ML&OC24: Machine Learning and Optimal Control summer school

On May 29-30, 2024, Prof. Enrique Zuazua is giving a course on “Control and Machine Learning” at the ML&OC24 summer school “Machine Learning and Optimal Control” on May 27-31, 2024 at Gaeta (Italy).

Abstract. In this course we shall present some recent results on the interplay between control and Machine Learning, and more precisely, Supervised Learning, Universal Approximation and Normaliying flows. We adopt the perspective of the simultaneous or ensemble control of systems of Residual Neural Networks (ResNets). Roughly, each item to be classified corresponds to a different initial datum for the Cauchy problem of the ResNets, leading to an ensemble of solutions to be driven to the corresponding targets, associated to the labels, by means of the same control.

We present a genuinely nonlinear and constructive method, allowing to show that such an ambitious goal can be achieved, estimating the complexity of the control strategies. This property is rarely fulfilled by the classical dynamical systems in Mechanics and the very nonlinear nature of the activation function governing the ResNet dynamics plays a determinant role. It allows deforming half of the phase space while the other half remains invariant, a property that classical models in mechanics do not fulfill. The turnpike property is also analyzed in this context, showing that a suitable choice of the cost functional used to train the ResNet leads to more stable and robust dynamics.

This lecture is inspired in joint work, among others, with Borjan Geshkovski (MIT), Domènec Ruiz-Balet (IC, London), Martin Hernandez (FAU) and Antonio Alvarez (UAM)

Courses
6 hours/course

• Prof. Enrique Zuazua, FAU. Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Control and Machine Learning

• Prof. Lars Grüne, Universität Bayreuth (Germany)
High-dimensional (optimal) feedback control with neural networks

• Prof. Huyen Pham, Université Paris Cité (France)
Deep (reinforcement) learning methods for stochastic control PDEs

Schedule of the Course

Organizers
• Alessandro Alla. Università Ca` Foscari Venezia
• Elisabetta Carlini. Sapienza, Università di Roma
• Giovanni Colombo. Università di Padova
• Michele Palladino. Università de L’Aquila
• Cristina Pignotti. Università de L’Aquila