In problems where input features have varying amounts of noise, using distinct regularization hyperparameters for different features provides an effective means of managing model complexity. While regularizers for neural networks and support vector machines often rely on multiple hyperparameters, regularizers for structured prediction models (used in tasks such as sequence labeling or parsing) typically rely only on a single shared hyperparameter for all features. In this paper, we consider the problem of choosing regularization hyperparameters for log-linear models, a class of structured prediction probabilistic models which includes conditional random fields (CRFs). Using an implicit differentiation trick, we derive an efficient gradient-based method for learning Gaussian regularization priors with multiple hyperparameters. In both simulations and the real-world task of computational RNA secondary structure prediction, we find that multiple hyperparameter learning can provide a significant boost in accuracy compared to using only a single regularization hyperparameter.