[Paper Review] Efficient hyperparameter optimization by way of PAC-Bayes bound minimization

John J. Cherian, Andrew G. Taube+7 more|arXiv (Cornell University)|Aug 14, 2020

Machine Learning and Data Classification48 references4 citations

TL;DR

This paper proposes a novel hyperparameter optimization method based on minimizing a PAC-Bayes bound to reduce overfitting in high-dimensional hyperparameter settings. By formulating the objective as a differentiable PAC-Bayes generalization bound and using gradient-based optimization, the method achieves better out-of-sample performance than standard approaches, with asymptotic complexity matching or improving upon existing methods.

ABSTRACT

Identifying optimal values for a high-dimensional set of hyperparameters is a problem that has received growing attention given its importance to large-scale machine learning applications such as neural architecture search. Recently developed optimization methods can be used to select thousands or even millions of hyperparameters. Such methods often yield overfit models, however, leading to poor performance on unseen data. We argue that this overfitting results from using the standard hyperparameter optimization objective function. Here we present an alternative objective that is equivalent to a Probably Approximately Correct-Bayes (PAC-Bayes) bound on the expected out-of-sample error. We then devise an efficient gradient-based algorithm to minimize this objective; the proposed method has asymptotic space and time complexity equal to or better than other gradient-based hyperparameter optimization methods. We show that this new method significantly reduces out-of-sample error when applied to hyperparameter optimization problems known to be prone to overfitting.

Motivation & Objective

• To address the problem of overfitting in high-dimensional hyperparameter optimization, especially in large-scale machine learning applications like neural architecture search.
• To develop a new optimization objective that better generalizes to unseen data by leveraging PAC-Bayes theory.
• To design an efficient gradient-based algorithm that minimizes the PAC-Bayes bound with optimal space and time complexity.
• To empirically demonstrate improved out-of-sample performance on hyperparameter optimization problems prone to overfitting.

Proposed method

• The method formulates hyperparameter optimization as minimization of a PAC-Bayes bound on the expected out-of-sample error.
• It introduces a differentiable objective function derived from PAC-Bayes generalization bounds, enabling gradient-based optimization.
• The algorithm uses stochastic gradient descent to optimize the hyperparameters by backpropagating through the model's generalization error estimate.
• It maintains asymptotic space and time complexity equal to or better than existing gradient-based hyperparameter optimization methods.
• The approach treats hyperparameters as random variables with a posterior distribution, enabling Bayesian generalization bounds to guide optimization.
• The method is scalable to thousands or even millions of hyperparameters, suitable for modern deep learning workloads.

Experimental results

Research questions

• RQ1 Can a PAC-Bayes-based objective function reduce overfitting in high-dimensional hyperparameter optimization compared to standard empirical risk minimization?
• RQ2 How does the proposed gradient-based optimization method compare in terms of computational complexity to existing hyperparameter optimization techniques?
• RQ3 Does minimizing a PAC-Bayes bound lead to better generalization performance on unseen data in practical hyperparameter tuning tasks?
• RQ4 Can the method be efficiently scaled to large-scale hyperparameter spaces common in neural architecture search?
• RQ5 What is the empirical impact of using a PAC-Bayes objective on out-of-sample error in benchmark hyperparameter optimization problems?

Key findings

• The proposed method significantly reduces out-of-sample error compared to standard hyperparameter optimization techniques on problems known to be prone to overfitting.
• The method achieves asymptotic space and time complexity equal to or better than existing gradient-based hyperparameter optimization methods.
• By minimizing a PAC-Bayes bound, the approach improves generalization without requiring additional hyperparameter tuning or validation data.
• The method demonstrates robust performance across diverse hyperparameter optimization tasks, particularly in high-dimensional settings.
• Empirical results confirm that the PAC-Bayes objective leads to models that generalize better to unseen data, validating the theoretical foundation.