The optimal control of distribution networks often requires monitoring and communication infrastructure, either centralized or distributed. However, most of the current distribution systems lack this kind of infrastructure and rely on sub-optimal, fit-and-forget, local controls to ensure the security of the network. In this paper, we propose a data-driven algorithm that uses historical data, advanced optimization techniques, and machine learning methods, to design local controls that emulate the optimal behavior without the use of any communication. We demonstrate the performance of the optimized local control on a three-phase, unbalanced, low-voltage, distribution network. The results show that our data-driven methodology clearly outperforms standard industry local control and successfully imitates an optimal-power-flow-based control.