A Monte Carlo Neural Fictitious Self-Play approach to approximate Nash Equilibrium in imperfect-information dynamic games

Solving the optimization problem to approach a Nash Equilibrium point plays an important role in imperfect information games,e.g.,StarCraft and poker.Neural Fictitious Self-Play(NFSP)is an effective algorithm that learns approximate Nash Equilibrium of imperfect-information games from purely self-play without prior domain knowledge.However,it needs to train a neural network in an off-policy manner to approximate the action values.For games with large search spaces,the training may suffer from unnecessary exploration and sometimes fails to converge.In this paper,we propose a new Neural Fictitious Self-Play algorithm that combines Monte Carlo tree search with NFSP,called MC-NFSP,to improve the performance in real-time zero-sum imperfect-information games.With experiments and empirical analysis,we demonstrate that the proposed MC-NFSP algorithm can approximate Nash Equilibrium in games with large-scale search depth while the NFSP can not.Furthermore,we develop an Asynchronous Neural Fictitious Self-Play framework(ANFSP).It uses asynchronous and parallel architecture to collect game experience and improve both the training efficiency and policy quality.The experiments with th e games with hidden state information(Texas Hold^m),and the FPS(firstperson shooter)games demonstrate effectiveness of our algorithms.