Seminario del 2027

Gennaio
25
Lunedì
Huyên PHAM
Mean-Field Control: Theory, Methods, from Foundations to Learning
ore 15:30
presso Centro Congressi "Alla Sosta dell'Imperatore" Strada dei Margeni, 18 38025 Dimaro Folgarida (TN)
 Webpage della 3nd Dolomites Winter School on Mean-field Control, Mean-field Games and Applications
probabilità
These lectures cover the optimal control of McKean-Vlasov equations, a topic that has attracted growing interest in connection with mean-field game theory, large population stochastic control, and more recently machine learning. We start with mean-field Markov decision processes in discrete time, where the key ideas — propagation of chaos, lifting to the Wasserstein space, dynamic programming — can be introduced transparently. We then develop the continuous-time theory of controlled McKean-Vlasov SDEs, building the necessary tools: differentiation with respect to probability measures, Itô's formula along flows of marginal laws, the Master Bellman equation, and the stochastic maximum principle with its associated FBSDE system. Linear-quadratic problems serve as a running illustration throughout. The last part of the course is devoted to numerical methods and applications. We present neural network-based algorithms and reinforcement learning approaches for solving mean-field control problems on the Wasserstein space, and discuss recent extensions to non-exchangeable mean-field control for heterogeneous interacting systems. We conclude with an application to generative modeling, where learning stochastic dynamics from distributional observations is formulated as a McKean-Vlasov control problem, with optimality conditions given by a tractable FBSDE system.
organizzato da: Andrea Pascucci
nell'ambito del Progetto P.R.I.N. PRIN2022_PASCUCCI CUP J53D23003800006 del prof. Andrea Pascucci

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