Satellite-aerial-ground integrated networks (SAGINs) have emerged as a promising infrastructure for next-generation wireless networks. Considering the fading effects of obstacles over longer transmission distances, in this article, we equip reconfigurable intelligent surfaces (RIS) on the unmanned aerial vehicle (UAV) to reflect the uplink signals from the ground vehicle transmitter (VT) to high altitude platform (HAP). The HAP then acts as a relay to forward the signals to satellites through hybrid free space optics (FSO) links. This article focuses on optimizing the system ergodic sum rate in SAGINs. To address the high-dimensional non-convex optimization problems, an asymmetric long short-term memory (LSTM)-deep deterministic policy gradient (DDPG) algorithm, called AL-DDPG, is proposed. The AL-DDPG algorithm leverages hidden states in partially observable Markov states using a memory inference method to address the training convergence problem. Numerical results demonstrate the superiority of the AL-DDPG algorithm, with a 16% improvement in the system sum rate compared to the traditional optimization algorithm. Besides, we provide insights into the impacts of various factors on system performance.