Download or read book On Multi armed Bandit in Dynamic Systems written by Keqin Liu and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-armed bandit (MAB) is a classical problem in stochastic optimization with a wide range of engineering applications. The first MAB problem was proposed in 1933 for the application of clinical trial. The problem, however, remained open for over 40 years until the breakthrough by Gittins in 1974. Under a Bayesian formulation, Gittins proved that an index policy is optimal, thus reducing the complexity of finding the optimal policy from exponential to linear with the systemsize. In 1985, Lai and Robbins established the optimal policy for the MAB under a non-Bayesian formulation. Since these milestones, MAB have attracted numerous research efforts on generalizing the associated mathematical theory and broadening the applications. In this thesis, we present our contributions to the basic theories of both the Bayesian and the non-Bayesian frameworks of MAB motivated by engineering problems in dynamic systems. Within the Bayesian framework, we address an important and still largely open extension of the classic MAB---the Restless Multi-Armed Bandit (RMAB). In 1988, Whittle generalized the classic MAB to RMAB that considers the scenario where the system dynamics cannot be directlycontrolled. This generalization significantly broadens the application area of MAB but renders Gittins index policy suboptimal. As shown by Papadimitriou and Tsitsiklis, finding the optimal solution to an RMAB is PSPACE-hard in general. Whittle proposed a heuristic index policy with linear complexity, which was shown to be asymptotically (when the system size, i.e., the number of arms, approaches infinity) optimal under certain conditions by Weber and Weiss in 1990. The difficulty of implementing Whittle index policy lies in the complexity of establishing its existence (the so-called indexability), computing the index, and establishing its optimality in the finite regime. The study of Whittle index policy often relies on numerical calculation that is infeasible for RMAB with infinite state space. In this thesis, we show that for a significant class of RMAB with an infinite state space, the indexability can be established, Whittle index can be obtained in closed-form, and, under certain conditions, achieves the optimal performance with a simple semi-universal structure that is robust against model mismatch and variations. To our best knowledge, this appears to be the first nontrivial RMAB for which Whittle index policy is proven to be optimal for a finite-size system. This class of RMAB finds a broad range of applications, from dynamic multichannel access in communication networks to bio/chemical monitoring systems, from target tracking/collecting in multi-agent systems to resource-constrained jamming/anti-jamming, from network anomaly detection to supervisory control systems. Furthermore, our approach to establishing the indexability, solving for Whittle index and characterizing its optimality is not limited to this class of RMAB and provides a set of possible techniques for analyzing the general RMAB. For the non-Bayesian framework, we extend the classic MAB that assumes a single player to the case of multiple distributed players. Players make decisions solely based on their local observationand decision histories without exchanging information. We formulate the problem as a decentralized MAB under general reward, observation, and collision models. We show that the optimal performance (measured by system regret) in the decentralized MAB achieves the same logarithmic order as that in the classic centralized MAB where players act collectively as a single entity by exchanging observations and making decisions jointly. Based on a Time Division and Fair Sharing (TDFS) structure, a general framework of constructing order-optimal and fair decentralized polices is proposed. The generality of the TDFS framework leads to its wide applications to distributed learning problems in multi-channel communication systems, multi-agent systems, web search and internet advertising, social networks, etc.
Download or read book Introduction to Multi Armed Bandits written by Aleksandrs Slivkins and published by . This book was released on 2019-10-31 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Regret Analysis of Stochastic and Nonstochastic Multi armed Bandit Problems written by Sébastien Bubeck and published by Now Pub. This book was released on 2012 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bandit Algorithms written by Tor Lattimore and published by Cambridge University Press. This book was released on 2020-07-16 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and rigorous introduction for graduate students and researchers, with applications in sequential decision-making problems.
Download or read book Learning in a Changing World written by Haoyang Liu and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the restless multi-armed bandit (RMAB) problem withunknown dynamics in which a player chooses one out of N arms to play at each time. The reward state of each arm transits accordingto an unknown Markovian rule when it is played and evolves according to an arbitrary unknown random process when it is passive. The performance of an arm selection policy is measured by regret, defined as the reward loss with respect to the case where the player knows which arm is the most rewarding and always plays the best arm. We construct a policy with an interleaving exploration andexploitation epoch structure that achieves a regret with logarithmicorder. We further extend the problem to a decentralized settingwhere multiple distributed players share the arms withoutinformation exchange. Under both an exogenous restless model and an endogenous restless model, we show that a decentralized extension of the proposed policy preserves the logarithmic regret order as in the centralized setting. The results apply to adaptive learning in various dynamic systems and communication networks, as well as financial investment.
Download or read book Multi Armed Bandits written by Qing Zhao and published by Morgan & Claypool Publishers. This book was released on 2019-11-21 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-armed bandit problems pertain to optimal sequential decision making and learning in unknown environments. Since the first bandit problem posed by Thompson in 1933 for the application of clinical trials, bandit problems have enjoyed lasting attention from multiple research communities and have found a wide range of applications across diverse domains. This book covers classic results and recent development on both Bayesian and frequentist bandit problems. We start in Chapter 1 with a brief overview on the history of bandit problems, contrasting the two schools—Bayesian and frequentis —of approaches and highlighting foundational results and key applications. Chapters 2 and 4 cover, respectively, the canonical Bayesian and frequentist bandit models. In Chapters 3 and 5, we discuss major variants of the canonical bandit models that lead to new directions, bring in new techniques, and broaden the applications of this classical problem. In Chapter 6, we present several representative application examples in communication networks and social-economic systems, aiming to illuminate the connections between the Bayesian and the frequentist formulations of bandit problems and how structural results pertaining to one may be leveraged to obtain solutions under the other.
Download or read book Multi armed Bandit Allocation Indices written by John Gittins and published by John Wiley & Sons. This book was released on 2011-02-18 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Bandit Algorithms for Website Optimization written by John Myles White and published by "O'Reilly Media, Inc.". This book was released on 2012-12-10 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Foundations and Applications of Sensor Management written by Alfred Olivier Hero and published by Springer. This book was released on 2007-11-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers control theory signal processing and relevant applications in a unified manner. It introduces the area, takes stock of advances, and describes open problems and challenges in order to advance the field. The editors and contributors to this book are pioneers in the area of active sensing and sensor management, and represent the diverse communities that are targeted.
Download or read book Multi armed Bandits in Large scale Complex Systems written by Xiao Xu and published by . This book was released on 2020 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation focuses on the multi-armed bandit problem (MAB) where the objective is a sequential arm selection policy that maximizes the total reward over time. In canonical formulations of MAB, the following assumptions are adopted: the size of the action space is much smaller than the length of the time horizon, computation resources such as memory are unlimited in the learning process, and the generative models of arm rewards are time-invariant. This dissertation aims to relax these assumptions, which are unrealistic in emerging applications involving large-scale complex systems, and develop corresponding techniques to address the resulting new issues. The first part of the dissertation aims to address the issue of a massive number of actions. A stochastic bandit problem with side information on arm similarity and dissimilarity is studied. The main results include a unit interval graph (UIG) representation of the action space that succinctly models the side information and a two-step learning structure that fully exploits the topological structure of the UIG to achieve an optimal scaling of the learning cost with the size of the action space. Specifically, in the UIG representation, each node represents an arm and the presence (absence) of an edge between two nodes indicates similarity (dissimilarity) between their mean rewards. Based on whether the UIG is fully revealed by the side information, two settings with complete and partial side information are considered. For each setting, a two-step learning policy consisting of an offline reduction of the action space and online aggregation of reward observations from similar arms is developed. The computation efficiency and the order optimality of the proposed strategies in terms of the size of the action space and the time length are established. Numerical experiments on both synthetic and real-world datasets are conducted to verify the performance of the proposed policies in practice. In the second part of the dissertation, the issue of limited memory during the learning process is studied in the adversarial bandit setting. Specifically, a learning policy can only store the statistics of a subset of arms summarizing their reward history. A general hierarchical learning structure that trades off the regret order with memory complexity is developed based on multi-level partitions of the arm set into groups and the time horizon into epochs. The proposed learning policy requires only a sublinear order of memory space in terms of the number of arms. Its sublinear regret orders with respect to the time horizon are established for both weak regret and shifting regret in expectation and/or with high probability, when appropriate learning strategies are adopted as subroutines at all levels. By properly choosing the number of levels in the adopted hierarchy, the policy adapts to different sizes of the available memory space. A memory-dependent regret bound is established to characterize the tradeoff between memory complexity and the regret performance of the policy. Numerical examples are provided to verify the performance of the policy. The third part of the dissertation focuses on the issue of time-varying rewards within the contextual bandit framework, which finds applications in various online recommendation systems. The main results include two reward models characterizing the fact that the preferences of users toward different items change asynchronously and distinctly, and a learning algorithm that adapts to the dynamic environment. In particular, the two models assume disjoint and hybrid rewards. In the disjoint setting, the mean reward of playing an arm is determined by an arm-specific preference vector, which is piecewise-stationary with asynchronous change times across arms. In the hybrid setting, the mean reward of an arm also depends on a joint coefficient vector shared by all arms representing the time-invariant component of user interests, in addition to the arm-specific one that is time-varying. Two algorithms based on change detection and restarts are developed in the two settings respectively, of which the performance is verified through simulations on both synthetic and real-world data. Theoretical regret analysis of the algorithm with certain modifications is provided under the disjoint reward model, which shows that a near-optimal regret order in the time length is achieved.
Download or read book Bandit problems written by Donald A. Berry and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Restless Multi Armed Bandit in Opportunistic Scheduling written by Kehao Wang and published by Springer Nature. This book was released on 2021-05-19 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides foundations for the understanding and design of computation-efficient algorithms and protocols for those interactions with environment, i.e., wireless communication systems. The book provides a systematic treatment of the theoretical foundation and algorithmic tools necessarily in the design of computation-efficient algorithms and protocols in stochastic scheduling. The problems addressed in the book are of both fundamental and practical importance. Target readers of the book are researchers and advanced-level engineering students interested in acquiring in-depth knowledge on the topic and on stochastic scheduling and their applications, both from theoretical and engineering perspective.
Download or read book Mean Field Analysis of Multi Armed Bandit Games written by Ramki Gummadi and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much of the classical work on algorithms for multi-armed bandits focuses on rewards that are stationary over time. By contrast, we study multi-armed bandit (MAB) games, where the rewards obtained by an agent also depend on how many other agents choose the same arm (as might be the case in many competitive or cooperative scenarios). Such systems are naturally nonstationary due to the interdependent evolution of agents, and in general MAB games can be intractable to analyze using typical equilibrium concepts (such as perfect Bayesian equilibrium). We introduce a general model of multi-armed bandit games, and study the dynamics of these games under a large system approximation. We investigate conditions under which the bandit dynamics have a steady state we refer to as a mean field steady state (MFSS). In an MFSS, the proportion of agents playing the various arms, called the population profile, is assumed stationary over time; the steady state definition then requires a consistency check that this stationary profile arises from the policies chosen by the agents. We establish the following results in the paper. First, we establish existence of an MFSS under broad conditions. Second, we show under a contraction condition that the MFSS is unique, and that the population profile converges to it from any initial state. Finally, we show that under the contraction condition, MFSS is a good approximation to the behavior of finite systems with many agents. The contraction condition requires that the agent population regenerates sufficiently often, and that the sensitivity of the reward function to the population profile is low enough. Through numerical experiments, we find that in settings with negative externalities among the agents, convergence obtains even when our condition is violated; while in settings with positive externalities among the agents, our condition is tighter.
Download or read book Multi Armed Bandit Allocation Indices written by J. C. Gittins and published by . This book was released on 1989-04-03 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statisticians are familiar with bandit problems, operations researchers with scheduling programs, and economists with problems of resource allocation. For most of these problems, accurate solutions cannot be obtained unless the problem is small-scale. However, Gittins and Jones showed in 1974 that there is a large class of allocation problems for which the optimal solution is expressible in terms of a priority index that can be calculated. This book is the first definitive account of the theory and applications of this index, which has become known as the Gittens index. Includes 22 previously unpublished tables of index values.
Download or read book Reinforcement Learning second edition written by Richard S. Sutton and published by MIT Press. This book was released on 2018-11-13 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: The significantly expanded and updated new edition of a widely used text on reinforcement learning, one of the most active research areas in artificial intelligence. Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives while interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the field's key ideas and algorithms. This second edition has been significantly expanded and updated, presenting new topics and updating coverage of other topics. Like the first edition, this second edition focuses on core online learning algorithms, with the more mathematical material set off in shaded boxes. Part I covers as much of reinforcement learning as possible without going beyond the tabular case for which exact solutions can be found. Many algorithms presented in this part are new to the second edition, including UCB, Expected Sarsa, and Double Learning. Part II extends these ideas to function approximation, with new sections on such topics as artificial neural networks and the Fourier basis, and offers expanded treatment of off-policy learning and policy-gradient methods. Part III has new chapters on reinforcement learning's relationships to psychology and neuroscience, as well as an updated case-studies chapter including AlphaGo and AlphaGo Zero, Atari game playing, and IBM Watson's wagering strategy. The final chapter discusses the future societal impacts of reinforcement learning.
Download or read book A Tutorial on Thompson Sampling written by Daniel J. Russo and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this tutorial is to explain when, why, and how to apply Thompson sampling.
Download or read book Hands On Reinforcement Learning for Games written by Micheal Lanham and published by Packt Publishing Ltd. This book was released on 2020-01-03 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore reinforcement learning (RL) techniques to build cutting-edge games using Python libraries such as PyTorch, OpenAI Gym, and TensorFlow Key FeaturesGet to grips with the different reinforcement and DRL algorithms for game developmentLearn how to implement components such as artificial agents, map and level generation, and audio generationGain insights into cutting-edge RL research and understand how it is similar to artificial general researchBook Description With the increased presence of AI in the gaming industry, developers are challenged to create highly responsive and adaptive games by integrating artificial intelligence into their projects. This book is your guide to learning how various reinforcement learning techniques and algorithms play an important role in game development with Python. Starting with the basics, this book will help you build a strong foundation in reinforcement learning for game development. Each chapter will assist you in implementing different reinforcement learning techniques, such as Markov decision processes (MDPs), Q-learning, actor-critic methods, SARSA, and deterministic policy gradient algorithms, to build logical self-learning agents. Learning these techniques will enhance your game development skills and add a variety of features to improve your game agent’s productivity. As you advance, you’ll understand how deep reinforcement learning (DRL) techniques can be used to devise strategies to help agents learn from their actions and build engaging games. By the end of this book, you’ll be ready to apply reinforcement learning techniques to build a variety of projects and contribute to open source applications. What you will learnUnderstand how deep learning can be integrated into an RL agentExplore basic to advanced algorithms commonly used in game developmentBuild agents that can learn and solve problems in all types of environmentsTrain a Deep Q-Network (DQN) agent to solve the CartPole balancing problemDevelop game AI agents by understanding the mechanism behind complex AIIntegrate all the concepts learned into new projects or gaming agentsWho this book is for If you’re a game developer looking to implement AI techniques to build next-generation games from scratch, this book is for you. Machine learning and deep learning practitioners, and RL researchers who want to understand how to use self-learning agents in the game domain will also find this book useful. Knowledge of game development and Python programming experience are required.
