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An entropy minimization approach to second-order variational mean-field games

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mfg-entropic-july.pdf (2.453Mb)
Date
2018
Publishing date
08-2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01848370
Dewey
Analyse
Sujet
Mean-Field Games; Fokker-Planck equation; entropy minimization; Schrödinger bridges; Sinkhorn algorithm
URI
https://basepub.dauphine.fr/handle/123456789/17952
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Benamou, Jean-David
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Carlier, Guillaume
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Marino, Simone
status unknown
Nenna, Luca
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
32
Abstract (EN)
We propose a new viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We show the equivalence of such mean-field games with a relative entropy minimization at the level of probabilities on curves. We also address the time-discretization of such problems, establish Γ-convergence results as the time step vanishes and propose an efficient algorithm relying on this entropic interpretation as well as on the Sinkhorn scaling algorithm.

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