Data hiding is one widely used approach for protecting authentication and ownership. Most multimedia content like images and videos are transmitted or saved in the compressed form. This kind of lossy compression, such as JPEG, can destroy the hidden data, which raises the need of robust data hiding. It is still an open challenge to achieve the goal of data hiding that can be against these compressions. Recently, deep learning has shown large success in data hiding, while non-differentiability of JPEG makes it challenging to train a deep pipeline for improving robustness against lossy compression. The existing SOTA approaches replace the non-differentiable parts with differentiable modules that perform similar operations. Multiple limitations exist: (a) large engineering effort; (b) requiring a white-box knowledge of compression attacks; (c) only works for simple compression like JPEG. In this work, we propose a simple yet effective approach to address all the above limitations at once. Beyond JPEG, our approach has been shown to improve robustness against various image and video lossy compression algorithms.