Affiliations: Department of Computer and Information Science, Indiana University Purdue University Indianapolis, 723 W Michigan St SL 280 Indianapolis, Indiana 46202, United States. E-mails: thamnguy@iupui.edu, smukhopa@iupui.edu
Abstract: In this paper, we explore the capability of selective decentralization in improving the reinforcement learning performance for unknown systems using model-based approaches. In selective decentralization, we automatically select the best communication policies among agents. Our learning design, which is built on the control system principles, includes two phases. First, we apply system identification to train an approximated model for the unknown systems. Second, we find the suboptimal solution of the Hamilton–Jacobi–Bellman (HJB) equation to derive the suboptimal control. For linear systems, the HJB equation transforms to the well-known Riccati equation with closed-form solution. In nonlinear system, we discretize the approximation model as a Markov Decision Process (MDP) in order to determine the control using dynamic programming algorithms. Since the theoretical foundation of using MDP to control the nonlinear system has not been thoroughly developed, we prove that the control law learned by the discrete-MDP approach is guarantee to stabilize the system, which is the learning goal, given several sufficient conditions. These learning and control techniques could be applied in centralized, completely decentralized and selectively decentralized manner. Our results show that selective decentralization outperforms the complete decentralization and the centralization approaches when the systems are completely decoupled or strongly interconnected.
Keywords: Decentralized control, Hamilton–Jacobi–Bellman equation, Markov process, multi-agent systems
