New Mathematical Challenges of the Optimization of Large Stochastic Systems
Abstract
This is a three-year single PI proposal for the development of analytical tools for the advancement of the theory of Mean Field Games. The goal is to break some of the barriers forced by the limitations of the original paradigm requiring restrictive symmetry assumptions and full connectivity of the graph of interactions between the individuals included in the model. The research project is focused on the analysis of large stochastic systems and the identification of their equilibriums and their stability. We identified three challenging domain areas, the theoretical understanding of which will lead to significant progress in practical applications of interest. The focus of our investigations will be as follows- a) our proposed study of the stability and possible bifurcations of large complex networks will lead to a better understanding of spontaneous synchronization phenomena, and of jet-lag recovery; b) the developments of mean field reinforcement learning which we propose will have significant impact in robotics and in particular, the control of large fleets of robots; c) for all intents and purposes, the control of conditional processes has not been investigated in the applied mathematics literature, and we propose a systematic approach based on an original formulation in terms of the control of dynamical systems of Gibbs probability measures, and we explain why this new recasting of the problem will lead to original solutions of previously unsolved questions.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 06, 2024
- Source ID
- FA95502310324
Entities
People
- René Carmona
Organizations
- Air Force Office of Scientific Research
- Trustees of Princeton University
- United States Air Force