SHAQ::Incorporating Shapley Value Theory into Multi-Agent Q-Learning

• DOI: 10.48550/arxiv.2105.15013
• Publication Date: 2021-01-01
• Authors: Wang, Jianhong; Zhang, Yuan; Gu, Yunjie; Kim, Tae-Kyun
• Keywords: FOS: Computer and information sciences; Computer Science - Machine Learning; 0209 industrial biotechnology; Computer Science - Artificial Intelligence; Multi-agent systems; 02 engineering and technology; Multi-agent reinforcement learning; Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Game Theory; 0202 electrical engineering, electronic engineering, information engineering; Computer Science - Multiagent Systems; multi-agent coordination; Multiagent Systems (cs.MA)

Value factorisation is a useful technique for multi-agent reinforcement learning (MARL) in global reward game, however its underlying mechanism is not yet fully understood. This paper studies a theoretical framework for value factorisation with interpretability via Shapley value theory. We generalise Shapley value to Markov convex game called Markov Shapley value (MSV) and apply it as a value factorisation method in global reward game, which is obtained by the equivalence between the two games. Based on the properties of MSV, we derive Shapley-Bellman optimality equation (SBOE) to evaluate the optimal MSV, which corresponds to an optimal joint deterministic policy. Furthermore, we propose Shapley-Bellman operator (SBO) that is proved to solve SBOE. With a stochastic approximation and some transformations, a new MARL algorithm called Shapley Q-learning (SHAQ) is established, the implementation of which is guided by the theoretical results of SBO and MSV. We also discuss the relationship between SHAQ and relevant value factorisation methods. In the experiments, SHAQ exhibits not only superior performances on all tasks but also the interpretability that agrees with the theoretical analysis. The implementation of this paper is on https://github.com/hsvgbkhgbv/shapley-q-learning.<br/>Accepted paper for NeurIPS 2022<br/>