Soft robots driven by stimuli-responsive materials have their own unique advantages over traditional rigid robots such as large actuation, light weight, good flexibility and biocompatibility. However, the large actuation of soft robots inherently co-exists with difficulty in control with high precision. This article presents a soft artificial muscle driven robot mimicking cuttlefish with a fully integrated on-board system including power supply and wireless communication system. Without any motors, the movements of the cuttlefish robot are solely actuated by dielectric elastomer which exhibits muscle-like properties including large deformation and high energy density. Reinforcement learning is used to optimize the control strategy of the cuttlefish robot instead of manual adjustment. From scratch, the swimming speed of the robot is enhanced by 91% with reinforcement learning, reaching to 21 mm/s (0.38 body length per second). The design principle behind the structure and the control of the robot can be potentially useful in guiding device designs for demanding applications such as flexible devices and soft robots.