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