Abstract
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.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Ackley, D. H., Hinton, G. H., & Sejnowski, T. J. (1985). A learning algorithm for Boltzmann machines. Cognitive Science, 9, 147–169.
Anderson, C. W. (1986). Learning and problem solving with multilayer connectionist systems. Doctoral dissertation. Department of Computer and Information Science. University of Massachusetts, Amherst.
Anderson, C. W. (1987). Strategy learning with multilayer connectionist representations. Proceedings of the Fourth International Workshop on Machine Learning (pp. 103–114). Irvine. CA: Morgan Kaufmann.
Barto, A. G. (1985). Learning by statistical cooperation of self-interested neuron-like computing elements. Human Neurobiology, 4, 229–256.
Barto, A. G., Sutton, R. S., & Anderson, C. W. (1983). Neuronlike elements that can solve difficult learning control problems. IEEE Transactions on Systems. Man, and Cybernetics, 13, 834–846.
Booker, L. B. (1982). Intelligent behavior as an adaptation to the task environment. Doctoral dissertation. Department of Computer and Communication Sciences, University of Michigan. Ann Arbor.
Christensen, J. (1986). Learning static evaluation functions by linear regression. In T. M. Mitchell, J. G. Carbonell, & R. S. Michalski (Eds.). Machine learning: A guide to current research. Boston: Kluwer Academic
Christensen, J., & Korf, R. E. (1986). A unified theory of hemistic evaluation functions and its application to learning. Proceedings of the Fifth National Conference on Artificial Intelligence (pp. 148–152). Philadelphia, PA: Morgan Kaufmann.
Denardo, E. V. (1982). Dynamic programming: Models and applications. Englewood Cliffs, NJ: Prentice-Hall.
Dietterich, T. G., & Michalski, R. S. (1986). Learning to predict sequences. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell (Eds.). Machine learning: An artificial intelligence approach (Vol. 2). Los Altos, CA Morgan Kaufmann.
Gelperin, A., Hopfield, J. J., Tank, D. W. (1985). The logic of Limax learning. In A. Selverston (Ed.), Model neural networks and behavior. New York: Plenum Press.
Hampson, S. E. (1983). A neural model of adaptive behavior. Doctoral dissertation, Department of Information and Computer Science. University of California, Irvine.
Hampson, S. E., & Volper, D. J. (1987). Disjunctive models of boolean category learning. Biological Cybernetics, 56, 121–137.
Holland, J. H. (1986). Escaping brittleness: The possibilities of general-purpose learning algorithms applied to parallel rule-based systems. In R. S. Michalski, J. G. Carbonell, & T. M. Mitchell (Eds.). Machine learning: An artificial intelligence approach (Vol. 2). Los Altos, CA: Morgan Kaufmann.
Kehoe, E. J., Schreurs, B. G., & Graham, P. (1987). Temporal primacy over-rides prior training in serial compound conditioning of the rabbit's nictitating membrane response. Animal Learning and Behavior, 15, 455–464.
Kemeny, J. G., & Snell, J. L. (1976). Finite Markov chains, New York: Springer-Verlag.
Klopf, A. H. (1987). A neuronal model of classical conditioning (Technical Report 87–1139). OH: Wright-Patterson Air Force Base, Wright Aeronautical Laboratories.
Moore, J. W., Desmond, J. E., Berthier, N. E., Blazis, D. E. J., Sutton, R. S., & Barto, A. G. (1986). Simulation of the classically conditioned nictitating membrane response by a neuron-like adaptive element: Response topography, neuronal firing and interstimulus intervals. Behavioral Brain Research, 21, 143–154.
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1985). Learning internal representations by error propagation (Technical Report No. 8506). La Jolla: University of California, San Diego, Institute for Cognitive Science. Also in D. E. Rumelhart & J. L. McClelland (Eds.). Paralled distributed processing: Explorations in the microstructure of cognition (Vol. 1). Cambridge, MA: MIT Press.
Samuel, A. L. (1959). Some studies in machine learning using the game of checkers. IBM Journal on Research and Development, 3, 210–229. Reprinted in E. A. Feigenbaum & J. Feldman (Eds.). Computers and though. New York: McGraw-Hill.
Sutton, R. S. (1984). Temporal credit assignment in reinforcement learning Doctoral dissertation, Department of Computer and Information Science. University of Massachusetts. Amherst.
Sutton, R. S., & Barto, A. G. (1981a). Toward a modern theory of adaptive networks: Expectation and prediction. Psychological Review, 88, 135–171.
Sutton, R. S., & Barto, A. G. (1981b). An adaptive network that constructs and uses an internal model of its environment. Cognition and Brain Theory, 4, 217–246.
Sutton, R. S., & Barto, A. G. (1987). A temporal-difference model of classical conditioning. Proceedings of the Ninth Annual Conference of the Cognitive Science Society (pp. 355–378). Seattle, WA: Lawrence Erlbaum.
Sutton, R. S., & Pinette, B. (1985). The learning of world models by connectionist networks. Proceedings of the Seventh Annual Conference of the Cognitive Science Society (pp. 54–64). Irvine, CA: Lawrence Erlbaum.
Varga, R. S. (1962). Matrix iterative analysis. Englewood Cliffs, NJ: Prentice-Hall.
Widrow B., & Hoff, M. E. (1960). Adaptive switching circuits, 1960 WESCON Convention Record, Part IV (pp. 96–104).
Widrow, B., & Stearns, S. D. (1985). Adaptive signal processing. Englewood Cliffs, NJ: Prentice-Hall.
Williams, R. J. (1986). Reinforcement learning in connectionist networks: A mathematical analysis (Technical Report No. 8605). La Jolla: University of California. San Diego. Institute for Cognitive Science.
Witten, I. H. (1977). An adaptive optimal controller for discrete-time Markov environments. Information and Control, 34, 286–295.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sutton, R.S. Learning to predict by the methods of temporal differences. Mach Learn 3, 9–44 (1988). https://doi.org/10.1007/BF00115009
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00115009