Abstract Rigid Point Cloud Registration (PCReg) refers to the problem of finding the rigid transformation between two sets of point clouds. This problem is particularly important due to the advances in new 3D sensing hardware, and it is challenging because neither the correspondence nor the transformation parameters are known. Traditional local PCReg methods (e.g., ICP) rely on local optimization algorithms, which can get trapped in bad local minima in the presence of noise, outliers, bad initializations, etc. To alleviate these issues, this paper proposes Inverse Composition Discriminative Optimization (ICDO), an extension of Discriminative Optimization (DO), which learns a sequence of update steps from synthetic training data that search the parameter space for an improved solution. Unlike DO, ICDO is object-independent and generalizes even to unseen shapes. We evaluated ICDO on both synthetic and real data, and show that ICDO can match the speed and outperform the accuracy of state-of-the-art PCReg algorithms