Ophthalmic microsurgery is technically difficult because the scale of required surgical tool manipulations challenge the limits of the surgeon's visual acuity, sensory perception, and physical dexterity. Intraoperative optical coherence tomography (OCT) imaging with micrometer-scale resolution is increasingly being used to monitor and provide enhanced real-time visualization of ophthalmic surgical maneuvers, but surgeons still face physical limitations when manipulating instruments inside the eye. Autonomously controlled robots are one avenue for overcoming these physical limitations. We demonstrate the feasibility of using learning from demonstration and reinforcement learning with an industrial robot to perform OCT-guided corneal needle insertions in an ex vivo model of deep anterior lamellar keratoplasty (DALK) surgery. Our reinforcement learning agent trained on ex vivo human corneas, then outperformed surgical fellows in reaching a target needle insertion depth in mock corneal surgery trials. This work shows the combination of learning from demonstration and reinforcement learning is a viable option for performing OCT guided robotic ophthalmic surgery.