The Starcraft results also seem fine, but not so strong as it make it obvious that committed exploration is a crucial empirical improvement for QMIX - while MAVEN agents learn faster in 3s5z, the final performance looks the same; MAVEN agents seem to have less variability in final win rate on 5m_vs_6m; and QMIX actually seems to have better final performance on 10m_vs_11m. The results in figure 2 and 4 do however suggest that there may be scenarios where the advantage of MAVEN is higher. Minor comments: 1) line 64 and others: the subscript "qmix" should probably be wrapped in a "\text{}" 2) first eqn in section 3: inconsistency between using subscripts and superscripts, i.e. u_i and u i 3) line 81: perhaps better phrased as: "the *best* action of agent i..." 4) line 86: u_n i - u_ U i? 5) line 87: I was confused by what "the set of all possible such orderings over the action-values" means. Besides a degeneracy when some of the Q values are identical, isn't there only one valid ordering? Or are you just trying to cover that degeneracy? 6) Definition 1: perhaps add an intuitive explanation, e.g. "Intuitively, a Q-function is non-monotonic if the ordering of best actions for agent i can be affected by the other agents action choices at that time step."

The paper presents a new exploration strategy for decentralized MARL that is based on a joint latent variable that is shared between the agent. This paper is a difficult case. While the theoretical insights concerning the difficulty of the exploration problem in decentralized MARL are insightful, the experimental results were not good enough in the original submission to convince the reviewers. The algorithm was only in one case considerably better than the competitor QMix and other baseline comparison were missing. However, in the rebuttal the authors provided much better results as well as additional comparison to Qtrans.

Centralised training with decentralised execution is an important setting for cooperative deep multi-agent reinforcement learning due to communication constraints during execution and computational tractability in training. In this paper, we analyse value-based methods that are known to have superior performance in complex environments. We specifically focus on QMIX, the current state-of-the-art in this domain. We show that the representation constraints on the joint action-values introduced by QMIX and similar methods lead to provably poor exploration and suboptimality. Furthermore, we propose a novel approach called MAVEN that hybridises value and policy-based methods by introducing a latent space for hierarchical control.

Centralised training with decentralised execution is an important setting for cooperative deep multi-agent reinforcement learning due to communication constraints during execution and computational tractability in training. In this paper, we analyse value-based methods that are known to have superior performance in complex environments. We specifically focus on QMIX, the current state-of-the-art in this domain. We show that the representation constraints on the joint action-values introduced by QMIX and similar methods lead to provably poor exploration and suboptimality. Furthermore, we propose a novel approach called MAVEN that hybridises value and policy-based methods by introducing a latent space for hierarchical control. The value-based agents condition their behaviour on the shared latent variable controlled by a hierarchical policy.