Distributed Dynamic Programming and an O.D.E. Framework of Distributed TD-Learning for Networked Multi-Agent Markov Decision Processes

The primary objective of this paper is to investigate distributed dynamic programming (DP) and distributed temporal difference (TD) learning algorithms for networked multi-agent Markov decision problems (MAMDPs). In our study, we adopt a distributed multi-agent framework where individual agents have access only to their own rewards, lacking insights into the rewards of other agents. Additionally, each agent has the ability to share its parameters with neighboring agents through a communication network, represented by a graph. Our contributions can be summarized in two key points: 1) We introduce a novel distributed DP, inspired by the averaging consensus method in the continuous-time domain. The convergence of this DP is assessed through control theory perspectives. 2) Building upon the aforementioned DP, we devise a new distributed TD-learning algorithm and prove its convergence. A standout feature of our proposed distributed DP is its incorporation of two independent dynamic systems, each with a distinct role. This characteristic sets the stage for a novel distributed TD-learning strategy, the convergence of which can be directly established using the Borkar-Meyn theorem.