On the Sample Complexity of Storage Control

Understanding the data value for energy-storage control is critical. The performance of the control policy is highly related to the quality of demand information. An accurate prediction about future demand can better the performance of energy storage control. Thus, the storage control asks for sufficient data-sample collection for qualified prediction. However, there lacks of a theory to quantify the data sufficiency for the energy-storage control problem. Meanwhile, demand data samples include privacy information while the storage managers have to procure the data from data owners. Thus, it is necessary to determine the relationship between the data size and the storage-control performance. In addition, a growing number of studies have proposed many storage-control policies. However, we are unknown how to theoretically verify their data-use efficiency. Here, we develop the sample complexity theory of storage-control problem, which enables us to theoretically measure the data-use efficiency of the control strategy and assess the data value. We proposed the sample-based dynamic programming (SDP) algorithm that is both cost-minimization and data-use efficient. Based on the SDP and the sample complexity theory, we manifest the trade-off between data size, computational load, and storage-control performances. Finally, we used real-world data to conduct numerical experiments to validate the effectiveness of the proposed method.