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Generalized conditional gradient and learning in potential mean field games

Abstract : 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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03341776
Contributor : Pierre Lavigne Connect in order to contact the contributor
Submitted on : Sunday, September 12, 2021 - 5:01:01 PM
Last modification on : Tuesday, September 14, 2021 - 3:38:02 AM

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  • HAL Id : hal-03341776, version 1
  • ARXIV : 2109.05785

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

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