Paris Bachelier Seminar: Turpike Control and Machine Learning

Tomorrow May 21st. our Head Enrique Zuazua will talk on the Paris Bachelier Seminar about “Turpike Control and Machine Learning“, an event organized jointly with the Centre de Mathematiques Appliquées (Ecole Polytechnique), the CEREMADE (Université Paris Dauphine), the Centre de Recherche en Economie et Statistiques (CREST), the Laboratoire de Probabilités et modèles aleatoires (Universite de Paris VI- VII), the Laboratoire de Mathématiques et de Modélisation (Université d’Evry), and the Université de Marne La Vallée.

Abstract. We first present the classical concept of turnpike control, assuring that, often, in long time-horizons, optimal controls and trajectories are essentially of a steady-state nature. We then show how it can be adapted to the models in Continuum Mechanics, leading a to substantial reduction of the computational cost. We then analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of the main challenges in Machine Learning and, in particular, data classification and Universal Approximation. More precisely, we adopt the perspective of the simultaneous control of systems of NODEs. We show how the turnpike principle can be adapted in this setting. We develop genuinely nonlinear and constructive methods allowing to estimate the complexity of the control strategies we develop. We also present the counterparts in the context of the control of neural transport equations, establishing a link towards optimal transport. Some open problems and perspective of research are also present.


Fri. May 21, 2021 at 11:15H


Via zoom meeting

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