Smart inverters have been considered the primary fast solution for voltage regulation in power distribution systems. Optimizing the coordination between inverters can be computationally challenging. Reactive power control using fixed local rules have been shown to be subpar. Here, nonlinear inverter control rules are proposed by leveraging machine learning tools. The designed control rules can be expressed by a set of coefficients. These control rules can be nonlinear functions of both remote and local inputs. The proposed control rules are designed to jointly minimize the voltage deviation across buses. By using the support vector machines, control rules with sparse representations are obtained which decrease the communication between the operator and the inverters. The designed control rules are tested under different grid conditions and compared with other reactive power control schemes. The results show promising performance.