In recent years, many applications have deployed incentive mechanisms to promote users' attention and engagement. Most incentive mechanisms determine specific incentive values based on users' attributes (e.g., preferences), while such information is unavailable in many real-world applications. Meanwhile, due to budget restrictions, realizing successful incentivization for all users can be challenging to complete. In this light, we consider leveraging social influence to maximize the incentivization result. We can directly incentivize influential users to affect more users, so the cost of incentivizing these users can be decreased. However, identifying influential users in a social network requires complete information about influence strength among users, which is impractical to acquire in real-world situations. In this research, we propose an end-to-end reinforcement learning-based framework, called Geometric Actor-Critic (GAC), to tackle the abovementioned problem. The proposed approach can realize effective incentive allocation without having prior knowledge about users' attributes. Three real-world social network datasets have been adopted in the experiments to evaluate the performance of GAC. The experimental results indicate that GAC can learn and apply effective incentive allocation policies in unknown social networks and outperform existing incentive allocation approaches.