense. Stochastic gradient methods are well studied for single-level problems, and there have been some recent advances for bilevel problems or multi-objective single-level problems, but many application problems exhibit features such as conflicting objectives at different levels, more than two levels, or discrete variables, which have never been studied from a stochastic approximation viewpoint. This project aims to fill this gap by leveraging ideas from stochastic bilevel and multi-objective optimization to extend the algorithmic framework and convergence analysis beyond classic stochastic gradient methods. The project will investigate several stochastic problems such as bilevel problems with constraints at the lower level, bilevel problems with multiple objective functions in at least one of the levels, trilevel optimization problems, and bilevel problems with some of the variables restricted to be integer.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 29, 2024
- Source ID
- FA95502310217
Entities
People
- Luis Nunes Vicente
Organizations
- Air Force Office of Scientific Research
- Lehigh University
- United States Air Force