Mean-Field optimal control and other type of games
by Massimo Fornasier (TU München)
In the first part of the course we introduce the concept of mean-field optimal control, which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional optimal control problem with a constraint given by a PDE of Vlasov-type, governing the dynamics of the probability distribution of interacting agents. In the second part of the course we introduce and study a mean-field model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the interaction between different players and return a feedback on the velocity field guiding their motion.
26/11, 11:30-13:00, Aula Verde, Ca' Vignal.
27/11, 09:00-10:30, SPC, Polo S. Marta.
29/11, 11:30-12:30, SPC, Polo S. Marta.
Numerical methods for Control and Games over Multiscale Agent-Based Models
by Dante Kalise (IC London)
We will discuss different approximation techniques for the solution of optimal control problems and games where the governing dynamics are give by multiscale models. We will start by reviewing some classical results concerning the solution of nonlinear optimal control problems, illustrating some of the difficulties which arise when the number of agents increases. This will lead us to mean-field and multiscale models, for which we will study their approximation within the framework provided by PDE-constrained optimization. Finally, starting from mean-field type control problems, we will move towards the numerical solution of mean field games.
27/11, 15:00-16:00, SMT02, Polo S. Marta.
30/11, 09:30-10:30, Aula Alfa, Ca' Vignal 2.
Each mini-course is self-contained, and does not require Part A, and Part C.