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71
Reinforcement learning: a survey
 Journal of Artificial Intelligence Research
, 1996
"... This paper surveys the field of reinforcement learning from a computerscience perspective. It is written to be accessible to researchers familiar with machine learning. Both the historical basis of the field and a broad selection of current work are summarized. Reinforcement learning is the problem ..."
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Cited by 1309 (22 self)
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This paper surveys the field of reinforcement learning from a computerscience perspective. It is written to be accessible to researchers familiar with machine learning. Both the historical basis of the field and a broad selection of current work are summarized. Reinforcement learning is the problem faced by an agent that learns behavior through trialanderror interactions with a dynamic environment. The work described here has a resemblance to work in psychology, but differs considerably in the details and in the use of the word "reinforcement." The paper discusses central issues of reinforcement learning, including trading off exploration and exploitation, establishing the foundations of the field via Markov decision theory, learning from delayed reinforcement, constructing empirical models to accelerate learning, making use of generalization and hierarchy, and coping with hidden state. It concludes with a survey of some implemented systems and an assessment of the practical utility of current methods for reinforcement learning.
Planning and acting in partially observable stochastic domains
 ARTIFICIAL INTELLIGENCE
, 1998
"... In this paper, we bring techniques from operations research to bear on the problem of choosing optimal actions in partially observable stochastic domains. We begin by introducing the theory of Markov decision processes (mdps) and partially observable mdps (pomdps). We then outline a novel algorithm ..."
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Cited by 832 (30 self)
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In this paper, we bring techniques from operations research to bear on the problem of choosing optimal actions in partially observable stochastic domains. We begin by introducing the theory of Markov decision processes (mdps) and partially observable mdps (pomdps). We then outline a novel algorithm for solving pomdps offline and show how, in some cases, a finitememory controller can be extracted from the solution to a pomdp. We conclude with a discussion of how our approach relates to previous work, the complexity of finding exact solutions to pomdps, and of some possibilities for finding approximate solutions.
Generalization in Reinforcement Learning: Safely Approximating the Value Function
 Advances in Neural Information Processing Systems 7
, 1995
"... To appear in: G. Tesauro, D. S. Touretzky and T. K. Leen, eds., Advances in Neural Information Processing Systems 7, MIT Press, Cambridge MA, 1995. A straightforward approach to the curse of dimensionality in reinforcement learning and dynamic programming is to replace the lookup table with a genera ..."
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Cited by 252 (3 self)
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To appear in: G. Tesauro, D. S. Touretzky and T. K. Leen, eds., Advances in Neural Information Processing Systems 7, MIT Press, Cambridge MA, 1995. A straightforward approach to the curse of dimensionality in reinforcement learning and dynamic programming is to replace the lookup table with a generalizing function approximator such as a neural net. Although this has been successful in the domain of backgammon, there is no guarantee of convergence. In this paper, we show that the combination of dynamic programming and function approximation is not robust, and in even very benign cases, may produce an entirely wrong policy. We then introduce GrowSupport, a new algorithm which is safe from divergence yet can still reap the benefits of successful generalization. 1 INTRODUCTION Reinforcement learningthe problem of getting an agent to learn to act from sparse, delayed rewardshas been advanced by techniques based on dynamic programming (DP). These algorithms compute a value function ...
Residual Algorithms: Reinforcement Learning with Function Approximation
 In Proceedings of the Twelfth International Conference on Machine Learning
, 1995
"... A number of reinforcement learning algorithms have been developed that are guaranteed to converge to the optimal solution when used with lookup tables. It is shown, however, that these algorithms can easily become unstable when implemented directly with a general functionapproximation system, such ..."
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Cited by 237 (5 self)
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A number of reinforcement learning algorithms have been developed that are guaranteed to converge to the optimal solution when used with lookup tables. It is shown, however, that these algorithms can easily become unstable when implemented directly with a general functionapproximation system, such as a sigmoidal multilayer perceptron, a radialbasisfunction system, a memorybased learning system, or even a linear functionapproximation system. A new class of algorithms, residual gradient algorithms, is proposed, which perform gradient descent on the mean squared Bellman residual, guaranteeing convergence. It is shown, however, that they may learn very slowly in some cases. A larger class of algorithms, residual algorithms, is proposed that has the guaranteed convergence of the residual gradient algorithms, yet can retain the fast learning speed of direct algorithms. In fact, both direct and residual gradient algorithms are shown to be special cases of residual algorithms, and it is s...
Learning policies for partially observable environments: Scaling up
, 1995
"... Partially observable Markov decision processes (pomdp's) model decision problems in which an agent tries to maximize its reward in the face of limited and/or noisy sensor feedback. While the study of pomdp's is motivated by a need to address realistic problems, existing techniques for finding optim ..."
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Cited by 233 (11 self)
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Partially observable Markov decision processes (pomdp's) model decision problems in which an agent tries to maximize its reward in the face of limited and/or noisy sensor feedback. While the study of pomdp's is motivated by a need to address realistic problems, existing techniques for finding optimal behavior do not appear to scale well and have been unable to find satisfactory policies for problems with more than a dozen states. After a brief review of pomdp's, this paper discusses several simple solution methods and shows that all are capable of finding nearoptimal policies for a selection of extremely small pomdp's taken from the learning literature. In contrast, we show that none are able to solve a slightly larger and noisier problem based on robot navigation. We find that a combination of two novel approaches performs well on these problems and suggest methods for scaling to even larger and more complicated domains. 1 Introduction Mobile robots must act on the basis of thei...
Algorithms for Sequential Decision Making
, 1996
"... Sequential decision making is a fundamental task faced by any intelligent agent in an extended interaction with its environment; it is the act of answering the question "What should I do now?" In this thesis, I show how to answer this question when "now" is one of a finite set of states, "do" is one ..."
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Cited by 177 (8 self)
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Sequential decision making is a fundamental task faced by any intelligent agent in an extended interaction with its environment; it is the act of answering the question "What should I do now?" In this thesis, I show how to answer this question when "now" is one of a finite set of states, "do" is one of a finite set of actions, "should" is maximize a longrun measure of reward, and "I" is an automated planning or learning system (agent). In particular,
Valuefunction approximations for partially observable Markov decision processes
 Journal of Artificial Intelligence Research
, 2000
"... Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a set of imperfect or noisy observations. The modeling advanta ..."
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Cited by 129 (0 self)
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Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a set of imperfect or noisy observations. The modeling advantage of POMDPs, however, comes at a price — exact methods for solving them are computationally very expensive and thus applicable in practice only to very simple problems. We focus on efficient approximation (heuristic) methods that attempt to alleviate the computational problem and trade off accuracy for speed. We have two objectives here. First, we survey various approximation methods, analyze their properties and relations and provide some new insights into their differences. Second, we present a number of new approximation methods and novel refinements of existing techniques. The theoretical results are supported by experiments on a problem from the agent navigation domain. 1.
Hierarchical Control and Learning for Markov Decision Processes
, 1998
"... This dissertation investigates the use of hierarchy and problem decomposition as a means of solving large, stochastic, sequential decision problems. These problems are framed as Markov decision problems (MDPs). The new technical content of this dissertation begins with a discussion of the concept o ..."
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Cited by 109 (2 self)
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This dissertation investigates the use of hierarchy and problem decomposition as a means of solving large, stochastic, sequential decision problems. These problems are framed as Markov decision problems (MDPs). The new technical content of this dissertation begins with a discussion of the concept of temporal abstraction. Temporal abstraction is shown to be equivalent to the transformation of a policy defined over a region of an MDP to an action in a semiMarkov decision problem (SMDP). Several algorithms are presented for performing this transformation efficiently. This dissertation introduces the HAM method for generating hierarchical, temporally abstract actions. This method permits the partial specification of abstract actions in a way that corresponds to an abstract plan or strategy. Abstr...
Policy Iteration for Factored MDPs
 In Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI00
, 2000
"... Many large MDPs can be represented compactly using a dynamic Bayesian network. Although the structure of the value function does not retain the structure of the process, recent work has suggested that value functions in factored MDPs can often be approximated well using a factored value functi ..."
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Cited by 74 (6 self)
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Many large MDPs can be represented compactly using a dynamic Bayesian network. Although the structure of the value function does not retain the structure of the process, recent work has suggested that value functions in factored MDPs can often be approximated well using a factored value function: a linear combination of restricted basis functions, each of which refers only to a small subset of variables. An approximate factored value function for a particular policy can be computed using approximate dynamic programming, but this approach (and others) can only produce an approximation relative to a distance metric which is weighted by the stationary distribution of the current policy. This type of weighted projection is illsuited to policy improvement.
Maxnorm Projections for Factored MDPs
 In IJCAI
, 2001
"... Markov Decision Processes (MDPs) provide a coherent mathematical framework for planning under uncertainty. ..."
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Cited by 68 (11 self)
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Markov Decision Processes (MDPs) provide a coherent mathematical framework for planning under uncertainty.