Learning Hyperparameters via a Data-Emphasized Variational Objective

Abstract: When training large flexible models on limited data, avoiding overfitting is a practical concern. Common grid search or smarter search methods rely on expensive separate runs at each candidate hyperparameter while carving out a validation set that reduces available training data. In this paper, we consider direct gradient-based learning of regularization hyperparameters on the full training set via the evidence lower bound ("ELBo") objective from Bayesian variational methods. We focus on scenarios where the model is over-parameterized for flexibility while the approximate posterior is chosen to be Gaussian with isotropic covariance for tractability, even though it cannot match the true posterior exactly. In such scenarios, we find the ELBo prioritizes posteriors that match the prior variance, which leads to severely underfitting the data. Instead, we recommend a data-emphasized ELBo that upweights the influence of the data likelihood relative to the prior. In Bayesian transfer learning of classifiers for text and images, our method reduces 88+ hour grid searches of past work to under 3 hours while delivering comparable accuracy. We further demonstrate how our approach enables efficient yet accurate approximations of Gaussian processes with learnable length-scale kernels.