A Multi-Population Mean-Field Game Approach for Large-Scale Agents Cooperative Attack-Defense Evolution in High-Dimensional Environments †

Abstract

As one of the important issues of multi-agent collaboration, the large-scale agents’ cooperative attack–defense evolution requires a large number of agents to make stress-effective strategies to achieve their goals in complex environments. Multi-agent attack and defense in high-dimensional environments (3D obstacle scenarios) present the challenge of being able to accurately control high-dimensional state quantities. Moreover, the large scale makes the dynamic interactions in the attack and defense problems increase dramatically, which, using traditional optimal control techniques, can cause a dimensional explosion. How to model and solve the cooperative attack–defense evolution problem of large-scale agents in high-dimensional environments have become a challenge. We jointly considered energy consumption, inter-group attack and defense, intra-group collision avoidance, and obstacle avoidance in their cost functions. Meanwhile, the high-dimensional state dynamics were used to describe the motion of agents under environmental interference. Then, we formulated the cooperative attack–defense evolution of large-scale agents in high-dimensional environments as a multi-population high-dimensional stochastic mean-field game (MPHD-MFG), which significantly reduced the communication frequency and computational complexity. We tractably solved the MPHD-MFG with a generative-adversarial-network (GAN)-based method using the MFGs’ underlying variational primal–dual structure. Based on our approach, we carried out an integrative experiment in which we analytically showed the fast convergence of our cooperative attack–defense evolution algorithm by the convergence of the Hamilton–Jacobi–Bellman equation’s residual errors. The experiment also showed that a large number of drones can avoid obstacles and smoothly evolve their attack and defense behaviors while minimizing their energy consumption. In addition, the comparison with the baseline methods showed that our approach is advanced.