This paper addresses the dual-secure communication problem in a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided integrated sensing and communication (ISAC) system. The system aims to maximize the long-term average security rate for legitimate users (LUs) while ensuring the echo signal-to-noise ratio (SNR) thresholds and rate constraints. To tackle the complex non-convex optimization problem, deep deterministic policy gradient (DDPG) and soft actor-critic (SAC) algorithms are proposed. The DDPG algorithm is used for continuous actions, while SAC is designed for discrete actions. Simulation results show that the proposed algorithms effectively optimize the system performance, with STAR-RIS outperforming conventional RIS and dual-spliced RIS in terms of security rate. The SAC algorithm, despite higher computational complexity, demonstrates superior exploration capabilities and learning efficiency. The study highlights the benefits of STAR-RIS in enhancing communication and sensing performance, particularly in high-frequency bands and challenging environments.This paper addresses the dual-secure communication problem in a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided integrated sensing and communication (ISAC) system. The system aims to maximize the long-term average security rate for legitimate users (LUs) while ensuring the echo signal-to-noise ratio (SNR) thresholds and rate constraints. To tackle the complex non-convex optimization problem, deep deterministic policy gradient (DDPG) and soft actor-critic (SAC) algorithms are proposed. The DDPG algorithm is used for continuous actions, while SAC is designed for discrete actions. Simulation results show that the proposed algorithms effectively optimize the system performance, with STAR-RIS outperforming conventional RIS and dual-spliced RIS in terms of security rate. The SAC algorithm, despite higher computational complexity, demonstrates superior exploration capabilities and learning efficiency. The study highlights the benefits of STAR-RIS in enhancing communication and sensing performance, particularly in high-frequency bands and challenging environments.