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

Jianhong Wang, Yuan Zhang, Yunjie Gu, Tae Kyun Kim

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

6 Citations (SciVal)


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 placed on

Original languageEnglish
Title of host publication36th Conference on Neural Information Processing Systems, NeurIPS 2022
EditorsS. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh
PublisherNeural Information Processing Systems Foundation, Inc.
ISBN (Electronic)9781713871088
Publication statusPublished - 28 Nov 2022
Event36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans, USA United States
Duration: 28 Nov 20229 Dec 2022

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference36th Conference on Neural Information Processing Systems, NeurIPS 2022
Country/TerritoryUSA United States
CityNew Orleans

Bibliographical note

Funding Information:
This work is sponsored by the Engineering and Physical Sciences Research Council of UK (EPSRC) under awards EP/S000909/1. Tae-Kyun Kim is partly sponsored by KAIA grant (22CTAP-C163793-02, MOLIT), NST grant (CRC 21011, MSIT), KOCCA grant (R2022020028, MCST) and the Samsung Display corporation. Yuan Zhang is sponsored by the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 953348 (ELO-X).

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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