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Value factorisation proves to be a very useful technique in multi-agent reinforcement learning (MARL), but the underlying mechanism is not yet fully understood. This paper explores a theoretic basis for value factorisation. We generalise the Shapley value in the coalitional game theory to a Markov convex game (MCG) and use it to guide value factorisation in MARL. We show that the generalised Shapley value possesses several features such as (1) accurate estimation of the maximum global value, (2) fairness in the factorisation of the global value, and (3) being sensitive to dummy agents. The proposed theory yields a new learning algorithm called Sharpley Q-learning (SHAQ), which inherits the important merits of ordinary Q-learning but extends it to MARL. In comparison with prior-arts, SHAQ has a much weaker assumption (MCG) that is more compatible with real-world problems, but has superior explainability and performance in many cases. We demonstrated SHAQ and verified the theoretic claims on Predator-Prey and StarCraft Multi-Agent Challenge (SMAC).
VDN and QMIX are two popular value-based algorithms for cooperative MARL that learn a centralized action value function as a monotonic mixing of per-agent utilities. While this enables easy decentralization of the learned policy, the restricted joint
Social learning is a key component of human and animal intelligence. By taking cues from the behavior of experts in their environment, social learners can acquire sophisticated behavior and rapidly adapt to new circumstances. This paper investigates
Reinforcement learning in multi-agent scenarios is important for real-world applications but presents challenges beyond those seen in single-agent settings. We present an actor-critic algorithm that trains decentralized policies in multi-agent settin
We explore value-based multi-agent reinforcement learning (MARL) in the popular paradigm of centralized training with decentralized execution (CTDE). CTDE has an important concept, Individual-Global-Max (IGM) principle, which requires the consistency
This paper proposes a definition of system health in the context of multiple agents optimizing a joint reward function. We use this definition as a credit assignment term in a policy gradient algorithm to distinguish the contributions of individual a