Today, system operators rely on local control of distributed energy resources (DERs), such as photovoltaic units, wind turbines and batteries, to increase operational flexibility. These schemes offer a communication-free, robust, cheap, but rather sub-optimal solution and do not fully exploit the DER capabilities. The operational flexibility of active distribution networks can be greatly enhanced by the optimal control of DERs. However, it usually requires remote monitoring and communication infrastructure, which current distribution networks lack due to the high cost and complexity. In this paper, we investigate data-driven control algorithms that use historical data, advanced off-line optimization techniques, and machine learning methods, to design local controls that emulate the optimal behavior without the use of any communication. We elaborate on the suitability of various schemes based on different local features, we investigate safety challenges arising from data-driven control schemes, and we show the performance of the optimized local controls on a three-phase, unbalanced, low-voltage, distribution network.