The stability of vertical emittance is a critical performance metric for modern high-brightness synchrotron light sources. This paper presents a real-time, RL-based correction framework based on Deep Reinforcement Learning (DRL) by employing Dueling Deep Q-Network (DQN) with a discrete action space to dynamically adjust skew quadrupole magnets. To ensure operational safety and accelerate convergence, we introduce a curriculum learning strategy and leverage a high-fidelity simulation of the Shanghai Synchrotron Radiation Facility (SSRF) for systematic hyperparameter optimization. Experimental results demonstrate that the agent, trained in-situ on the real machine, successfully achieves stabilization of the beam-size readback at the sub-micrometer fluctuation level and exhibits rapid adaptability to target changes. This work validates the feasibility of using RL for robust, online accelerator optimization during user beam delivery.