This paper surveys the field of reinforcement learning from a computer-science 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 trial-and-error 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.

This article introduces a class of incremental learning procedures specialized for prediction – that is, for using past experience with an incompletely known system to predict its future behavior. Whereas conventional prediction-learning methods assign credit by means of the difference between predicted and actual outcomes, the new methods assign credit by means of the difference between temporally successive predictions. Although such temporal-difference methods have been used in Samuel's checker player, Holland's bucket brigade, and the author's Adaptive Heuristic Critic, they have remained poorly understood. Here we prove their convergence and optimality for special cases and relate them to supervised-learning methods. For most real-world prediction problems, temporal-difference methods require less memory and less peak computation than conventional methods and they produce more accurate predictions. We argue that most problems to which supervised learning is currently applied are really prediction problems of the sort to which temporal-difference methods can be applied to advantage.

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Dyna is an AI architecture that integrates learning, planning, and reactive execution. Learning methods are used in Dyna both for compiling planning results and for updating a model of the effects of the agent's actions on the world. Planning is incremental and can use the probabilistic and ofttimes incorrect world models generated by learning processes. Execution is fully reactive in the sense that no planning intervenes between perception and action. Dyna relies on machine learning methods for learning from examples -- these are among the basic building blocks making up the architecture -- yet is not tied to any particular method. This paper briefly introduces Dyna and discusses its strengths and weaknesses with respect to other architectures.

This paper examines whether temporal difference methods for training connectionist networks, such as Suttons's TD(lambda) algorithm can be successfully applied to complex real-world problems. A number of important practical issues are identified and discussed from a general theoretical perspective. These practical issues are then examined in the context of a case study in which TD(lambda) is applied to learning the game of backgammon from the outcome of self-play. This is apparently the first application of this algorithm to a complex nontrivial task. It is found that, with zero knowledge built in, the network is able to learn from scratch to play the entire game at a fairly strong intermediate level of performance which is clearly better than conventional commercial programs and which in fact surpasses comparable networks trained on a massive human expert data set. This indicates that TD learning may work better in practice than one would expect based on current theory, and it suggests that further analysis of TD methods, as well as applications in other complex domains may be worth investigating.

On large problems, reinforcement learning systems must use parameterized function approximators such as neural networks in order to generalize between similar situations and actions. In these cases there are no strong theoretical results on the accuracy of convergence, and computational results have been mixed. In particular, Boyan and Moore reported at last year's meeting a series of negative results in attempting to apply dynamic programming together with function approximation to simple control problems with continuous state spaces. In this paper, we present positive results for all the control tasks they attempted, and for one that is significantly larger. The most important differences are that we used sparse-coarse-coded function approximators (CMACs) whereas they used mostly global function approximators, and that we learned online whereas they learned offline. Boyan and Moore and others have suggested that the problems they encountered could be solved by using actual outcomes (...

A major goal of research on networks of neuron-like processing units is to discover efficient learning procedures that allow these networks to construct complex internal representations of their environment. The learning procedures must be capable of modifying the connection strengths in such a way that internal units which are not part of the input or output come to represent important features of the task domain. Several interesting gradient-descent procedures have recently been discovered. Each connection computes the derivative, with respect to the connection strength, of a global measure of the error in the performance of the network. The strength is then adjusted in the direction that decreases the error. These relatively simple, gradient-descent learning procedures work well for small tasks and the new challenge is to find ways of improving their convergence rate and their generalization abilities so that they can be applied to larger, more realistic tasks.

We present a new algorithm, Prioritized Sweeping, for e cient prediction and control of stochas-tic Markov systems. Incremental learning methods such asTemporal Di erencing and Q-learning have fast real time performance. Classical methods are slower, but more accurate, because they make full use of the observations. Prioritized Sweeping aims for the best of both worlds. It uses all previous experiences both to prioritize important dynamic programming sweeps and to guide the exploration of state-space. We compare Prioritized Sweeping with other reinforcement learning schemes for a number of di erent stochastic optimal control prob-lems. It successfully solves large state-space real time problems with which other methods have di culty. 1 1

Function approximation is essential to reinforcement learning, but the standard approach of approximating a value function and determining a policy from it has so far proven theoretically intractable. In this paper we explore an alternative approach in which the policy is explicitly represented by its own function approximator, independent of the value function, and is updated according to the gradient of expected reward with respect to the policy parameters. Williams’s REINFORCE method and actor–critic methods are examples of this approach. Our main new result is to show that the gradient can be written in a form suitable for estimation from experience aided by an approximate action-value or advantage function. Using this result, we prove for the first time that a version of policy iteration with arbitrary differentiable function approximation is convergent to a locally optimal policy.

Abstract. This article presents a general class of associative reinforcement learning algorithms for connectionist networks containing stochastic units. These algorithms, called REINFORCE algorithms, are shown to make weight adjustments in a direction that lies along the gradient of expected reinforcement in both immediate-reinforcement tasks and certain limited forms of delayed-reinforcement tasks, and they do this without explicitly computing gradient estimates or even storing information from which such estimates could be computed. Specific examples of such algorithms are presented, some of which bear a close relationship to certain existing algorithms while others are novel but potentially interesting in their own right. Also given are results that show how such algorithms can be naturally integrated with backpropagation. We close with a brief discussion of a number of additional issues surrounding the use of such algorithms, including what is known about their limiting behaviors as well as further considerations that might be used to help develop similar but potentially more powerful reinforcement learning algorithms.