Compressing an image with more bits automatically allocated to the region of interest (ROI) than to the background can both protect key information and reduce substantial redundancy. This paper models ROI image compression as an optimization problem of minimizing a weighted sum of the rate of the image and distortion of the ROI. The traditional framework solves this problem by cascading ROI prediction and ROI coding, through which achieving the optimized solution is impossible. To improve coding performance, we propose a novel deep-learning-based unified framework that can achieve rate distortion optimization for ROI compression. Specifically, the proposed framework includes a pair of ROI encoder and decoder convolutional neural networks and a learned entropy codec. The encoder network simultaneously generates multiscale representations that support efficient rate allocation and an implicit ROI mask that guides rate allocation. The proposed framework can automatically complete ROI image compression, and it can be optimized from data in an end-to-end manner. To effectively train the framework by back propagation, we develop a soft-to-hard ROI prediction scheme to make the entire framework differential. To improve visual quality, we propose a hierarchical distortion loss function to protect both pixel-level fidelity for ROI and structural similarity for the entire image. The proposed framework is implemented in two scenarios: salient-target and face-target ROI compression. Comparative experiments demonstrate the advantages of the proposed framework over the traditional framework, including considerably better subjective visual quality, significantly higher objective ROI compression performance and execution efficiency.