  Learning sparse coordination graphs adaptive to the coordination dynamics
among agents is a long-standing problem in cooperative multi-agent learning.
This paper studies this problem and proposes a novel method using the variance
of payoff functions to construct context-aware sparse coordination topologies.
We theoretically consolidate our method by proving that the smaller the
variance of payoff functions is, the less likely action selection will change
after removing the corresponding edge. Moreover, we propose to learn action
representations to effectively reduce the influence of payoff functions'
estimation errors on graph construction. To empirically evaluate our method, we
present the Multi-Agent COordination (MACO) benchmark by collecting classic
coordination problems in the literature, increasing their difficulty, and
classifying them into different types. We carry out a case study and
experiments on the MACO and StarCraft II micromanagement benchmark to
demonstrate the dynamics of sparse graph learning, the influence of graph
sparseness, and the learning performance of our method. (The MACO benchmark and
codes are publicly available at
https://github.com/TonghanWang/CASEC-MACO-benchmark.)
