Hyperparameter optimization with approximate gradient

TL;DR

This paper introduces an approximate gradient-based algorithm for hyperparameter optimization that allows for early updates and demonstrates competitive empirical performance on regularization tasks.

Contribution

It proposes a novel method for hyperparameter optimization using inexact gradients with proven convergence conditions.

Findings

Method performs well on logistic regression and kernel Ridge regression.

Empirical results are competitive with state-of-the-art approaches.

Allows hyperparameter updates before full model convergence.

Abstract

Most models in machine learning contain at least one hyperparameter to control for model complexity. Choosing an appropriate set of hyperparameters is both crucial in terms of model accuracy and computationally challenging. In this work we propose an algorithm for the optimization of continuous hyperparameters using inexact gradient information. An advantage of this method is that hyperparameters can be updated before model parameters have fully converged. We also give sufficient conditions for the global convergence of this method, based on regularity conditions of the involved functions and summability of errors. Finally, we validate the empirical performance of this method on the estimation of regularization constants of L2-regularized logistic regression and kernel Ridge regression. Empirical benchmarks indicate that our approach is highly competitive with respect to state of the art methods.