Policy space response oracle (PSRO) is a population-based algorithm that can be used to solve two-player zero-sum games. In the PSRO solution framework, optimizing policy diversity is crucial for addressing nontransitive game problems, helping the agent population avoid exploitation by unfamiliar opponents. In addition, while deep reinforcement learning is highly effective in solving complex game environments, its integration with PSRO remains fragmented and lacking in effective coordination. In this study, we propose distributed PSRO to efficiently solve complex game scenarios. To enhance diversity while managing optimization costs, we introduce TOP-K truncation, which prioritizes high-quality opponents and limits the size of the policy pool during sampling. This approach not only reduces interference from less effective strategies but also ensures computational efficiency by seamlessly integrating with our distributed training framework. We also design the distributed training framework to incorporate diversity estimation directly into the sampling process, achieving diversity optimization without incurring additional computational overhead. Furthermore, we introduce the opponent first (OF) method, which enhances decision-making by leveraging opponent information during interaction sampling. We perform experimental validation using a nontransitive mixture model and AlphaStar888 to confirm the effectiveness of the TOP-K truncation approach. Finally, we demonstrate the feasibility and efficiency of the distributed training framework and the OF approach in a Google Research Football 11 versus 11 scenario.

Policy space response oracles (PSRO) is an important algorithmic framework for approximating Nash equilibria in two-player zero-sum games. Enhancing policy diversity has been shown to improve the performance of PSRO in this approximation process significantly. However, existing diversity metrics are often prone to redundancy, which can hinder optimal strategy convergence. In this paper, we introduce the policy similarity measure (PSM), a novel approach that combines Gaussian and cosine similarity measures to assess policy similarity. We further incorporate the PSM into the PSRO framework as a regularization term, effectively fostering a more diverse policy population. We demonstrate the effectiveness of our method in two distinct game environments: a non-transitive mixture model and Leduc poker. The experimental results show that the PSM-augmented PSRO outperforms baseline methods in reducing exploitability by approximately 7% and exhibits greater policy diversity in visual analysis. Ablation studies further validate the benefits of combining Gaussian and cosine similarities in cultivating more diverse policy sets. This work provides a valuable method for measuring and improving the policy diversity in two-player zero-sum games.

Self-play methods have achieved remarkable success in two-player zero-sum games, attaining superhuman performance in many complex game domains. Parallelizing learners is a feasible approach to handle complex games. However, parallelizing learners often leads to the suboptimal exploitation of computational resources, resulting in inefficiencies. This paper introduces the Mixed Hierarchical Oracle (MHO), which is designed to enhance training efficiency and performance in complex two-player zero-sum games. MHO efficiently leverages interaction data among parallelized solvers during the Parallelized Oracle (PO) process, while employing Model Soups (MS) to consolidate fragmented computational resources and Hierarchical Exploration (HE) to balance exploration and exploitation. These carefully designed enhancements for parallelized systems significantly improve the training performance of self-play. Additionally, MiniStar is introduced as an open source environment focused on small-scale combat scenarios, developed to facilitate research in self-play algorithms. The MHO is evaluated on both the AlphaStar888 matrix game and MiniStar environment, and ablation studies further demonstrates its effectiveness in improving the agent’s decision-making capabilities. This work highlight the potential of the MHO to optimize compute resource utilization and improve performance in self-play methods.