QMIX is a popular $Q$-learning algorithm for cooperative MARL in the centralised training and decentralised execution paradigm. In order to enable easy decentralisation, QMIX restricts the joint action $Q$-values it can represent to be a monotonic mixing of each agent's utilities. However, this restriction prevents it from representing value functions in which an agent's ordering over its actions can depend on other agents' actions. To analyse this representational limitation, we first formalise the objective QMIX optimises, which allows us to view QMIX as an operator that first computes the $Q$-learning targets and then projects them into the space representable by QMIX. This projection returns a representable $Q$-value that minimises the unweighted squared error across all joint actions. We show in particular that this projection can fail to recover the optimal policy even with access to $Q^*$, which primarily stems from the equal weighting placed on each joint action. We rectify this by introducing a weighting into the projection, in order to place more importance on the better joint actions. We propose two weighting schemes and prove that they recover the correct maximal action for any joint action $Q$-values, and therefore for $Q^*$ as well. Based on our analysis and results in the tabular setting we introduce two scalable versions of our algorithm, Centrally-Weighted (CW) QMIX and Optimistically-Weighted (OW) QMIX and demonstrate improved performance on both predator-prey and challenging multi-agent StarCraft benchmark tasks (Samvelyan et al., 2019).

The proof of your theory lacks discussion of POMDP settings. Although the framework in focused in solving the Dec-POMDP problem, most parts of the proof are under MDP setting. But there is no more discussion on that phenomenon. The use of weighting is not that convinced. In Section 6.2.3, the performance of the Weighted QMIX method is unacceptable.

I want to thank the authors for preparing the detailed rebuttal. This paper was discussed among all the reviewers during the post-rebuttal discussion phase. Also, given the borderline scores, we requested an additional emergency reviewer for this paper. While the rebuttal helped clarify some of the reviewers' questions, the reviewers shared a few concerns regarding the experimental evaluation, comparisons to SOTA, and the relationship of the proposed approach w.r.t. the relevant literature. Overall, the reviewers have a positive assessment of the paper and appreciated the technical insights to design the weighted QMIX algorithm.

QMIX is a popular Q -learning algorithm for cooperative MARL in the centralised training and decentralised execution paradigm. In order to enable easy decentralisation, QMIX restricts the joint action Q -values it can represent to be a monotonic mixing of each agent's utilities. However, this restriction prevents it from representing value functions in which an agent's ordering over its actions can depend on other agents' actions. To analyse this representational limitation, we first formalise the objective QMIX optimises, which allows us to view QMIX as an operator that first computes the Q -learning targets and then projects them into the space representable by QMIX. This projection returns a representable Q -value that minimises the unweighted squared error across all joint actions.