Reinforcement Learning for Nash Noncoperative and Pareto Cooperative Optimal Linear Systems

In this paper we use the reinforcement learning techniques for optimal control of linear-quadratic systems, and consider two situations: when controllers cooperate (Pareto strategies) and when they do not cooperate (Nash strategies). These situations are encountered in optimal control and reinforcement learning of several engineering systems (especially in energy systems), economics, and in general machine learning. We compare the corresponding optimal costs using normalized data assuming that the system initial conditions are uniformly distributed on the unit sphere, and provide an estimate how much cooperation helps in learning optimal controllers for these kind of problems. The theoretical results are demonstrated on an example of an electric power system.