Polynomial & Optimization for ML and Data Analysis chair

The Polynomial Optimization chair is concerned with four main research directions:

  • Develop efficient optimization algorithms in view of their application to help analyze and/or solve challenging hard problems in Machine Learning (ML).
    A particular emphasis is on ad-hoc positivity certificates (based on linear/second-order/semidefinite programming) from real algebraic geometry to provide efficient scalable convex relaxations to hard non convex ML problems.

  • Data driven approach to control dynamical systems via a combination of Koopman operator and convex relaxations. For instance this approach can be used to determine the maximum positively invariant set from data.

  • Stability and performance verification of dynamical systems controlled by neural networks using semialgebraic representation of nonlinearities and efficient positivity certificates. This allows one to search rigorous certificates of stability for dynamical systems controlled by neural networks trained from data.

  • Promoting the Christoffel-Darboux (CD) kernel (and associated Christoffel function), as a powerful (and easy to use) tool from theory of approximation and orthogonal polynomials, largely ignored in analysis of (discrete) clouds of data points. It can be used to encode clouds of data points, to detect outliers, and for support inference as well.

Programs: Acceptable, certifiable & collaborative AI 


Themes: Learning with little or complex data, optimization and game theory for AI, data and anomalies

Chair holder:
Jean-Bernard Lasserre, Directeur de recherche émérite, CNRS. Laas, Toulouse

Co-chairs:

  • Milan Korda,co-chair: CNRS, LAAS Toulouse
  • Victor Magron,co-chair: CNRS, LAAS Toulouse

Sites

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In AI too, we think global and act local - with Jean-Bernard Lasserre

For the mathematician Jean-Bernard Lasserre, every problem has a local, imperfect solution, and a global solution, the best absolutely. The researcher is testing global optimization methods in artificial intelligence. He also promotes the use of the mathematical function of Christoffel, for certain problems in data analysis.

Read the article in French

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