Bayesian Optimization in Action

Apply advanced techniques for optimizing machine learning processes. Bayesian optimization helps pinpoint the best configuration for your machine learning models with speed and accuracy. In Bayesian Optimization in Action you will learn how to: • Train Gaussian processes on both sparse and large data sets • Combine Gaussian processes with deep neural networks to make them flexible and expressive • Find the most successful strategies for hyperparameter tuning • Navigate a search space and identify high-performing regions • Apply Bayesian optimization to practical use cases such as cost-constrained, multi-objective, and preference optimization • Use PyTorch, GPyTorch, and BoTorch to implement Bayesian optimization Bayesian Optimization in Action shows you how to optimize hyperparameter tuning, A/B testing, and other aspects of the machine learning process by applying cutting-edge Bayesian techniques. Using clear language, illustrations, and concrete examples, this book proves that Bayesian optimization doesn’t have to be difficult! You’ll get in-depth insights into how Bayesian optimization works and learn how to implement it with cutting edge Python libraries. The book’s easy-to-reuse code samples let you hit the ground running by plugging them straight into your own projects. About the technology Experimenting in science and engineering can be costly and time-consuming, especially without a reliable way to narrow down your choices. Bayesian optimization helps you identify optimal configurations to pursue in a search space. It uses a Gaussian process and machine learning techniques to model an objective function and quantify the uncertainty of predictions. Whether you’re tuning machine learning models, recommending products to customers, or engaging in research, Bayesian optimization can help you make better decisions, faster. About the book Bayesian Optimization in Action teaches you how to build Bayesian optimization systems from the ground up. This book transforms state-of-the-art research into usable techniques that you can easily put into practice, all fully illustrated with useful code samples. In it, you’ll hone your understanding of Bayesian optimization through engaging examples—from forecasting the weather, to finding the optimal amount of sugar for coffee, and even deciding if someone is psychic! Along the way, you’ll explore scenarios for when there are multiple objectives, when each decision has its own cost, and when feedback is in the form of pairwise comparisons. With this collection of techniques, you’ll be ready to find the optimal solution for everything from transport and logistics to cancer treatments. About the reader For machine learning practitioners who are confident in math and statistics. About the author Quan Nguyen is a Python programmer and machine learning enthusiast. He is interested in solving decision-making problems that involve uncertainty. Quan has authored several books on Python programming and scientific computing. He is currently pursuing a Ph.D. degree in computer science at Washington University in St. Louis where he does research on Bayesian methods in machine learning. Bayesian Optimization in Action contents forewords preface acknowledgments about this book Who should read this book? How this book is organized: A roadmap About the code liveBook discussion forum about the author About the technical editor about the cover illustration 1 Introduction to Bayesian optimization 1.1 Finding the optimum of an expensive black box function 1.1.1 Hyperparameter tuning as an example of an expensive black box optimization problem 1.1.2 The problem of expensive black box optimization 1.1.3 Other real-world examples of expensive black box optimization problems 1.2 Introducing Bayesian optimization 1.2.1 Modeling with a Gaussian process 1.2.2 Making decisions with a BayesOpt policy 1.2.3 Combining the GP and the optimization policy to form the optimization loop 1.2.4 BayesOpt in action 1.3 What will you learn in this book? Summary Part 1—Modeling with Gaussian processes 2 Gaussian processes as distributions over functions 2.1 How to sell your house the Bayesian way 2.2 Modeling correlations with multivariate Gaussian distributions and Bayesian updates 2.2.1 Using multivariate Gaussian distributions to jointly model multiple variables 2.2.2 Updating MVN distributions 2.2.3 Modeling many variables with high-dimensional Gaussian distributions 2.3 Going from a finite to an infinite Gaussian 2.4 Implementing GPs in Python 2.4.1 Setting up the training data 2.4.2 Implementing a GP class 2.4.3 Making predictions with a GP 2.4.4 Visualizing predictions of a GP 2.4.5 Going beyond one-dimensional objective functions 2.5 Exercise Summary 3 Customizing a Gaussian process with the mean and covariance functions 3.1 The importance of priors in Bayesian models 3.2 Incorporating what you already know into a GP 3.3 Defining the functional behavior with the mean function 3.3.1 Using the zero mean function as the base strategy 3.3.2 Using the constant function with gradient descent 3.3.3 Using the linear function with gradient descent 3.3.4 Using the quadratic function by implementing a custom mean function 3.4 Defining variability and smoothness with the covariance function 3.4.1 Setting the scales of the covariance function 3.4.2 Controlling smoothness with different covariance functions 3.4.3 Modeling different levels of variability with multiple length scales 3.5 Exercise Summary Part 2—Making decisions with Bayesian optimization 4 Refining the best result with improvement-based policies 4.1 Navigating the search space in BayesOpt 4.1.1 The BayesOpt loop and policies 4.1.2 Balancing exploration and exploitation 4.2 Finding improvement in BayesOpt 4.2.1 Measuring improvement with a GP 4.2.2 Computing the Probability of Improvement 4.2.3 Running the PoI policy 4.3 Optimizing the expected value of improvement 4.4 Exercises 4.4.1 Exercise 1: Encouraging exploration with PoI 4.4.2 Exercise 2: BayesOpt for hyperparameter tuning Summary 5 Exploring the search space with bandit-style policies 5.1 Introduction to the MAB problem 5.1.1 Finding the best slot machine at a casino 5.1.2 From MAB to BayesOpt 5.2 Being optimistic under uncertainty with the Upper Confidence Bound policy 5.2.1 Optimism under uncertainty 5.2.2 Balancing exploration and exploitation 5.2.3 Implementation with BoTorch 5.3 Smart sampling with the Thompson sampling policy 5.3.1 One sample to represent the unknown 5.3.2 Implementation with BoTorch 5.4 Exercises 5.4.1 Exercise 1: Setting an exploration schedule for the UCB 5.4.2 Exercise 2: BayesOpt for hyperparameter tuning Summary 6 Using information theory with entropy-based policies 6.1 Measuring knowledge with information theory 6.1.1 Measuring uncertainty with entropy 6.1.2 Looking for a remote control using entropy 6.1.3 Binary search using entropy 6.2 Entropy search in BayesOpt 6.2.1 Searching for the optimum using information theory 6.2.2 Implementing entropy search with BoTorch 6.3 Exercises 6.3.1 Exercise 1: Incorporating prior knowledge into entropy search 6.3.2 Exercise 2: Bayesian optimization for hyperparameter tuning Summary Part 3—Extending Bayesian optimization to specialized settings 7 Maximizing throughput with batch optimization 7.1 Making multiple function evaluations simultaneously 7.1.1 Making use of all available resources in parallel 7.1.2 Why can’t we use regular BayesOpt policies in the batch setting? 7.2 Computing the improvement and upper confidence bound of a batch of points 7.2.1 Extending optimization heuristics to the batch setting 7.2.2 Implementing batch improvement and UCB policies 7.3 Exercise 1: Extending TS to the batch setting via resampling 7.4 Computing the value of a batch of points using information theory 7.4.1 Finding the most informative batch of points with cyclic refinement 7.4.2 Implementing batch entropy search with BoTorch 7.5 Exercise 2: Optimizing airplane designs Summary 8 Satisfying extra constraints with constrained optimization 8.1 Accounting for constraints in a constrained optimization problem 8.1.1 Constraints can change the solution of an optimization problem 8.1.2 The constraint-aware BayesOpt framework 8.2 Constraint-aware decision-making in BayesOpt 8.3 Exercise 1: Manual computation of constrained EI 8.4 Implementing constrained EI with BoTorch 8.5 Exercise 2: Constrained optimization of airplane design Summary 9 Balancing utility and cost with multifidelity optimization 9.1 Using low-fidelity approximations to study expensive phenomena 9.2 Multifidelity modeling with GPs 9.2.1 Formatting a multifidelity dataset 9.2.2 Training a multifidelity GP 9.3 Balancing information and cost in multifidelity optimization 9.3.1 Modeling the costs of querying different fidelities 9.3.2 Optimizing the amount of information per dollar to guide optimization 9.4 Measuring performance in multifidelity optimization 9.5 Exercise 1: Visualizing average performance in multifidelity optimization 9.6 Exercise 2: Multifidelity optimization with multiple low-fidelity approximations Summary 10 Learning from pairwise comparisons with preference optimization 10.1 Black-box optimization with pairwise comparisons 10.2 Formulating a preference optimization problem and formatting pairwise comparison data 10.3 Training a preference-based GP 10.4 Preference optimization by playing king of the hill Summary 11 Optimizing multiple objectives at the same time 11.1 Balancing multiple optimization objectives with BayesOpt 11.2 Finding the boundary of the most optimal data points 11.3 Seeking to improve the optimal data boundary 11.4 Exercise: Multiobjective optimization of airplane design Summary Part 4—Special Gaussian process models 12 Scaling Gaussian processes to large datasets 12.1 Training a GP on a large dataset 12.1.1 Setting up the learning task 12.1.2 Training a regular GP 12.1.3 Problems with training a regular GP 12.2 Automatically choosing representative points from a large dataset 12.2.1 Minimizing the difference between two GPs 12.2.2 Training the model in small batches 12.2.3 Implementing the approximate model 12.3 Optimizing better by accounting for the geometry of the loss surface 12.4 Exercise Summary 13 Combining Gaussian processes with neural networks 13.1 Data that contains structures 13.2 Capturing similarity within structured data 13.2.1 Using a kernel with GPyTorch 13.2.2 Working with images in PyTorch 13.2.3 Computing the covariance of two images 13.2.4 Training a GP on image data 13.3 Using neural networks to process complex structured data 13.3.1 Why use neural networks for modeling? 13.3.2 Implementing the combined model in GPyTorch Summary Appendix—Solutions to the exercises A.1 Chapter 2: Gaussian processes as distributions over functions A.2 Chapter 3: Incorporating prior knowledge with the mean and covariance functions A.3 Chapter 4: Refining the best result with improvement-based policies A.3.1 Exercise 1: Encouraging exploration with Probability of Improvement A.3.2 Exercise 2: BayesOpt for hyperparameter tuning A.4 Chapter 5: Exploring the search space with bandit-style policies A.4.1 Exercise 1: Setting an exploration schedule for Upper Confidence Bound A.4.2 Exercise 2: BayesOpt for hyperparameter tuning A.5 Chapter 6: Using information theory with entropy-based policies A.5.1 Exercise 1: Incorporating prior knowledge into entropy search A.5.2 Exercise 2: BayesOpt for hyperparameter tuning A.6 Chapter 7: Maximizing throughput with batch optimization A.6.1 Exercise 1: Extending TS to the batch setting via resampling A.6.2 Exercise 2: Optimizing airplane designs A.7 Chapter 8: Satisfying extra constraints with constrained optimization A.7.1 Exercise 1: Manual computation of constrained EI A.7.2 Exercise 2: Constrained optimization of airplane design A.8 Chapter 9: Balancing utility and cost with multifidelity optimization A.8.1 Exercise 1: Visualizing average performance in multifidelity optimization A.8.2 Exercise 2: Multifidelity optimization with multiple low-fidelity approximations A.9 Chapter 11: Optimizing multiple objectives at the same time A.10 Chapter 12: Scaling Gaussian processes to large data sets index A B C D E F G H I J K L M N O P Q R S T U V W Bayesian optimization helps pinpoint the best configuration for your machine learning models with speed and accuracy. Put its advanced techniques into practice with this hands-on guide.In Bayesian Optimization in Action you will learn how to: Train Gaussian processes on both sparse and large data sets Combine Gaussian processes with deep neural networks to make them flexible and expressive Find the most successful strategies for hyperparameter tuning Navigate a search space and identify high-performing regions Apply Bayesian optimization to cost-constrained, multi-objective, and preference optimization Implement Bayesian optimization with PyTorch, GPyTorch, and BoTorch Bayesian Optimization in Action shows you how to optimize hyperparameter tuning, A/B testing, and other aspects of the machine learning process by applying cutting-edge Bayesian techniques. Using clear language, illustrations, and concrete examples, this book proves that Bayesian optimization doesn't have to be difficult! You'll get in-depth insights into how Bayesian optimization works and learn how to implement it with cutting-edge Python libraries. The book's easy-to-reuse code samples let you hit the ground running by plugging them straight into your own projects. Forewords by Luis Serrano and David Sweet. About the technology In machine learning, optimization is about achieving the best predictions—shortest delivery routes, perfect price points, most accurate recommendations—in the fewest number of steps. Bayesian optimization uses the mathematics of probability to fine-tune ML functions, algorithms, and hyperparameters efficiently when traditional methods are too slow or expensive. About the book Bayesian Optimization in Action teaches you how to create efficient machine learning processes using a Bayesian approach. In it, you'll explore practical techniques for training large datasets, hyperparameter tuning, and navigating complex search spaces. This interesting book includes engaging illustrations and fun examples like perfecting coffee sweetness, predicting weather, and even debunking psychic claims. You'll learn how to navigate multi-objective scenarios, account for decision costs, and tackle pairwise comparisons. What's inside Gaussian processes for sparse and large datasets Strategies for hyperparameter tuning Identify high-performing regions Examples in PyTorch, GPyTorch, and BoTorch About the reader For machine learning practitioners who are confident in math and statistics. About the author Quan Nguyen is a research assistant at Washington University in St. Louis. He writes for the Python Software Foundation and has authored several books on Python programming. Table of Contents 1 Introduction to Bayesian optimization 2 Gaussian processes as distributions over functions 3 Customizing a Gaussian process with the mean and covariance functions 4 Refining the best result with improvement-based policies 5 Exploring the search space with bandit-style policies 6 Leveraging information theory with entropy-based policies 7 Maximizing throughput with batch optimization 8 Satisfying extra constraints with constrained optimization 9 Balancing utility and cost with multifidelity optimization 10 Learning from pairwise comparisons with preference optimization 11 Optimizing multiple objectives at the same time 12 Scaling Gaussian processes to large datasets 13 Combining Gaussian processes with neural networks Bayesian optimization helps pinpoint the best configuration for your machine learning models with speed and accuracy. Put its advanced techniques into practice with this hands-on guide. In Bayesian Optimization in Action you will learn how Bayesian Optimization in Action shows you how to optimize hyperparameter tuning, A/B testing, and other aspects of the machine learning process by applying cutting-edge Bayesian techniques. Using clear language, illustrations, and concrete examples, this book proves that Bayesian optimization doesnt have to be difficult! Youll get in-depth insights into how Bayesian optimization works and learn how to implement it with cutting-edge Python libraries. The books easy-to-reuse code samples let you hit the ground running by plugging them straight into your own projects. Forewords by Luis Serrano and David Sweet . Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology In machine learning, optimization is about achieving the best predictionsshortest delivery routes, perfect price points, most accurate recommendationsin the fewest number of steps. Bayesian optimization uses the mathematics of probability to fine-tune ML functions, algorithms, and hyperparameters efficiently when traditional methods are too slow or expensive. About the book Bayesian Optimization in Action teaches you how to create efficient machine learning processes using a Bayesian approach. In it, youll explore practical techniques for training large datasets, hyperparameter tuning, and navigating complex search spaces. This interesting book includes engaging illustrations and fun examples like perfecting coffee sweetness, predicting weather, and even debunking psychic claims. Youll learn how to navigate multi-objective scenarios, account for decision costs, and tackle pairwise comparisons. What's inside About the reader For machine learning practitioners who are confident in math and statistics. About the author Quan Nguyen is a research assistant at Washington University in St. Louis. He writes for the Python Software Foundation and has authored several books on Python programming. Table of Contents 1 Introduction to Bayesian optimization PART 1 MODELING WITH GAUSSIAN PROCESSES 2 Gaussian processes as distributions over functions 3 Customizing a Gaussian process with the mean and covariance functions PART 2 MAKING DECISIONS WITH BAYESIAN OPTIMIZATION 4 Refining the best result with improvement-based policies 5 Exploring the search space with bandit-style policies 6 Leveraging information theory with entropy-based policies PART 3 EXTENDING BAYESIAN OPTIMIZATION TO SPECIALIZED SETTINGS 7 Maximizing throughput with batch optimization 8 Satisfying extra constraints with constrained optimization 9 Balancing utility and cost with multifidelity optimization 10 Learning from pairwise comparisons with preference optimization 11 Optimizing multiple objectives at the same time PART 4 SPECIAL GAUSSIAN PROCESS MODELS 12 Scaling Gaussian processes to large datasets 13 Combining Gaussian processes with neural networks