Towards Understanding Linear Value Decomposition in Cooperative Multi-Agent Q-Learning

Abstract

Value decomposition is a popular and promising approach to scaling up multi-agent reinforcement learning in cooperative settings. However, the theoretical understanding of such methods is limited. In this paper, we introduce a variant of the fitted Q-iteration framework for analyzing multi-agent Q-learning with value decomposition. Based on this framework, we derive a closed-form solution to the empirical Bellman error minimization with linear value decomposition. With this novel solution, we further reveal two interesting insights: 1) linear value decomposition implicitly implements a classical multi-agent credit assignment called counterfactual difference rewards; and 2) On-policy data distribution or richer Q function classes can improve the training stability of multi-agent Q-learning. In the empirical study, our experiments demonstrate the realizability of our theoretical closed-form formulation and implications in the didactic examples and a broad set of StarCraft II unit micromanagement tasks, respectively.