Off-Policy Reinforcement Learning for Synchronization in Multiagent Graphical Games

This paper develops an off-policy reinforcement learning (RL) algorithm to solve optimal synchronization of multiagent systems. This is accomplished by using the framework of graphical games. In contrast to traditional control protocols, which require complete knowledge of agent dynamics, the proposed off-policy RL algorithm is a model-free approach, in that it solves the optimal synchronization problem without knowing any knowledge of the agent dynamics. A prescribed control policy, called behavior policy, is applied to each agent to generate and collect data for learning. An off-policy Bellman equation is derived for each agent to learn the value function for the policy under evaluation, called target policy, and find an improved policy, simultaneously. Actor and critic neural networks along with least-square approach are employed to approximate target control policies and value functions using the data generated by applying prescribed behavior policies. Finally, an off-policy RL algorithm is presented that is implemented in real time and gives the approximate optimal control policy for each agent using only measured data. It is shown that the optimal distributed policies found by the proposed algorithm satisfy the global Nash equilibrium and synchronize all agents to the leader. Simulation results illustrate the effectiveness of the proposed method.