Shapley Value Based Multi-Agent Reinforcement Learning: Theory, Method and Its Application to Energy Network

Multi-agent reinforcement learning is an area of rapid advancement in artificial intelligence and machine learning. One of the important questions to be answered is how to conduct credit assignment in a multi-agent system. There have been many schemes designed to conduct credit assignment by multi-agent reinforcement learning algorithms. Although these credit assignment schemes have been proved useful in improving the performance of multi-agent reinforcement learning, most of them are designed heuristically without a rigorous theoretic basis and therefore infeasible to understand how agents cooperate. In this thesis, we aim at investigating the foundation of credit assignment in multi-agent reinforcement learning via cooperative game theory. We first extend a game model called convex game and a payoff distribution scheme called Shapley value in cooperative game theory to Markov decision process, named as Markov convex game and Markov Shapley value respectively. We represent a global reward game as a Markov convex game under the grand coalition. As a result, Markov Shapley value can be reasonably used as a credit assignment scheme in the global reward game. Markov Shapley value possesses the following virtues: (i) efficiency; (ii) identifiability of dummy agents; (iii) reflecting the contribution and (iv) symmetry, which form the fair credit assignment. Based on Markov Shapley value, we propose three multi-agent reinforcement learning algorithms called SHAQ, SQDDPG and SMFPPO. Furthermore, we extend Markov convex game to partial observability to deal with the partially observable problems, named as partially observable Markov convex game. In application, we evaluate SQDDPG and SMFPPO on the real-world problem in energy networks.