Exploiting Geometric Structures for Modeling Multi-Agent Behaviors: A New Thinking

In this paper, we rethink model agent behaviors from a geometric structure perspective in multi-agent reinforcement learning. Modeling agent behaviors is essential for understanding how agents interact and facilitating effective decisions. The key lies in capturing the dependencies and sequential relationships among agent decisions. Since each decision influences the subsequent choices, this forms a hierarchical and nested tree-like structure of interdependencies. While modeling tree-like data in Euclidean spaces could cause distortion, which results in a loss of agent decision structure information. Motivated by this, we reconsider model agent behaviors in hyperbolic space, and propose the Hyperbolic Multi-Agent Representations (HMAR) method, which projects the agent behaviors into a Poincaré ball and leverages hyperbolic neural networks to learn agent policy representations. Additionally, we designed a contrastive loss function to train this network, minimizing the distance in feature space between different representations of the same agent while maximizing the distance between representations of distinct agents. Experimental results provide empirical evidence for the effectiveness of the HMAR method in cooperative and competitive environments, demonstrating the potential of hyperbolic agent representations for effective decision-making in multi-agent environments.