  Optimization of deep learning algorithms to approach Nash Equilibrium remains
a significant problem in imperfect information games, e.g. StarCraft and poker.
Neural Fictitious Self-Play (NFSP) has provided an effective way to learn
approximate Nash Equilibrium without prior domain knowledge in imperfect
information games. However, optimality gap was left as an optimization problem
of NFSP and by solving the problem, the performance of NFSP could be improved.
In this study, focusing on the optimality gap of NFSP, we have proposed a new
method replacing NFSP's best response computation with regret matching method.
The new algorithm can make the optimality gap converge to zero as it iterates,
thus converge faster than original NFSP. We have conduct experiments on three
typical environments of perfect-information games and imperfect information
games in OpenSpiel and all showed that our new algorithm performances better
than original NFSP.
