Title: Dealing with Non-Stationarity in MARL via Trust-Region Decomposition. Abstract: Non-stationarity is one thorny issue in cooperative multi-agent reinforcement learning (MARL). One of the reasons is the policy changes of agents during the learning process. Some existing works have discussed various consequences caused by non-stationarity with several kinds of measurement indicators. This makes the objectives or goals of existing algorithms are inevitably inconsistent and disparate. In this paper, we introduce a novel notion, the $\delta$-$stationarity$ measurement, to explicitly measure the non-stationarity of a policy sequence, which can be further proved to be bounded by the KL-divergence of consecutive joint policies. A straightforward but highly non-trivial way is to control the joint policies' divergence, which is difficult to estimate accurately by imposing the trust-region constraint on the joint policy. Although it has lower computational complexity to decompose the joint policy and impose trust-region constraints on the factorized policies, simple policy factorization like mean-field approximation will lead to more considerable policy divergence, which can be considered as the trust-region decomposition dilemma. We model the joint policy as a pairwise Markov random field and propose a trust-region decomposition network (TRD-Net) based on message passing to estimate the joint policy divergence more accurately. The Multi-Agent Mirror descent policy algorithm with Trust region decomposition, called MAMT, is established by adjusting the trust-region of the local policies adaptively in an end-to-end manner. MAMT can approximately constrain the consecutive joint policies' divergence to satisfy $\delta$-stationarity and alleviate the non-stationarity problem. Our method can bring noticeable and stable performance improvement compared with baselines in cooperative tasks of different complexity.