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

Benamou, Jean-David; Carlier, Guillaume; Marino, Simone; Nenna, Luca (2019), An entropy minimization approach to second-order variational mean-field games, Mathematical Models and Methods in Applied Sciences (M3AS), 29, 8, p. 1553-1583. 10.1142/S0218202519500283

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Mathematical Models and Methods in Applied Sciences (M3AS)
Volume
29
Number
8
Publisher
World Scientific
Pages
1553-1583
Publication identifier
Metadata
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Author(s)
Benamou, Jean-David
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Marino, Simone
Scuola Normale Superiore di Pisa [SNS]
Nenna, Luca
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laboratoire de Mathématiques d'Orsay [LMO]
Abstract (EN)
We propose an entropy minimization viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We carefully analyze 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.
Subjects / Keywords
Γ-convergence entropy minimization; Fokker-Planck equation; Entropy minimization; Schrödinger bridges; Sinkhorn algorithm; Mean-Field Games