  In a multi-agent system, agents share their local observations to gain global
situational awareness for decision making and collaboration using a message
passing system. When to send a message, how to encode a message, and how to
leverage the received messages directly affect the effectiveness of the
collaboration among agents. When training a multi-agent cooperative game using
reinforcement learning (RL), the message passing system needs to be optimized
together with the agent policies. This consequently increases the model's
complexity and poses significant challenges to the convergence and performance
of learning. To address this issue, we propose the Belief-map Assisted
Multi-agent System (BAMS), which leverages a neuro-symbolic belief map to
enhance training. The belief map decodes the agent's hidden state to provide a
symbolic representation of the agent's understanding of the environment and
other agent's status. The simplicity of symbolic representation allows the
gathering and comparison of the ground truth information with the belief, which
provides an additional channel of feedback for the learning. Compared to the
sporadic and delayed feedback coming from the reward in RL, the feedback from
the belief map is more consistent and reliable. Agents using BAMS can learn a
more effective message passing network to better understand each other,
resulting in better performance in a cooperative predator and prey game with
varying levels of map complexity and compare it to previous multi-agent message
passing models. The simulation results showed that BAMS reduced training epochs
by 66\%, and agents who apply the BAMS model completed the game with 34.62\%
fewer steps on average.
