Safety and efficiency are crucial for autonomous driving in roundabouts, especially mixed traffic with both autonomous vehicles (AVs) and human-driven vehicles. This paper presents a learning-based algorithm that promotes safe and efficient driving across varying roundabout traffic conditions. A deep Q-learning network is used to learn optimal strategies in complex multi-vehicle roundabout scenarios, while a Kolmogorov-Arnold Network (KAN) improves the AVs' environmental understanding. To further enhance safety, an action inspector filters unsafe actions, and a route planner optimizes driving efficiency. Moreover, model predictive control ensures stability and precision in execution. Experimental results demonstrate that the proposed system consistently outperforms state-of-the-art methods, achieving fewer collisions, reduced travel time, and stable training with smooth reward convergence.