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Bayesian Optimization for Hyperparameters Tuning in Neural Networks

Gabriele Onorato

TL;DR

This work demonstrates the efficiency of BO in reducing the number of hyperparameter tuning trials while achieving competitive model performance and underlines the potential of BO in automating neural network tuning, contributing to improved accuracy and computational efficiency in machine learning pipelines.

Abstract

This study investigates the application of Bayesian Optimization (BO) for the hyperparameter tuning of neural networks, specifically targeting the enhancement of Convolutional Neural Networks (CNN) for image classification tasks. Bayesian Optimization is a derivative-free global optimization method suitable for expensive black-box functions with continuous inputs and limited evaluation budgets. The BO algorithm leverages Gaussian Process regression and acquisition functions like Upper Confidence Bound (UCB) and Expected Improvement (EI) to identify optimal configurations effectively. Using the Ax and BOTorch frameworks, this work demonstrates the efficiency of BO in reducing the number of hyperparameter tuning trials while achieving competitive model performance. Experimental outcomes reveal that BO effectively balances exploration and exploitation, converging rapidly towards optimal settings for CNN architectures. This approach underlines the potential of BO in automating neural network tuning, contributing to improved accuracy and computational efficiency in machine learning pipelines.

Bayesian Optimization for Hyperparameters Tuning in Neural Networks

TL;DR

This work demonstrates the efficiency of BO in reducing the number of hyperparameter tuning trials while achieving competitive model performance and underlines the potential of BO in automating neural network tuning, contributing to improved accuracy and computational efficiency in machine learning pipelines.

Abstract

This study investigates the application of Bayesian Optimization (BO) for the hyperparameter tuning of neural networks, specifically targeting the enhancement of Convolutional Neural Networks (CNN) for image classification tasks. Bayesian Optimization is a derivative-free global optimization method suitable for expensive black-box functions with continuous inputs and limited evaluation budgets. The BO algorithm leverages Gaussian Process regression and acquisition functions like Upper Confidence Bound (UCB) and Expected Improvement (EI) to identify optimal configurations effectively. Using the Ax and BOTorch frameworks, this work demonstrates the efficiency of BO in reducing the number of hyperparameter tuning trials while achieving competitive model performance. Experimental outcomes reveal that BO effectively balances exploration and exploitation, converging rapidly towards optimal settings for CNN architectures. This approach underlines the potential of BO in automating neural network tuning, contributing to improved accuracy and computational efficiency in machine learning pipelines.

Paper Structure

This paper contains 85 sections, 2 theorems, 35 equations, 17 figures, 2 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Mathematical Optimization
  3. Linear Programming
  4. Efficiency of the Simplex Algorithm
  5. Nonlinear Programming
  6. Integer Programming
  7. Neural Networks
  8. Overview
  9. Machine Learning
  10. Historical Context
  11. Basic Structure of Neural Networks
  12. Input Layer
  13. Hidden Layers
  14. Output Layer
  15. Learning Process
  16. ...and 70 more sections

Key Result

Theorem 1.2.1

Consider the LP problem pl:general, if the polyhedron $P = \{x \in R^n | Ax \geq b\}$ does not contain any line, then only and only one of the subsequent statement is true:

Figures (17)

  • Figure 1: Example of a simple Feedfoward Neural Network
  • Figure 5: The four most commonly used activation functions are showed here, with LeakyReLU featuring $a$ as a hyperparameter.
  • Figure 6: L1 and L2 regularization techniques
  • Figure 7: Binary Cross Entropy Loss
  • Figure 10: Example Classes of the CIFAR-10 Dataset
  • ...and 12 more figures

Theorems & Definitions (2)

  • Theorem 1.2.1: Fundamental Theorem of Linear Programming
  • Theorem 3.6.1: Weierstrass