Co-designing autonomous robotic agents involves simultaneously optimizing the controller and the agent’s physical design. Its inherent bi-level optimization formulation necessitates an outer loop design optimization driven by an inner loop control optimization. This can be challenging when the design space is large and each design evaluation involves a data-intensive reinforcement learning process for control optimization. To improve the sample efficiency of co-design, we propose a multi-fidelity-based exploration strategy in which we tie the controllers learned across the design spaces through a universal policy learner for warm-starting subsequent controller learning problems. Experiments performed on a wide range of agent design problems demonstrate the superiority of our method compared to baselines. Additionally, analysis of the optimized designs shows interesting design alterations including design simplifications and non-intuitive alterations.