Entropic Fictitious Play

Résumé

The classical fictitious play is a common algorithm for solving games. However, once the cost functions of the players are non-convex, the method becomes hard to implement. In our study we add the entropic regulariser, a common strategy for non-convex optimisation, to the cost functions, and look into the analog of fictitious play in this context. We shall further see that the entropic fictitious play not only helps to solve non-convex game, but also can be used to solve optimisations on the space of probability measures, and thus can be applied to train neural networks.