Reinforcement Learning: An Introduction

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Reinforcement Learning: An Introduction

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Reinforcement Learning: An Introduction

Richard S. Sutton¹, Andrew G. Barto•Institutions (1)

01 Jan 1988-

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.

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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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Deep Learning

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Ian Goodfellow¹, Yoshua Bengio², Aaron Courville²•Institutions (2)

Google¹, Université de Montréal²

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.

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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.

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38,208 citations

Journal Article•DOI•

Human-level control through deep reinforcement learning

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Volodymyr Mnih¹, Koray Kavukcuoglu¹, David Silver¹, Andrei Rusu¹, Joel Veness¹, Marc G. Bellemare¹, Alex Graves¹, Martin Riedmiller¹, Andreas K. Fidjeland¹, Georg Ostrovski¹, Stig Petersen¹, Charles Beattie¹, Amir Sadik¹, Ioannis Antonoglou¹, Helen King¹, Dharshan Kumaran¹, Daan Wierstra¹, Shane Legg¹, Demis Hassabis¹ - Show less +15 more•Institutions (1)

Google¹

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.

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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.

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23,074 citations

Journal Article•DOI•

Deep learning in neural networks

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Jürgen Schmidhuber¹•Institutions (1)

University of Lugano¹

01 Jan 2015-Neural Networks

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.

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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 Article•DOI•

Mastering the game of Go with deep neural networks and tree search

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David Silver¹, Aja Huang¹, Chris J. Maddison¹, Arthur Guez¹, Laurent Sifre¹, George van den Driessche¹, Julian Schrittwieser¹, Ioannis Antonoglou¹, Veda Panneershelvam¹, Marc Lanctot¹, Sander Dieleman¹, Dominik Grewe¹, John Nham¹, Nal Kalchbrenner¹, Ilya Sutskever¹, Timothy P. Lillicrap¹, Madeleine Leach¹, Koray Kavukcuoglu¹, Thore Graepel¹, Demis Hassabis¹ - Show less +16 more•Institutions (1)

Google¹

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.

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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.

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14,377 citations

Pattern Recognition and Machine Learning

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Christopher M. Bishop¹•Institutions (1)

Microsoft¹

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.

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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.

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10,141 citations

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References

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Journal Article•DOI•

Approximations of Dynamic Programs, I

[...]

Ward Whitt¹•Institutions (1)

Bell Labs¹

01 Aug 1978-Mathematics of Operations Research

TL;DR: The models considered are the monotone contraction operator models of Denardo Denardo, E. V. 1967, which include Markov decision processes and stochastic games with a criterion of discounted present value over an infinite horizon plus many finite-stage dynamic programs.

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Abstract: A general procedure is presented for constructing and analyzing approximations of dynamic programming models. The models considered are the monotone contraction operator models of Denardo Denardo, E. V. 1967. Contraction mappings in the theory underlying dynamic programming. SIAM Rev.9 165--177., which include Markov decision processes and stochastic games with a criterion of discounted present value over an infinite horizon plus many finite-stage dynamic programs. The approximations are typically achieved by replacing the original state and action spaces by subsets. Tight bounds are obtained for the distances between the optimal return function in the original model and 1 the extension of the optimal return function in the approximate model and 2 the return function associated with the extension of an optimal policy in the approximate model. Conditions are also given under which the sequence of bounds associated with a sequence of approximating models converges to zero.

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226 citations

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

...) There is now a fairly extensive literature on function approximation methods and DP, such as multigrid methods and methods using splines and orthogonal polynomials (e.g., Bellman and Dreyfus, 1959; Bellman, Kalaba, and Kotkin, 1973; Daniel, 1976; Whitt, 1978; Reetz, 1977; Schweitzer and Seidmann, 1985; Chow and Tsitsiklis, 1991; Kushner and Dupuis, 1992; Rust, 1996)....
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Journal Article•DOI•

Observable Operator Models for Discrete Stochastic Time Series

[...]

Herbert Jaeger¹•Institutions (1)

Center for Information Technology¹

01 Jun 2000-Neural Computation

TL;DR: A novel, simple characterization of linearly dependent processes, called observable operator models, is provided, which leads to a constructive learning algorithm for the identification of linially dependent processes.

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Abstract: A widely used class of models for stochastic systems is hidden Markov models. Systems that can be modeled by hidden Markov models are a proper subclass of linearly dependent processes, a class of s...

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223 citations

Journal Article•DOI•

The neural basis of associative reward learning in honeybees

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Martin Hammer¹•Institutions (1)

Free University of Berlin¹

01 Jun 1997-Trends in Neurosciences

TL;DR: Appetitive learning of food-predicting stimuli, an essential part of foraging behavior in honeybees, follows the rules of associative learning and its structural properties suggest that it organizes the interaction of functionally different neural nets during learning and experience-dependent behavior.

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222 citations

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

...The model is based on research by Hammer, Menzel, and colleagues (Hammer and Menzel, 1995; Hammer, 1997) showing that the neuromodulator octopamine acts as a reinforcement signal in the honeybee....
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Book Chapter•DOI•

Hierarchical learning in stochastic domains: preliminary results

[...]

Leslie Pack Kaelbling¹•Institutions (1)

Brown University¹

27 Jun 1993

TL;DR: The HDG algorithm, which is a descendent of Watkins' Q-learning algorithm, is described here and preliminary empirical results are presented.

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Abstract: This paper presents the HDG learning algorithm, which uses a hierarchical decomposition of the state space to make learning to achieve goals more efficient with a small penalty in path quality. Special care must be taken when performing hierarchical planning and learning in stochastic domains, because macro-operators cannot be executed ballistically. The HDG algorithm, which is a descendent of Watkins' Q-learning algorithm, is described here and preliminary empirical results are presented.

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219 citations

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

...Chapman and Kaelbling (1991) and Tan (1991) adapted decision-tree methods for learning value functions....
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...Reinforcement comparison methods were extensively developed by Sutton (1984) and further refined by Williams (1986, 1992), Kaelbling (1993), and Dayan (1991). These authors analyzed many variations of the idea including various eligibility terms that may significantly improve performance. Perhaps the earliest use of reinforcement comparison was by Barto, Sutton, and Brouwer (1981)....
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...Reinforcement comparison methods were extensively developed by Sutton (1984) and further refined by Williams (1986, 1992), Kaelbling (1993), and Dayan (1991)....
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...For additional general coverage of reinforcement learning, we refer the reader to the books by Bertsekas and Tsitsiklis (1996) and Kaelbling (1993). Two special issues of the journal Machine Learning focus on reinforcement learning: Sutton (1992) and Kaelbling (1996)....
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...For additional general coverage of reinforcement learning, we refer the reader to the books by Bertsekas and Tsitsiklis (1996) and Kaelbling (1993). Two special issues of the journal Machine Learning focus on reinforcement learning: Sutton (1992) and Kaelbling (1996). Useful surveys are provided by Barto (1995), Kaelbling, Littman, and Moore (1996), and Keerthi and Ravindran (1997)....
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Intelligent behavior as an adaptation to the task environment

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Lashon Bernard Booker

01 Jan 1982

TL;DR: This dissertation argues that examining more closely the way animate systems cope with real-world environments can provide valuable insights about the structural requirements for intelligent behavior.

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Abstract: As research in artificial intelligence focuses on increasingly complex task domains, a key question to be resolved is how to design a system that can efficiently acquire knowledge and gracefully adapt its behavior in an uncertain environment. This dissertation argues that examining more closely the way animate systems cope with real-world environments can provide valuable insights about the structural requirements for intelligent behavior. Accordingly, a class of simulated environments is designed that embodies many of the important functional properties characteristic of natural environments. A new type of adaptive system is then defined that uses pattern-directed, rule-based processing to cope with uncertain information. As a rule-based system, the system presented here is notable in that several rules can be active at once and there are no fixed priorities determining the order in which rules can be activated. Moreover, the syntax of each rule is simple enough to make a powerful learning heuristic applicable--one that is provably more efficient than the techniques used in most other adaptive rule-based systems. A simple version of the adaptive system is implemented as a hypothetical organism having to locate resources and avoid noxious stimuli by generating temporal sequences of actions in a simulated environment. Simulation results show that the naive organism quickly acquires the knowledge required to function effectively. Further experiments show that the system is capable of discriminating a large class of schematic patterns; and, that prior learning experiences transfer to novel situations. The results presented here demonstrate that activity in a collection of simple computational elements--operating in parallel and activated stochastically--can be orchestrated to produce reliable behavior in a challenging environment. The system touches on several issues related to cognitive functioning such as the generic representation of objects and the management of limited processing resources. These issues have been addressed in a way that is computationally feasible and that allows for rigorous testing.

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217 citations