A machine learning approach to the optimal control of the customer dynamics

We consider a continuous model of the optimal control of the customer dynamics based on marketing policies as a non-autonomous system of ODEs. The model tracks the history of the simultaneous changes from the beginning to the current time for the evolution of the company's regular, referral, and potential customers. We then present a new supervised machine-learning algorithm for the numerical simulation of the problem. The proposed learning algorithm implements a polynomial kernel to simplify the formulation of the method. To avoid computational complexity, the Bernstein kernels are used to get a simple optimization marketing strategy by using the Support Vector Regression (SVR) in a least-squares framework. Some numerical experiments are carried out to support the proposed model and the method. The method provides approximate numerical results with high accuracy by kernels of polynomials of low degree. The running time of the technique is also illustrated versus the increasing number of training points to see the polynomial behavior of the running time.