The falling costs of solar photovoltaic systems and energy storage mean that these are being increasingly deployed in microgrids across the globe. Distributed storage can provide benefits for its owner, but can also play a key role in improving microgrid stability and resilience. However, most approaches to date assume that a central authority can control multiple nodes or households in the network. This introduces significant communication and control requirements, and may introduce points of failure. In this work we provide an initial exploration of how a machine learning model, trained on optimal control solutions, can be used locally at each node in the network to emulate a similar behaviour. The aim is for the trained model to provide benefits both for the individual energy storage owners, while also enabling community-level cooperative behaviour - all in a low communication-overhead, privacy-preserving manner. It is experimentally shown that a neural network trained on limited data from optimal schedules can learn node interactions and network characteristics, and can achieve partial voltage regulation for the entire microgrid. This can be done while still achieving a small (3%) network-wide cost savings compared to a scenario in which no distributed storage is present, can be implemented only locally, and does not introduce any significant requirements for central control and communication.