The development of environmentally friendly, green communications is at the forefront of designing future Internet of Things (IoT) networks, although many opportunities to improve energy conservation from energy-harvesting (EH) sensors remain unexplored. Ubiquitous computing power, available in the form of cloudlets, enables the processing of the collected observations at the network edge. Often, the information that the Artificial Intelligence of Things (AIoT) application obtains by processing observations from one sensor can also be obtained by processing observations from another sensor. Consequently, a sensor can take advantage of the correlation between processed observations to avoid unnecessary transmissions and save energy. For example, when two cameras monitoring the same intersection detect the same vehicles, the system can recognize this overlap and reduce redundant data transmissions. This approach allows the network to conserve energy while still ensuring accurate vehicle detection, thereby maintaining the overall performance of the AIoT task. In this article, we consider such a system and develop a novel solution named balancing energy efficiency in sensor networks with multiagent reinforcement learning (BEES-MARL). Our proposed solution is capable of taking advantage of correlations in a system with multiple EH-powered sensors observing the same scene and transmitting their observations to a cloudlet. We evaluate the proposed solution in two data-driven use cases to verify its benefits and in a general setting to demonstrate scalability. Our solution improves task performance, measured by recall, by up to 16% over a heuristic approach, while minimizing latency and preventing outages.