Reinforcement Learning for Efficient Multi-Agent Task Allocation in Potential Game Model

The potential game has been widely used to describe multi-agent task allocation. However, The application of traditional game-theoretic algorithms has shown unsatisfactory performance in scenarios with a high agent count. For this, we employ reinforcement learning algorithm to enable each agent to independently make decision in response to other agents’ decisions and variations in the number of agents, ultimately working towards achieving a desired goal. First, we construct a potential game for multi-agent task allocation and design a corresponding utility function for each agent. Then, we propose a deep q-network algorithm based on graph neural network, and enhance the agent selection mechanism in this learning algorithm. During each iteration, a task is randomly selected for an agent from the participant set, and each agent updates its strategy accordingly. Finally, by comparing several representative game theoretical algorithms, the numerical simulations highlight the advantages and performance of our proposed GDQ-Net algorithm across various tasks and numbers of agents under the constructed model.