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Pré-Publication, Document De Travail Année : 2021

Generalized conditional gradient and learning in potential mean field games

J Frédéric Bonnans
  • Fonction : Auteur
Laurent Pfeiffer

Résumé

We apply the generalized conditional gradient algorithm to potential mean field games and we show its well-posedeness. It turns out that this method can be interpreted as a learning method called fictitious play. More precisely, each step of the generalized conditional gradient method amounts to compute the best-response of the representative agent, for a predicted value of the coupling terms of the game. We show that for the learning sequence δk = 2/(k + 2), the potential cost converges in O(1/k), the exploitability and the variables of the problem (distribution, congestion, price, value function and control terms) converge in O(1/ √ k), for specific norms.
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Dates et versions

hal-03341776 , version 1 (12-09-2021)
hal-03341776 , version 2 (07-10-2022)
hal-03341776 , version 3 (17-08-2023)

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J Frédéric Bonnans, Pierre Lavigne, Laurent Pfeiffer. Generalized conditional gradient and learning in potential mean field games. 2021. ⟨hal-03341776v1⟩
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