Bandit Problems

Our purpose in writing this monograph is to give a comprehensive treatment of the subject. We define bandit problems and give the necessary foundations in Chapter 2. Many of the important results that have appeared in the literature are presented in later chapters; these are interspersed with new results. We give proofs unless they are very easy or the result is not used in the sequel. We have simplified a number of arguments so many of the proofs given tend to be conceptual rather than calculational. All results given have been incorporated into our style and notation. The exposition is aimed at a variety of types of readers. Bandit problems and the associated mathematical and technical issues are developed from first principles. Since we have tried to be comprehens ive the mathematical level is sometimes advanced; for example, we use measure-theoretic notions freely in Chapter 2. But the mathema tically uninitiated reader can easily sidestep such discussion when it occurs in Chapter 2 and elsewhere. We have tried to appeal to graduate students and professionals in engineering, biometry, econ omics, management science, and operations research, as well as those in mathematics and statistics. The monograph could serve as a reference for professionals or as a telA in a semester or year-long graduate level course.

A comprehensive and rigorous introduction for graduate students and researchers, with applications in sequential decision-making problems.

In this monograph, the focus is on two extreme cases in which the analysis of regret is particularly simple and elegant: independent and identically distributed payoffs and adversarial payoffs. Besides the basic setting of finitely many actions, it analyzes some of the most important variants and extensions, such as the contextual bandit model.

Multi-armed bandits is a rich, multi-disciplinary area that has been studied since 1933, with a surge of activity in the past 10-15 years. This is the first book to provide a textbook like treatment of the subject.

This book constitutes the refereed proceedings of the 20th International Conference on Algorithmic Learning Theory, ALT 2009, held in Porto, Portugal, in October 2009, co-located with the 12th International Conference on Discovery Science, DS 2009. The 26 revised full papers presented together with the abstracts of 5 invited talks were carefully reviewed and selected from 60 submissions. The papers are divided into topical sections of papers on online learning, learning graphs, active learning and query learning, statistical learning, inductive inference, and semisupervised and unsupervised learning. The volume also contains abstracts of the invited talks: Sanjoy Dasgupta, The Two Faces of Active Learning; Hector Geffner, Inference and Learning in Planning; Jiawei Han, Mining Heterogeneous; Information Networks By Exploring the Power of Links, Yishay Mansour, Learning and Domain Adaptation; Fernando C.N. Pereira, Learning on the Web.

In recent years, the multi-armed bandit (MAB) framework has attracted a lot of attention in various applications, from recommender systems and information retrieval to healthcare and finance. This success is due to its stellar performance combined with attractive properties, such as learning from less feedback. The multiarmed bandit field is currently experiencing a renaissance, as novel problem settings and algorithms motivated by various practical applications are being introduced, building on top of the classical bandit problem. This book aims to provide a comprehensive review of top recent developments in multiple real-life applications of the multi-armed bandit. Specifically, we introduce a taxonomy of common MAB-based applications and summarize the state-of-the-art for each of those domains. Furthermore, we identify important current trends and provide new perspectives pertaining to the future of this burgeoning field.

In 1989 the first edition of this book set out Gittins' pioneering index solution to the multi-armed bandit problem and his subsequent investigation of a wide of sequential resource allocation and stochastic scheduling problems. Since then there has been a remarkable flowering of new insights, generalizations and applications, to which Glazebrook and Weber have made major contributions. This second edition brings the story up to date. There are new chapters on the achievable region approach to stochastic optimization problems, the construction of performance bounds for suboptimal policies, Whittle's restless bandits, and the use of Lagrangian relaxation in the construction and evaluation of index policies. Some of the many varied proofs of the index theorem are discussed along with the insights that they provide. Many contemporary applications are surveyed, and over 150 new references are included. Over the past 40 years the Gittins index has helped theoreticians and practitioners to address a huge variety of problems within chemometrics, economics, engineering, numerical analysis, operational research, probability, statistics and website design. This new edition will be an important resource for others wishing to use this approach.

Implement reinforcement learning techniques and algorithms with the help of real-world examples and recipes Key FeaturesUse PyTorch 1.x to design and build self-learning artificial intelligence (AI) modelsImplement RL algorithms to solve control and optimization challenges faced by data scientists todayApply modern RL libraries to simulate a controlled environment for your projectsBook Description Reinforcement learning (RL) is a branch of machine learning that has gained popularity in recent times. It allows you to train AI models that learn from their own actions and optimize their behavior. PyTorch has also emerged as the preferred tool for training RL models because of its efficiency and ease of use. With this book, you'll explore the important RL concepts and the implementation of algorithms in PyTorch 1.x. The recipes in the book, along with real-world examples, will help you master various RL techniques, such as dynamic programming, Monte Carlo simulations, temporal difference, and Q-learning. You'll also gain insights into industry-specific applications of these techniques. Later chapters will guide you through solving problems such as the multi-armed bandit problem and the cartpole problem using the multi-armed bandit algorithm and function approximation. You'll also learn how to use Deep Q-Networks to complete Atari games, along with how to effectively implement policy gradients. Finally, you'll discover how RL techniques are applied to Blackjack, Gridworld environments, internet advertising, and the Flappy Bird game. By the end of this book, you'll have developed the skills you need to implement popular RL algorithms and use RL techniques to solve real-world problems. What you will learnUse Q-learning and the state–action–reward–state–action (SARSA) algorithm to solve various Gridworld problemsDevelop a multi-armed bandit algorithm to optimize display advertisingScale up learning and control processes using Deep Q-NetworksSimulate Markov Decision Processes, OpenAI Gym environments, and other common control problemsSelect and build RL models, evaluate their performance, and optimize and deploy themUse policy gradient methods to solve continuous RL problemsWho this book is for Machine learning engineers, data scientists and AI researchers looking for quick solutions to different reinforcement learning problems will find this book useful. Although prior knowledge of machine learning concepts is required, experience with PyTorch will be useful but not necessary.

When looking for ways to improve your website, how do you decide which changes to make? And which changes to keep? This concise book shows you how to use Multiarmed Bandit algorithms to measure the real-world value of any modifications you make to your site. Author John Myles White shows you how this powerful class of algorithms can help you boost website traffic, convert visitors to customers, and increase many other measures of success. This is the first developer-focused book on bandit algorithms, which were previously described only in research papers. You’ll quickly learn the benefits of several simple algorithms—including the epsilon-Greedy, Softmax, and Upper Confidence Bound (UCB) algorithms—by working through code examples written in Python, which you can easily adapt for deployment on your own website. Learn the basics of A/B testing—and recognize when it’s better to use bandit algorithms Develop a unit testing framework for debugging bandit algorithms Get additional code examples written in Julia, Ruby, and JavaScript with supplemental online materials