Optical wireless communication (OWC) provides high aggregate data rates in the range of Terabits per second (Tb/s). Specifically, OWC using infrared lasers as transmitters has been considered as a strong candidate in the next generation of wireless communication. Rate splitting (RS) is a transmission scheme derived to improve spectral efficiency in dense wireless networks. In RS, the transmitted power is allocated to different messages, common and private messages, serving multiple users simultaneously, where each user can decode the desired message following a certain procedure. Moreover, two-tier precoding RS scheme has been proposed to overcome the limitations of traditional RS in multi-group scenarios. In this context, power allocation (PA) is a crucial issue, which can affect the performance of RS. Therefore, we formulate a PA optimization problem to enhance the data rates of RS-based OWC networks. However, such optimization problems are complex due to the use of different messages intended to the users. In this paper, we design and train a deep neural network (DNN) model to determine the power allocated to the messages of RS, while fulfilling the demands of users. The results show the accuracy of our trained DNN model when used in an online phase.