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Reinforcement learning encompasses both a science of adaptive behavior of rational beings in uncertain environments and a computational methodology for finding optimal behaviors for challenging problems in control, optimization and adaptive behavior of intelligent agents. As a field, reinforcement learning has progressed tremendously in the past decade.

The main goal of this book is to present an up-to-date series of survey articles on the main contemporary sub-fields of reinforcement learning. This includes surveys on partially observable environments, hierarchical task decompositions, relational knowledge representation and predictive state representations. Furthermore, topics such as transfer, evolutionary methods and continuous spaces in reinforcement learning are surveyed. In addition, several chapters review reinforcement learning methods in robotics, in games, and in computational neuroscience. In total seventeen different subfields are presented by mostly young experts in those areas, and together they truly represent a state-of-the-art of current reinforcement learning research.

Marco Wiering works at the artificial intelligence department of the University of Groningen in the Netherlands. He has published extensively on various reinforcement learning topics. Martijn van Otterlo works in the cognitive artificial intelligence group at the Radboud University Nijmegen in The Netherlands. He has mainly focused on expressive knowledge
representation in reinforcement learning settings.



Introductory Part


Reinforcement Learning and Markov Decision Processes

Situated in between supervised learning and unsupervised learning, the paradigm of reinforcement learning deals with learning in sequential decision making problems in which there is limited feedback. This text introduces the intuitions and concepts behind Markov decision processes and two classes of algorithms for computing optimal behaviors: reinforcement learning and dynamic programming. First the formal framework of Markov decision process is defined, accompanied by the definition of value functions and policies. The main part of this text deals with introducing foundational classes of algorithms for learning optimal behaviors, based on various definitions of optimality with respect to the goal of learning sequential decisions. Additionally, it surveys efficient extensions of the foundational algorithms, differing mainly in the way feedback given by the environment is used to speed up learning, and in the way they concentrate on relevant parts of the problem. For both model-based and model-free settings these efficient extensions have shown useful in scaling up to larger problems.

Martijn van Otterlo, Marco Wiering

Efficient Solution Frameworks


Batch Reinforcement Learning

Batch reinforcement learning is a subfield of dynamic programming-based reinforcement learning. Originally defined as the task of learning the best possible policy from a fixed set of a priori-known transition samples, the (batch) algorithms developed in this field can be easily adapted to the classical online case, where the agent interacts with the environment while learning. Due to the efficient use of collected data and the stability of the learning process, this research area has attracted a lot of attention recently. In this chapter, we introduce the basic principles and the theory behind batch reinforcement learning, describe the most important algorithms, exemplarily discuss ongoing research within this field, and briefly survey real-world applications of batch reinforcement learning.

Sascha Lange, Thomas Gabel, Martin Riedmiller

Least-Squares Methods for Policy Iteration

Approximate reinforcement learning deals with the essential problem of applying reinforcement learning in large and continuous state-action spaces, by using function approximators to represent the solution. This chapter reviews least-squares methods for policy iteration, an important class of algorithms for approximate reinforcement learning. We discuss three techniques for solving the core, policy evaluation component of policy iteration, called: least-squares temporal difference, least-squares policy evaluation, and Bellman residual minimization.We introduce these techniques starting from their general mathematical principles and detailing them down to fully specified algorithms. We pay attention to online variants of policy iteration, and provide a numerical example highlighting the behavior of representative offline and online methods. For the policy evaluation component as well as for the overall resulting approximate policy iteration, we provide guarantees on the performance obtained asymptotically, as the number of samples processed and iterations executed grows to infinity. We also provide finite-sample results, which apply when a finite number of samples and iterations are considered. Finally, we outline several extensions and improvements to the techniques and methods reviewed.

Lucian Buşoniu, Alessandro Lazaric, Mohammad Ghavamzadeh, Rémi Munos, Robert Babuška, Bart De Schutter

Learning and Using Models

As opposed to model-free RL methods, which learn directly from experience in the domain, model-based methods learn a model of the transition and reward functions of the domain on-line and plan a policy using this model. Once the method has learned an accurate model, it can plan an optimal policy on this model without any further experience in the world. Therefore, when model-based methods are able to learn a good model quickly, they frequently have improved sample efficiency over model-free methods, which must continue taking actions in the world for values to propagate back to previous states. Another advantage of model-based methods is that they can use their models to plan multi-step exploration trajectories. In particular, many methods drive the agent to explore where there is uncertainty in the model, so as to learn the model as fast as possible. In this chapter, we survey some of the types of models used in model-based methods and ways of learning them, as well as methods for planning on these models. In addition, we examine the typical architectures for combining model learning and planning, which vary depending on whether the designer wants the algorithm to run on-line, in batch mode, or in real-time. One of the main performance criteria for these algorithms is sample complexity, or how many actions the algorithm must take to learn.We examine the sample efficiency of a few methods, which are highly dependent on having intelligent exploration mechanisms. We survey some approaches to solving the exploration problem, including Bayesian methods that maintain a belief distribution over possible models to explicitly measure uncertainty in the model. We show some empirical comparisons of various model-based and model-free methods on two example domains before concluding with a survey of current research on scaling these methods up to larger domains with improved sample and computational complexity.

Todd Hester, Peter Stone

Transfer in Reinforcement Learning: A Framework and a Survey

Transfer in reinforcement learning is a novel research area that focuses on the development of methods to transfer knowledge from a set of source tasks to a target task. Whenever the tasks are similar, the transferred knowledge can be used by a learning algorithm to solve the target task and significantly improve its performance (e.g., by reducing the number of samples needed to achieve a nearly optimal performance). In this chapter we provide a formalization of the general transfer problem, we identify the main settings which have been investigated so far, and we review the most important approaches to transfer in reinforcement learning.

Alessandro Lazaric

Sample Complexity Bounds of Exploration

Efficient exploration is widely recognized as a fundamental challenge inherent in reinforcement learning. Algorithms that explore efficiently converge faster to near-optimal policies. While heuristics techniques are popular in practice, they lack formal guarantees and may not work well in general. This chapter studies algorithms with polynomial sample complexity of exploration, both model-based and model-free ones, in a unified manner. These so-called PAC-MDP algorithms behave near-optimally except in a “small” number of steps with high probability. A new learning model known as KWIK is used to unify most existing model-based PAC-MDP algorithms for various subclasses of Markov decision processes.We also compare the sample-complexity framework to alternatives for formalizing exploration efficiency such as regret minimization and Bayes optimal solutions.

Lihong Li

Constructive-Representational Directions


Reinforcement Learning in Continuous State and Action Spaces

Many traditional reinforcement-learning algorithms have been designed for problems with small finite state and action spaces. Learning in such discrete problems can been difficult, due to noise and delayed reinforcements. However, many real-world problems have continuous state or action spaces, which can make learning a good decision policy even more involved. In this chapter we discuss how to automatically find good decision policies in continuous domains. Because analytically computing a good policy from a continuous model can be infeasible, in this chapter we mainly focus on methods that explicitly update a representation of a value function, a policy or both. We discuss considerations in choosing an appropriate representation for these functions and discuss gradient-based and gradient-free ways to update the parameters. We show how to apply these methods to reinforcement-learning problems and discuss many specific algorithms. Amongst others, we cover gradient-based temporal-difference learning, evolutionary strategies, policy-gradient algorithms and (natural) actor-critic methods. We discuss the advantages of different approaches and compare the performance of a state-of-the-art actor-critic method and a state-of-the-art evolutionary strategy empirically.

Hado van Hasselt

Solving Relational and First-Order Logical Markov Decision Processes: A Survey

In this chapter we survey representations and techniques for Markov decision processes, reinforcement learning, and dynamic programming in worlds explicitly modeled in terms of objects and relations. Such relational worlds can be found everywhere in planning domains, games, real-world indoor scenes and many more. Relational representations allow for expressive and natural datastructures that capture the objects and relations in an explicit way, enabling generalization over objects and relations, but also over similar problems which differ in the number of objects. The field was recently surveyed completely in (van Otterlo, 2009b), and here we describe a large portion of the main approaches. We discuss model-free – both value-based and policy-based – and model-based dynamic programming techniques. Several other aspects will be covered, such as models and hierarchies, and we end with several recent efforts and future directions.

Martijn van Otterlo

Hierarchical Approaches

Hierarchical decomposition tackles complex problems by reducing them to a smaller set of interrelated problems. The smaller problems are solved separately and the results re-combined to find a solution to the original problem. It is well known that the naïve application of reinforcement learning (RL) techniques fails to scale to more complex domains. This Chapter introduces hierarchical approaches to reinforcement learning that hold out the promise of reducing a reinforcement learning problems to a manageable size. Hierarchical Reinforcement Learning (HRL) rests on finding good re-usable temporally extended actions that may also provide opportunities for state abstraction. Methods for reinforcement learning can be extended to work with abstract states and actions over a hierarchy of subtasks that decompose the original problem, potentially reducing its computational complexity. We use a four-room task as a running example to illustrate the various concepts and approaches, including algorithms that can automatically learn the hierarchical structure from interactions with the domain.

Bernhard Hengst

Evolutionary Computation for Reinforcement Learning

Algorithms for evolutionary computation, which simulate the process of natural selection to solve optimization problems, are an effective tool for discovering high-performing reinforcement-learning policies. Because they can automatically find good representations, handle continuous action spaces, and cope with partial observability, evolutionary reinforcement-learning approaches have a strong empirical track record, sometimes significantly outperforming temporal-difference methods. This chapter surveys research on the application of evolutionary computation to reinforcement learning, overviewing methods for evolving neural-network topologies and weights, hybrid methods that also use temporal-difference methods, coevolutionary methods for multi-agent settings, generative and developmental systems, and methods for on-line evolutionary reinforcement learning.

Shimon Whiteson

Probabilistic Models of Self and Others


Bayesian Reinforcement Learning

This chapter surveys recent lines of work that use Bayesian techniques for reinforcement learning. In Bayesian learning, uncertainty is expressed by a prior distribution over unknown parameters and learning is achieved by computing a posterior distribution based on the data observed. Hence, Bayesian reinforcement learning distinguishes itself from other forms of reinforcement learning by explicitly maintaining a distribution over various quantities such as the parameters of the model, the value function, the policy or its gradient. This yields several benefits: a) domain knowledge can be naturally encoded in the prior distribution to speed up learning; b) the exploration/exploitation tradeoff can be naturally optimized; and c) notions of risk can be naturally taken into account to obtain robust policies.

Nikos Vlassis, Mohammad Ghavamzadeh, Shie Mannor, Pascal Poupart

Partially Observable Markov Decision Processes

For reinforcement learning in environments in which an agent has access to a reliable state signal, methods based on the Markov decision process (MDP) have had many successes. In many problem domains, however, an agent suffers from limited sensing capabilities that preclude it from recovering a Markovian state signal from its perceptions. Extending the MDP framework, partially observable Markov decision processes (POMDPs) allow for principled decision making under conditions of uncertain sensing. In this chapter we present the POMDP model by focusing on the differences with fully observable MDPs, and we show how optimal policies for POMDPs can be represented. Next, we give a review of model-based techniques for policy computation, followed by an overview of the available model-free methods for POMDPs. We conclude by highlighting recent trends in POMDP reinforcement learning.

Matthijs T. J. Spaan

Predictively Defined Representations of State

The concept of state is central to dynamical systems. In any timeseries problem—such as filtering, planning or forecasting—models and algorithms summarize important information from the past into some sort of state variable. In this chapter, we start with a broad examination of the concept of state, with emphasis on the fact that there are many possible representations of state for a given dynamical system, each with different theoretical and computational properties. We then focus on modelswithpredictivelydefinedrepresentationsofstate that represent state as a set of statistics about the short-term future, as opposed to the classic approach of treating state as a latent, unobservable quantity. In other words, the past is summarized into predictions about the actions and observations in the short-term future, which can be used to make further predictions about the infinite future.While this representational idea applies to any dynamical system problem, it is particularly useful in a model-based RL context, when an agent must learn a representation of state and a model of system dynamics online: because the representation (and hence all of the model’s parameters) are defined using only statistics of observable quantities, their learning algorithms are often straightforward and have attractive theoretical properties. Here, we survey the basic concepts of predictively defined representations of state, important auxiliary constructs (such as the systems dynamics matrix), and theoretical results on their representational power and learnability.

David Wingate

Game Theory and Multi-agent Reinforcement Learning

Reinforcement Learning was originally developed for Markov Decision Processes (MDPs). It allows a single agent to learn a policy that maximizes a possibly delayed reward signal in a stochastic stationary environment. It guarantees convergence to the optimal policy, provided that the agent can sufficiently experiment and the environment in which it is operating is Markovian. However, when multiple agents apply reinforcement learning in a shared environment, this might be beyond the MDP model. In such systems, the optimal policy of an agent depends not only on the environment, but on the policies of the other agents as well. These situations arise naturally in a variety of domains, such as: robotics, telecommunications, economics, distributed control, auctions, traffic light control, etc. In these domains multi-agent learning is used, either because of the complexity of the domain or because control is inherently decentralized. In such systems it is important that agents are capable of discovering good solutions to the problem at hand either by coordinating with other learners or by competing with them. This chapter focuses on the application reinforcement learning techniques in multi-agent systems. We describe a basic learning framework based on the economic research into game theory, and illustrate the additional complexity that arises in such systems. We also described a representative selection of algorithms for the different areas of multi-agent reinforcement learning research.

Ann Nowé, Peter Vrancx, Yann-Michaël De Hauwere

Decentralized POMDPs

This chapter presents an overview of the decentralized POMDP (Dec- POMDP) framework. In a Dec-POMDP, a team of agents collaborates to maximize a global reward based on local information only. This means that agents do not observe a Markovian signal during execution and therefore the agents’ individual policies map fromhistories to actions. Searching for an optimal joint policy is an extremely hard problem: it is NEXP-complete. This suggests, assuming NEXP≠EXP, that any optimal solution method will require doubly exponential time in the worst case. This chapter focuses on planning for Dec-POMDPs over a finite horizon. It covers the forward heuristic search approach to solving Dec-POMDPs, as well as the backward dynamic programming approach. Also, it discusses how these relate to the optimal Q-value function of a Dec-POMDP. Finally, it provides pointers to other solution methods and further related topics.

Frans A. Oliehoek

Domains and Background


Psychological and Neuroscientific Connections with Reinforcement Learning

The field of Reinforcement Learning (RL) was inspired in large part by research in animal behavior and psychology. Early research showed that animals can, through trial and error, learn to execute behavior that would eventually lead to some (presumably satisfactory) outcome, and decades of subsequent research was (and is still) aimed at discovering the mechanisms of this learning process. This chapter describes behavioral and theoretical research in animal learning that is directly related to fundamental concepts used in RL. It then describes neuroscientific research that suggests that animals and many RL algorithms use very similar learning mechanisms. Along the way, I highlight ways that research in computer science contributes to and can be inspired by research in psychology and neuroscience.

Ashvin Shah

Reinforcement Learning in Games

Reinforcement learning and games have a long and mutually beneficial common history. From one side, games are rich and challenging domains for testing reinforcement learning algorithms. From the other side, in several games the best computer players use reinforcement learning. The chapter begins with a selection of games and notable reinforcement learning implementations.Without any modifications, the basic reinforcement learning algorithms are rarely sufficient for high-level gameplay, so it is essential to discuss the additional ideas, ways of inserting domain knowledge, implementation decisions that are necessary for scaling up. These are reviewed in sufficient detail to understand their potentials and their limitations. The second part of the chapter lists challenges for reinforcement learning in games, together with a review of proposed solution methods. While this listing has a game-centric viewpoint, and some of the items are specific to games (like opponent modelling), a large portion of this overview can provide insight for other kinds of applications, too. In the third part we review how reinforcement learning can be useful in game development and find its way into commercial computer games. Finally, we provide pointers for more in-depth reviews of specific games and solution approaches.

István Szita

Reinforcement Learning in Robotics: A Survey

As most action generation problems of autonomous robots can be phrased in terms of sequential decision problems, robotics offers a tremendously important and interesting application platform for reinforcement learning. Similarly, the real-world challenges of this domain pose a major real-world check for reinforcement learning. Hence, the interplay between both disciplines can be seen as promising as the one between physics and mathematics. Nevertheless, only a fraction of the scientists working on reinforcement learning are sufficiently tied to robotics to oversee most problems encountered in this context. Thus, we will bring the most important challenges faced by robot reinforcement learning to their attention. To achieve this goal, we will attempt to survey most work that has successfully applied reinforcement learning to behavior generation for real robots. We discuss how the presented successful approaches have been made tractable despite the complexity of the domain and will study how representations or the inclusion of prior knowledge can make a significant difference. As a result, a particular focus of our chapter lies on the choice between model-based and model-free as well as between value function-based and policy search methods. As a result, we obtain a fairly complete survey of robot reinforcement learning which should allow a general reinforcement learning researcher to understand this domain.

Jens Kober, Jan Peters



Conclusions, Future Directions and Outlook

This book has provided the reader with a thorough description of the field of reinforcement learning (RL). In this last chapter we will first discuss what has been accomplished with this book, followed by a description of those topics that were left out of this book, mainly because they are outside of the main field of RL or they are small (possibly novel and emerging) subfields within RL. After looking back what has been done in RL and in this book, a step into the future development of the field will be taken, and we will end with the opinions of some of the authors what they think will become the most important areas of research in RL.

Marco Wiering, Martijn van Otterlo


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