Policy Space Diversity for Non-Transitive Games
This work addresses a specific weakness in multi-agent reinforcement learning for non-transitive games, offering an incremental improvement over existing PSRO methods.
The paper tackles the problem of approximating Nash Equilibria in multi-agent non-transitive games by proposing a new diversity metric for Policy-Space Response Oracles (PSRO) that guarantees better approximation, resulting in PSD-PSRO, which empirically produces significantly less exploitable policies than state-of-the-art variants.
Policy-Space Response Oracles (PSRO) is an influential algorithm framework for approximating a Nash Equilibrium (NE) in multi-agent non-transitive games. Many previous studies have been trying to promote policy diversity in PSRO. A major weakness in existing diversity metrics is that a more diverse (according to their diversity metrics) population does not necessarily mean (as we proved in the paper) a better approximation to a NE. To alleviate this problem, we propose a new diversity metric, the improvement of which guarantees a better approximation to a NE. Meanwhile, we develop a practical and well-justified method to optimize our diversity metric using only state-action samples. By incorporating our diversity regularization into the best response solving in PSRO, we obtain a new PSRO variant, Policy Space Diversity PSRO (PSD-PSRO). We present the convergence property of PSD-PSRO. Empirically, extensive experiments on various games demonstrate that PSD-PSRO is more effective in producing significantly less exploitable policies than state-of-the-art PSRO variants.