We propose an efficient image registration strategy that is based on learned prior distributions of transformation parameters. These priors are used to constrain a finite- time multi-start optimization method. Motivation for this approach comes from the fact that standard affine brain image registration methods, especially those based on gradient descent optimization alone, are affected by the initial search position. While global optimization methods can resolve this problem, they are are often very time consuming. Our goal is to build an explicit prior model of the gap between a typical registration solution and the solution gained by a global optimization method. We use this learned prior model to restrict randomized search in the relevant parameter space surrounding the initial solution. Global optimization in this restricted parameter space provides, in finite time, results that are superior to both gradient descent and the general multi-start strategy. The performance of our method is illustrated on a data set of 67 elderly and neurodegenerative brains. Our novel learning strategy and the associated registration method are shown to outperform other approaches. Theoretical, synthetic and real-world examples illustrate this improvement.