Learning and Sparse Control of Multiagent Systems - A talk by Prof. Dr. Massimo Fornasier

Total number of participants: 12
Total number of guests outside of CBC: 6
Number of different nationalities represented: 6
Total number of speakers: 1
Total number of talks: 2

In addition to this one hour talk, Dr. Fornasier will also give a tutorial on Compressed Sensing and Sparse Recovery at October 04 and 05, 10:00-12:00, as part of the Machine Learning Seminar Series.

Dr. Fornasier holds a chair in Applied Numerical Analysis at the Technical University of Munich, Germany. The research of Dr. Fornasier and his Unit embraces a broad spectrum of problems in mathematical modeling, analysis and numerical analysis. He is particularly interested in the concept of compression as appearing in different forms in data analysis, image and signal processing, and in the adaptive numerical solutions of partial differential equations or high-dimensional optimization problems.

Massimo Fornasier is a member of VQR, a panel responsible for the evaluation of the quality of research in Italy. He is also a member of the editorial boards of Networks and Heterogeneous Media, Journal of Fourier Analysis and Applications and Calcolo.

We are very much looking to welcoming you to the seminar!

Abstract

In the past decade there has been a large scope of studies on mathematical models of social dynamics. Self-organization, i.e., the autonomous formation of patterns, has been so far the main driving concept. Usually first or second order models are considered with given predetermined nonlocal interaction potentials, tuned to reproduce, at least qualitatively, certain global patterns (such as flocks of birds, milling school of fish or line formations in pedestrian flows, etc.). However, often in practice we do not dispose of a precise knowledge of the governing dynamics. In the first part of this talk we present a variational and optimal transport framework leading to an algorithmic solution to the problem of learning the interaction potentials from the observation of the dynamics of a multiagent system. Moreover, it is common experience that self-organization of a society does not always spontaneously occur. In the second part of the talk we address the question of whether it is possible to externally and parsimoniously influence the dynamics, to promote the formation of certain desired patterns. In particular, we address the issue of finding the sparsest control strategy for finite agent models in order to lead the dynamics optimally towards a given outcome. We eventually mention the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints to an infinite dimensional sparse mean-field optimal control problem with a constraint given by a PDE of Vlasov-type, governing the dynamics of the probability distribution of the agent population.