The sim-to-real gap remains a critical challenge in robotics, hindering the deployment of algorithms trained in simulation to real-world systems. We propose a flexible Real-to-Sim-to-Real (RSR) framework whose central contribution is an information-theoretic cost function that explicitly accounts for sim-to-real discrepancies. This cost balances two objectives, completing the task and steering the policy to collect real-world samples that are maximally informative for improving transfer. It can be integrated seamlessly into existing reinforcement learning algorithms (e.g., PPO, SAC) and ensures a balanced exploration of critical regions in the real domain. The framework treats differentiable simulation as optional: when a differentiable simulator is available, the collected informative data can also be used to tune simulator parameters. We implement the framework with the MuJoCo MJX platform and demonstrate its generality by evaluating on both manipulation tasks with a 6-DOF robotic arm and locomotion tasks on a legged robot. Empirical results show that our RSR loop yields more efficient data acquisition and substantially improves task performance in real-world that achieves a smoother sim-to-real transfer.

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