Title: PMIC: Improving Multi-Agent Reinforcement Learning with Progressive Mutual Information Collaboration. Abstract: Learning to collaborate is critical in multi-agent reinforcement learning (MARL). A branch of previous works proposes to promote collaboration by maximizing the correlation of agents’ behaviors, which is typically characterised by mutual information (MI) in different forms. However, simply maximizing the MI of agents’ behaviors cannot guarantee achieving better collaboration because suboptimal collaboration can also lead to high MI. In this paper, we first propose a new collaboration criterion to evaluate collaboration from three perspectives, which arrives at a form of the mutual information between global state and joint policy. This bypasses the introduction of explicit additional input of policies and mitigates the scalability issue meanwhile. Moreover, to better leverage MI-based collaboration signals, we propose a novel MARL framework, called Progressive Mutual Information Collaboration (PMIC) which contains two main components. The first component is Dual Progressive Collaboration Buffer (DPCB) which separately stores superior and inferior trajectories in a progressive manner. The second component is Dual Mutual Information Estimator (DMIE), including two neural estimators of our new designed MI based on separate samples in DPCB. We then make use of the neural MI estimates to improve agents' policies: to maximize the MI lower bound associated with superior collaboration to facilitate better collaboration and to minimize the MI upper bound associated with inferior collaboration to avoid falling into local optimal. PMIC is general and can be combined with existing MARL algorithms. Experiments on a wide range of MARL benchmarks show the superior performance of PMIC compared with other MARL algorithms.