AFOSR YIP FINDING HIGHER-ORDER STATIONARY POINTS OF NONCONVEX OPTIMIZATION PROBLEMS IN MULTI-AGENT, UNCERTAIN AND ADVERSARIAL ENVIRONMENTS
Abstract
The effort is to efficiently compute stationary points for two types of optimization problems; the first is that of minimizing the sum of nonconvex local cost functions over a constrained region, and the second is robust optimization in the form of nonconvex min-max problems. For the first type, second-order stationary points (SOSPs) will be sought. The posed algorithms are Hessian-aware but are also Hessian-free in that they are aware and exploit curvature through tracking changes of the gradient but do not explicitly compute the Hessian matrix. For the second, first-order points will be studied. A third thrust will combine the two problem types for the purpose of developing new algorithms for finding SOSPs in the presence of optimization constraints, uncertainties, and in multi-agent and adversarial environments. The effort desires to enhance DoD’s ability to perform optimal decision-making with superior speed in uncertain environments. The research will be both theoretical and computational, with the theory focusing on convergence analysis, and the computations on implementing the designed algorithms in such settings as training robust machine learning models and generative adversarial networks, and beamformer design.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 07, 2023
- Source ID
- FA95502210192
Entities
People
- Meisam Razaviyayn
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Southern California