The purpose of this course is to address some mathematical and computational aspects of machine learning and of related large networks of artificial and biological neurons. 

The first part of the course will be an introduction to stochastic optimization, control and game theories. This includes stochastic gradient descents, stochastic gradient Langevin dynamics, dynamic programming principle, first order conditions, Hamilton-Jacobi equations and the notion of Nash equilibria. 

The second part will be dedicated to mathematical tools for large networks, including the concept of mean-field models from statistical physics. Illustration will be given in the framework of over-parametrized artificial networks and biological spiking neural networks. 

The third part will address computational aspects of some artificial networks, like generative adversarial networks and deep networks. This will include programming sessions.