In sum, the policy learning methods of imperfect information games based on Actor-Critic reinforcement learning perform well on poker and can be transferred to other imperfect information games. The experiments demonstrate the policies learned by the proposed methods perform well and gain steadily compared with the existing approaches. Finally, this paper takes the most popular six-player Texas hold ’em poker to validate the performance of the proposed optimal policy learning method.

Secondly, this paper proposes a novel multi-player poker policy update method: asynchronous policy update algorithm (APU) and dual-network asynchronous policy update algorithm (Dual-APU) for multi-player multi-policy scenarios and multi-player sharing-policy scenarios, respectively. Firstly, this paper builds the Actor network to make decisions with imperfect information and the Critic network to evaluate policies with perfect information. This paper proposes an optimal policy learning method for multi-player poker games based on Actor-Critic reinforcement learning. Therefore, designing an effective optimal policy learning method has more realistic significance. However, it is not clear that playing an equilibrium policy in multi-player games would be wise so far, and it is infeasible to theoretically validate whether a policy is optimal. Poker has been considered a challenging problem in both artificial intelligence and game theory because poker is characterized by imperfect information and uncertainty, which are similar to many realistic problems like auctioning, pricing, cyber security, and operations.

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