Primal-dual methods for the mean-field game (MFG) and control (MFC) problems via monotone inclusions

Levon Nurbekyan
University of California, Los Angeles (UCLA)
Mathematics and Statistics

We discuss primal-dual methods for MFG and MFC problems with mixed, local-nonlocal, couplings. Introducing dual variables for couplings of each type, we formulate the MFG system as a monotone inclusion and solve it via an extension of the primal-dual hybrid gradient (PDHG) algorithm. Building on our earlier work, we choose the dual variables for nonlocal terms in a Fourier space. Thus, we completely split all types of interactions in the system. Another appealing feature of our method is that it also handles non-potential MFGs with monotone couplings. To the best of our knowledge, this is the first instance of applying primal-dual optimization methods to non-potential MFG systems. This work is joint with Siting Liu.

Presentation (PDF File)

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