Extending deep Q-learning to cooperative multi-agent settings is challenging due to the exponential growth of the joint action space, the non-stationary environment, and the credit assignment problem. Value decomposition allows deep Q-learning to be applied at the joint agent level, at the cost of reduced expressivity. Building on past work in this direction, our paper proposes PairVDN, a novel method for decomposing the value function into a collection of pair-wise, rather than per-agent, functions, improving expressivity at the cost of requiring a more complex (but still efficient) dynamic programming maximisation algorithm. Our method enables the representation of value functions which cannot be expressed as a monotonic combination of per-agent functions, unlike past approaches such as VDN and QMIX. We implement a novel many-agent cooperative environment, Box Jump, and demonstrate improved performance over these baselines in this setting. We open-source our code and environment atthis https URL.
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