In this work, we use a multi-agent learning framework based on information theory concepts such as maximum entropy and rate distortion theory in order to control the reactive power sharing in an islanded microgrid. The distortion between each agent (distributed generator) and the environment behavior determines a fitness function that is used as a signal to control reactive power sharing in the system. The results, which were obtained through a simulated four nodes microgrid, show how the reactive power is shared in the system, specially when considerable load variations are present.