  Multi-agent systems (MAS) need to adaptively cope with dynamic environments,
changing agent populations, and diverse tasks. However, most of the multi-agent
systems cannot easily handle them, due to the complexity of the state and task
space. The social impact theory regards the complex influencing factors as
forces acting on an agent, emanating from the environment, other agents, and
the agent's intrinsic motivation, referring to the social force. Inspired by
this concept, we propose a novel gradient-based state representation for
multi-agent reinforcement learning. To non-trivially model the social forces,
we further introduce a data-driven method, where we employ denoising score
matching to learn the social gradient fields (SocialGFs) from offline samples,
e.g., the attractive or repulsive outcomes of each force. During interactions,
the agents take actions based on the multi-dimensional gradients to maximize
their own rewards. In practice, we integrate SocialGFs into the widely used
multi-agent reinforcement learning algorithms, e.g., MAPPO. The empirical
results reveal that SocialGFs offer four advantages for multi-agent systems: 1)
they can be learned without requiring online interaction, 2) they demonstrate
transferability across diverse tasks, 3) they facilitate credit assignment in
challenging reward settings, and 4) they are scalable with the increasing
number of agents.
