By employing neural network approximation architecture, the nonlinear discounted optimal regulation is handled under event-driven adaptive critic framework. The main idea lies in adopting an improved learning algorithm, so that the event-driven discounted optimal control law can be derived via training a neural network. The stability guarantee and simulation illustration are also included. It is highlighted that the initial stabilizing control policy is not required during the implementation process with the combined learning rule. Moreover, the closed-loop system is formulated as an impulsive model. Then, the related stability issue is addressed by using the Lyapunov approach. The simulation studies, including an application to a power system, are also conducted to verify the effectiveness of the present design method.