This chair is concerned with (i) optimization for some Machine Learning (ML) applications, (ii) data driven control of dynamical systems, and (iii) tools for data analysis.
(i)In many ML applications it is crucial to obtain global guarantees. Such instances include evaluation & certification of robustness of Deep Neural Networks, geometric perception and 3D shape reconstruction in computer vision, Optimum Power Flow (OPF) in energy networks. Powerful Positivity certificates from Real Algebraic Geometry are particularly well-suited tools, but in standard form they are computationally very expensive and do not scale well with the problem size. So one part of our activity is concerned with basic research on scalable positivity certificates in view of ML applications and management of energy networks.
(ii) In complex high-dimensional dynamical systems the model is often unknown and only observed data are available. In this data driven context two research directions are investigated. (a) To extend the Koopman operator approach to systems with control inputs, in conjunction with model predictive control. (b) To extend the moment-sum-of-squares approach to this data-driven setting.
(iii) A third research activity is concerned with data analysis, e.g. in some important ML applications like outlier detection, density estimation, support inference. The main goal is to promote Christoffel-Darboux kernels (well-known in approximation theory) as a powerful tool, and in particular to come up with a book on that topic, targeting the ML community.
Programmes : IA acceptable, certifiable & collaborative
Thèmes : apprentissages avec peu de données ou des données complexes, Optimisation et théorie des jeux pour l’IA, Données et anomalies
Jean-Bernard Lasserre, Directeur de recherche émérite, CNRS. Laas, Toulouse
Milan Korda, co-chair : Chargé de recherche CNRS, LAAS, Toulouse
Victor Magron, co-chair : Chargé de Recherche CNRS, LAAS Toulouse
Jie Wang : Post-doctoral student, LAAS-CNRS, Toulouse
Tong Chen : ANITI PhD student, Toulouse
Ngoc Hoang MAI, PhD student, LAAS-CNRS, Toulouse