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Reinforcement Learning: An Introduction

TL;DR: This book provides a clear and simple account of the key ideas and algorithms of reinforcement learning, which ranges from the history of the field's intellectual foundations to the most recent developments and applications.
Abstract: 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 when interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability. The book is divided into three parts. Part I defines the reinforcement learning problem in terms of Markov decision processes. Part II provides basic solution methods: dynamic programming, Monte Carlo methods, and temporal-difference learning. Part III presents a unified view of the solution methods and incorporates artificial neural networks, eligibility traces, and planning; the two final chapters present case studies and consider the future of reinforcement learning.

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Citations
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Book
18 Nov 2016
TL;DR: Deep learning as mentioned in this paper is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts, and it is used in many applications such as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames.
Abstract: Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

38,208 citations

Journal ArticleDOI
26 Feb 2015-Nature
TL;DR: This work bridges the divide between high-dimensional sensory inputs and actions, resulting in the first artificial agent that is capable of learning to excel at a diverse array of challenging tasks.
Abstract: The theory of reinforcement learning provides a normative account, deeply rooted in psychological and neuroscientific perspectives on animal behaviour, of how agents may optimize their control of an environment. To use reinforcement learning successfully in situations approaching real-world complexity, however, agents are confronted with a difficult task: they must derive efficient representations of the environment from high-dimensional sensory inputs, and use these to generalize past experience to new situations. Remarkably, humans and other animals seem to solve this problem through a harmonious combination of reinforcement learning and hierarchical sensory processing systems, the former evidenced by a wealth of neural data revealing notable parallels between the phasic signals emitted by dopaminergic neurons and temporal difference reinforcement learning algorithms. While reinforcement learning agents have achieved some successes in a variety of domains, their applicability has previously been limited to domains in which useful features can be handcrafted, or to domains with fully observed, low-dimensional state spaces. Here we use recent advances in training deep neural networks to develop a novel artificial agent, termed a deep Q-network, that can learn successful policies directly from high-dimensional sensory inputs using end-to-end reinforcement learning. We tested this agent on the challenging domain of classic Atari 2600 games. We demonstrate that the deep Q-network agent, receiving only the pixels and the game score as inputs, was able to surpass the performance of all previous algorithms and achieve a level comparable to that of a professional human games tester across a set of 49 games, using the same algorithm, network architecture and hyperparameters. This work bridges the divide between high-dimensional sensory inputs and actions, resulting in the first artificial agent that is capable of learning to excel at a diverse array of challenging tasks.

23,074 citations

Journal ArticleDOI
TL;DR: This historical survey compactly summarizes relevant work, much of it from the previous millennium, review deep supervised learning, unsupervised learning, reinforcement learning & evolutionary computation, and indirect search for short programs encoding deep and large networks.

14,635 citations


Cites background from "Reinforcement Learning: An Introduc..."

  • ...Such NNs learn to perceive/encode/predict/ classify patterns or pattern sequences, but they do not learn to act in the more general sense of Reinforcement Learning (RL) in unknown environments (see surveys, e.g., Kaelbling et al., 1996; Sutton & Barto, 1998; Wiering & van Otterlo, 2012)....

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  • ...The latter is often explained in a probabilistic framework (e.g., Sutton & Barto, 1998), but its basic idea can already be conveyed in a deterministic setting....

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  • ...Such NNs learn to perceive / encode / predict / classify patterns or pattern sequences, but they do not learn to act in the more general sense of Reinforcement Learning (RL) in unknown environments (e.g., Kaelbling et al., 1996; Sutton and Barto, 1998)....

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  • ...Many variants of traditional RL exist (e.g., Barto et al., 1983; Watkins, 1989; Watkins and Dayan, 1992; Moore and Atkeson, 1993; Schwartz, 1993; Baird, 1994; Rummery and Niranjan, 1994; Singh, 1994; Baird, 1995; Kaelbling et al., 1995; Peng and Williams, 1996; Mahadevan, 1996; Tsitsiklis and van Roy, 1996; Bradtke et al., 1996; Santamarı́a et al., 1997; Prokhorov and Wunsch, 1997; Sutton and Barto, 1998; Wiering and Schmidhuber, 1998b; Baird and Moore, 1999; Meuleau et al., 1999; Morimoto and Doya, 2000; Bertsekas, 2001; Brafman and Tennenholtz, 2002; Abounadi et al., 2002; Lagoudakis and Parr, 2003; Sutton et al., 2008; Maei and Sutton, 2010)....

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  • ...This assumption does not hold in the broader fields of Sequential Decision Making and Reinforcement Learning (RL) (Kaelbling et al., 1996; Sutton and Barto, 1998; Hutter, 2005) (Sec....

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Journal ArticleDOI
28 Jan 2016-Nature
TL;DR: Using this search algorithm, the program AlphaGo achieved a 99.8% winning rate against other Go programs, and defeated the human European Go champion by 5 games to 0.5, the first time that a computer program has defeated a human professional player in the full-sized game of Go.
Abstract: The game of Go has long been viewed as the most challenging of classic games for artificial intelligence owing to its enormous search space and the difficulty of evaluating board positions and moves. Here we introduce a new approach to computer Go that uses ‘value networks’ to evaluate board positions and ‘policy networks’ to select moves. These deep neural networks are trained by a novel combination of supervised learning from human expert games, and reinforcement learning from games of self-play. Without any lookahead search, the neural networks play Go at the level of stateof-the-art Monte Carlo tree search programs that simulate thousands of random games of self-play. We also introduce a new search algorithm that combines Monte Carlo simulation with value and policy networks. Using this search algorithm, our program AlphaGo achieved a 99.8% winning rate against other Go programs, and defeated the human European Go champion by 5 games to 0. This is the first time that a computer program has defeated a human professional player in the full-sized game of Go, a feat previously thought to be at least a decade away.

14,377 citations

Christopher M. Bishop1
01 Jan 2006
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

10,141 citations

References
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Journal ArticleDOI
TL;DR: The problems discussed provide limitations on connectionist models applied to human memory and in tasks where information to be learned is not all available during learning.
Abstract: Multilayer connectionist models of memory based on the encoder model using the backpropagation learning rule are evaluated. The models are applied to standard recognition memory procedures in which items are studied sequentially and then tested for retention. Sequential learning in these models leads to 2 major problems. First, well-learned information is forgotten rapidly as new information is learned. Second, discrimination between studied items and new items either decreases or is nonmonotonic as a function of learning. To address these problems, manipulations of the network within the multilayer model and several variants of the multilayer model were examined, including a model with prelearned memory and a context model, but none solved the problems. The problems discussed provide limitations on connectionist models applied to human memory and in tasks where information to be learned is not all available during learning. The first stage of the connectionist revolution in psychology is reaching maturity and perhaps drawing to an end. This stage has been concerned with the exploration of classes of models, and the criteria that have been used to evaluate the success of an application have been necessarily loose. In the early stages of development of a new approach, lax acceptability criteria are appropriate because of the large range of models to be examined. However, there comes a second stage when the models serve as competitors to existing models developed within other theoretical frameworks, and they have to be competitively evaluated according to more stringent criteria. A few notable connectionist models have reached these standards, whereas others have not. The second stage of development also requires that the connectionist models be evaluated in areas where their potential for success is not immediately obvious. One such area is recognition memory. The work presented in this article evaluates several variants of the multilayer connectionist model as accounts of empirical results in this area. I mainly discuss multilayer models using the error-correcting backpropagation algorithm and do not address other architectures such as adaptive resonance schemes (Carpenter & Grossberg, 1987). Before launching into the modeling of recognition memory, I need to specify the aims and rules under which this project was carried out. This is important in a new area of inquiry because there are many divergent views about what needs to be

859 citations

Journal ArticleDOI
Gerald Tesauro1
TL;DR: The latest version of TD-Gammon is now estimated to play at a strong master level that is extremely close to the world's best human players.
Abstract: TD-Gammon is a neural network that is able to teach itself to play backgammon solely by playing against itself and learning from the results, based on the TD(») reinforcement learning algorithm (Sutton 1988). Despite starting from random initial weights (and hence random initial strategy), TD-Gammon achieves a surprisingly strong level of play. With zero knowledge built in at the start of learning (i.e., given only a "raw" description of the board state), the network learns to play at a strong intermediate level. Furthermore, when a set of hand-crafted features is added to the network's input representation, the result is a truly staggering level of performance: the latest version of TD-Gammon is now estimated to play at a strong master level that is extremely close to the world's best human players.

852 citations

01 Jan 1984

828 citations


"Reinforcement Learning: An Introduc..." refers background or methods in this paper

  • ...Some of the earliest uses of eligibility traces were in the actor–critic methods discussed in Chapter 13 (Barto, Sutton, and Anderson, 1983; Sutton, 1984)....

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  • ...It influenced much later work in reinforcement learning, beginning with some of our own studies (Barto, Sutton, and Anderson, 1983; Sutton, 1984)....

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  • ...Methods that we now see as related to policy gradients were actually some of the earliest to be studied in reinforcement learning (Witten, 1977; Barto, Sutton, and Anderson, 1983; Sutton, 1984; Williams, 1987, 1992) and in predecessor fields (Phansalkar and Thathachar, 1995)....

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  • ...Our use of eligibility traces is based on Klopf’s work (Sutton, 1978a, 1978b, 1978c; Barto and Sutton, 1981a, 1981b; Sutton and Barto, 1981a; Barto, Sutton, and Anderson, 1983; Sutton, 1984)....

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  • ...5–6 Actor–critic methods were among the earliest to be investigated in reinforcement learning (Witten, 1977; Barto, Sutton, and Anderson, 1983; Sutton, 1984)....

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01 Jan 1968
TL;DR: Conditioned emotional response studies using rats already trained to press bar for food supply were conducted in this paper, where the authors used conditioned emotional response to evaluate the emotional response of rats.
Abstract: Conditioned emotional response studies using rats already trained to press bar for food supply

819 citations


"Reinforcement Learning: An Introduc..." refers background in this paper

  • ...3 The idea built into the Rescorla-Wagner model that learning occurs when animals are surprised is derived from Kamin (1969), who first reported blocking— now commonly known as Kamin blocking—in classical conditioning (Kamin, 1968)....

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  • ...3 The idea built into the Rescorla-Wagner model that learning occurs when animals are surprised is derived from Kamin (1969), who first reported blocking— now commonly known as Kamin blocking—in classical conditioning (Kamin, 1968). Moore and Schmajuk (2008) provide an excellent summary of the blocking phenomenon, the research it stimulated, and its lasting influence on...

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Book ChapterDOI
01 Jan 1988
TL;DR: The problem of constructing a computing routine or "program" for a modern general purpose computer which enables it to play chess is addressed in this article, where the authors propose a set of possibilities in this direction.
Abstract: This paper is concerned with the problem of constructing a computing routine or “program” for a modern general purpose computer which will enable it to play chess. Although perhaps of no practical importance, the question is of theoretical interest, and it is hoped that a satisfactory solution of this problem will act as a wedge in attacking other problems of a similar nature and of greater significance. Some possibilities in this direction are:- (1) Machines for designing filters, equalizers, etc. (2) Machines for designing relay and switching circuits. (3) Machines which will handle routing of telephone calls based on the individual circumstances rather than by fixed patterns. (4) Machines for performing symbolic (non-numerical) mathematical operations. (5) Machines capable of translating from one language to another. (6) Machines for making strategic decisions in simplified military operations. (7) Machines capable of orchestrating a melody. (8) Machines capable of logical deduction.

798 citations