Graph-based environments pose unique challenges to multi-agent reinforcement learning. In decentralized approaches, agents operate within a given graph and make decisions based on partial or outdated observations. The size of the observed neighborhood limits the generalizability to different graphs and affects the reactivity of agents, the quality of the selected actions, and the communication overhead. This work focuses on generalizability and resolves the trade-off in observed neighborhood size with a continuous information flow in the whole graph. We propose a recurrent message-passing model that iterates with the environment's steps and allows nodes to create a global representation of the graph by exchanging messages with their neighbors. Agents receive the resulting learned graph observations based on their location in the graph. Our approach can be used in a decentralized manner at runtime and in combination with a reinforcement learning algorithm of choice. We evaluate our method across 1000 diverse graphs in the context of routing in communication networks and find that it enables agents to generalize and adapt to changes in the graph.

We propose and analyse a novel nonparametric goodness of fit testing procedure for exchangeable exponential random graph models (ERGMs) when a single network realisation is observed. The test determines how likely it is that the observation is generated from a target unnormalised ERGM density. Our test statistics are derived from a kernel Stein discrepancy, a divergence constructed via Steins method using functions in a reproducing kernel Hilbert space, combined with a discrete Stein operator for ERGMs. The test is a Monte Carlo test based on simulated networks from the target ERGM. We show theoretical properties for the testing procedure for a class of ERGMs. Simulation studies and real network applications are presented.