Learning Hyperparameters via a Data-Emphasized Variational Objective

TL;DR

This paper introduces a data-emphasized variational objective for hyperparameter learning that avoids validation sets and significantly reduces tuning time while maintaining accuracy.

Contribution

It proposes a novel data-emphasized ELBO that improves hyperparameter optimization efficiency in Bayesian models, especially for large models with limited data.

Findings

Reduces hyperparameter tuning time from over 88 hours to under 3 hours.

Achieves comparable accuracy to traditional grid search methods.

Enables efficient Gaussian process approximations with learnable kernels.

Abstract

When training large models on limited data, avoiding overfitting is paramount. Common grid search or smarter search methods rely on expensive separate runs for each candidate hyperparameter, while carving out a validation set that reduces available training data. In this paper, we study gradient-based learning of hyperparameters via the evidence lower bound (ELBO) objective from Bayesian variational methods. This avoids the need for any validation set. We focus on scenarios where the model is over-parameterized for flexibility and the approximate posterior is chosen to be Gaussian with isotropic covariance for tractability, even though it cannot match the true posterior. In such scenarios, we find the ELBO prioritizes posteriors that match the prior, leading to severe underfitting. Instead, we recommend a data-emphasized ELBO that upweights the likelihood but not the prior. In Bayesian transfer learning of image and text classifiers, our method reduces the 88+ hour grid search 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 lengthscale kernels.