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Robotic-assisted surgical systems have demonstrated significant potential in enhancing surgical precision and minimizing human errors. However, existing systems lack the ability to accommodate the unique preferences and requirements of individual surgeons. Additionally, they primarily focus on general surgeries (e.g., laparoscopy) and are not suitable for highly precise microsurgeries, such as ophthalmic procedures. Thus, we propose a simulation-based image-guided approach for surgeon-centered autonomous agents that can adapt to the individual surgeon's skill level and preferred surgical techniques during ophthalmic cataract surgery. Our approach utilizes a simulated environment to train reinforcement and imitation learning agents guided by image data to perform all tasks of the incision phase of cataract surgery. By integrating the surgeon's actions and preferences into the training process with the surgeon-in-the-loop, our approach enables the robot to implicitly learn and adapt to the individual surgeon's unique approach through demonstrations. This results in a more intuitive and personalized surgical experience for the surgeon. Simultaneously, it ensures consistent performance for the autonomous robotic apprentice. We define and evaluate the effectiveness of our approach using our proposed metrics; and highlight the trade-off between a generic agent and a surgeon-centered adapted agent. Moreover, our approach has the potential to extend to other ophthalmic surgical procedures, opening the door to a new generation of surgeon-in-the-loop autonomous surgical robots. We provide an open-source simulation framework for …