Entropic fictitious play for mean field optimization problem
Résumé
It is well known that the training of the neural network can be viewed as a mean field optimization problem. In this paper we are inspired by the fictitious play, a classical algorithm in the game theory for learning the Nash equilibria, and propose a new algorithm, different from the conventional gradient-descent ones, to solve the mean field optimization. We rigorously prove its (exponential) convergence, and show some simple numerical examples.