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Counterfactual Regret Minimization (CFR)} is the popular method for findingapproximate Nash equilibrium in two-player zero-sum games with imperfectinformation. CFR solves games by travsersing the full game tree iteratively,which limits its scalability in larger games. When applying CFR to solvelarge-scale games in previously, large-scale games are abstracted intosmall-scale games firstly. Secondly, CFR is used to solve the abstract game.And finally, the solution strategy is mapped back to the original large-scalegame. However, this process requires considerable expert knowledge, and theaccuracy of abstraction is closely related to expert knowledge. In addition,the abstraction also loses certain information, which will eventually affectthe accuracy of the solution strategy. Towards this problem, a recent method,\textit{Deep CFR} alleviates the need for abstraction and expert knowledge byapplying deep neural networks directly to CFR in full games. In this paper, weintroduces \textit{Neural Network Counterfactual Regret Minimization (NNCFR)},an improved variant of \textit{Deep CFR} that has a faster convergence byconstructing a dueling netwok as the value network. Moreover, an evaluationmodule is designed by combining the value network and Monte Carlo, whichreduces the approximation error of the value network. In addition, a new lossfunction is designed in the procedure of training policy network in theproposed \textit{NNCFR}, which can be good to make the policy network morestable. The extensive experimental tests are conducted to show that the\textit{NNCFR} converges faster and performs more stable than \textit{DeepCFR}, and outperforms \textit{Deep CFR} with respect to exploitability andhead-to-head performance on test games.

D2CFR: Minimize Counterfactual Regret with Deep Dueling Neural Network