Quantitative MRI often relies on the acquisition of multiple images with different scan settings. Therefore, data redundancy can be exploited to further accelerate imaging by deep learning. We propose a unified model for joint reconstruction and $$$R_2^*$$$-mapping from sparse data and embed this in a Recurrent Inference Machine, an iterative inverse problem solving network. Applied to high-resolution multi-echo gradient echo data of a cohort study covering the entire adult life span, the error in $$$R_2^*$$$ significantly decreases. With increasing acceleration factor, an increasing reduction in error is observed, pointing to a larger benefit for sparser data.